Homework Assignment #5
Due Friday, October 14, START of Class
Homework should be turned in at the BEGINNING OF CLASS. All problem numbers refer to the 4th edition Hughes-Hallett, Gleason, McCallum, et al. book, the required text for the course. You should write up solutions neatly to all problems, making sure to SHOW ALL YOUR WORK. A nonempty subset will be graded. You are strongly encouraged to work on these problems with other classmates, although the solutions you turn in should be YOUR OWN WORK.
Note: Please list any students or faculty who you worked with on the assignment.
Section 2.4 (pp. 91 - 92)
Problems: 2, 8, 14, 18
Section 2.5 (pp. 97 - 98)
Problems: 2, 3, 4, 5, 12, 14, 16, 20, 21
Note: For problem #16b, "bottoming out" means the stocks price is declining and is beginning to level out at a fixed value.
Section 2.6 (pp. 101 - 103)
Problems: 1, 2, 3, 10, 12, 15
Section 3.1 (pp. 115 - 117)
Problems: 8, 16, 22, 28, 35, 42, 58, 60, 64
Hint: For problem #35, simplify the expression first, then take the derivative. For problem #42, the variables are w and q, so a and b are just constants. One interpretation of the Leibniz notation dw/dq is to take "the derivative of w with respect to q." Thus q is the input (domain) variable and w is the output (range) variable.
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Note that Prep problems are due at the beginning of class on the date listed to the left of the assignment. Study problem due dates will be announced in class.
Remember: Learning mathematics is like constructing a building; it first requires a strong foundation. We believe that completing all of the problems listed below provides a foundation for understanding the material in that section. Only the problems in bold red should be turned in. We strongly suggest working other problems in each section to reinforce these foundations and prepare you for upcoming material.
Study problems (due dates will be posted)
6.1: 1,3, 10 ,13,14, 18 ,21,23. 28 ,29,31, 32 ,38,39,40, 48. 50. 52. 54. 56 ,61,62, 64. 70 (due 5/9)
6.2: 26, 30, 50, 54,76 (due 5/15)
6.3: 14,18,24,26,30,34,38,42,46 (due 5/15)
review for final
review for final
All assignments are from Calculus I with Precalculus Review. by Larson Hostetler, and Edwards.
Late Homework Policy. Prep problems are due at the beginning of class. Late prep problems will not be accepted no matter what the reason. Study problems are due at the beginning of class; you should put them in the purple folder. If for some reason you don't put them in the folder during class, you should look to see if it is outside your professor's office and put them in it then. If the purple folders have been picked up, you can put your homework in the green folder. It will be counted as late and you will lose 30% of the points. If you miss getting your homework in either folder before it's graded, then the homework will not be accepted and you will get a 0 for that assignment.
Dec. 6th The practice final is post here. A review session has been scheduled in Monday, Dec. 11th, 12-1pm, at DRL 4C6. Dec. 3rd The final exam is a cumulative exam, which cover the coverages of first and second terms and §4.2, §4.3, §5.4, §5.4, §5.6, from Part II of Probability and Matrices. §2.1, §2.2, §2.4, §2.5. The style of final exam is the same as the midterms, i.e. it is multiple choice, closed book and no calculators. But we will grade all steps of your solutions regradless you have chosen the correct answer or not. Dec. 1st Final exam has been scheduled in Dec 14th from 12-2pm. Room DRL A7. Any time conflict should be reported to me as soon as possible. Nov. 11th The practise exam for the second midterm is post here. Nov. 10th, Preprarations for the second midterm 0. The rule will be the same as the first one. The coverage is Calculus book: §12.9, §13.1. Probability book: §1.5-§1.8; §2.1-§2.3; §3.1-§3.3 and §4.1. 1. There will be a sunday review in this sunday Nov. 12th. 2. There will be review session in the Thursday night (Nov. 16th) 7pm-8pm. Room A6. 3. The quizzes and homework for the nextweek will run as usual. Sept. 30th The practise exam for the first midterm is post here. Sept. 29th, Preprarations for the first midterm 1. There will be a sunday review in this sunday Oct. 1st. 2. There will be review session in the Thursday night 7pm-8pm. Room 4C2. 3. The quizzes and homework for the nextweek will run as usual. Sept. 22nd 1. The poll result on midterm exam is: Oct. 6th (13) ; Oct 11th (11) ; Oct. 13th (8) So we will schedule the first midterm exam on Oct. 6th. If everything follows my schedule, the materials for the first midterm should be 12.1 to 12.8. I will post the past exam and a practice exam in a few days. 2. Many of you have requested more office hours, especially the office hour after 3pm. So I decide to change the schedule of office hours as the following: MW 1-1:30, Tu 1:30-2:30 Th 3:30 -4:30. Sept. 18th 1. From now on, the Sunday review will be hold only upon students' request. If you need a Sunday review, you must let me know before the Friday prior to the Sunday.
2. For various reasons, I would like to schedule the first midterm exam a little ealier than original date Oct. 13th. The possible choices are Oct. 6th, Oct 11th or we can stick in Oct 13th.INSTRUCTOR:
Tong Liu Office: DRL 4C3, phone: 898-5974 (email: firstname.lastname@example.org ) Tentative office hours: MW 1-1:30, Tu 1:30-2:30 Th 3:30 -4:30.Teaching Assistant:
Dragos Deliu email: email@example.com Office: DRL 4N25 Office hours: Tuesday 4:30PM-5:30PM, Friday 3PM-4PM. Office phone: 898-7247TEXTS:
[C] Thomas/Finney, Calculus, 9th (or Alternate) Edition [P] DeGroot/Schervish Probability and Statistics, 3rd ed. [F] Lial, Greenwell, Ritchey Finite Mathematics, 7th ed. Maple/Calculus Lab Manual for Math 103/104/114/115HANDOUTS: TIME & PLACE:
Lectures: M W F 12-1 DRLB A8 Liu Recitations: 201 REC T 8:30-9:30 AM DRLB 3c4 Deliu 202 REC T 9:30-10:30 AM DRLB 3c4 Deliu 203 REC R 8:30-9:30 AM DRLB 3c4 Deliu 204 REC R 9:30-10:30 AM DRLB 3c4 Deliu Sunday Review: Sunday 7pm-9pm DRLB A6 GuptaCOURSE GRADE:
Homework 15% Quizzes 15% Midterms 20% each Final 30%. The quizzes, midterms, and final exam are all closed-book. Calculators are not allowed. In the midterms and final, but not in the quizzes, you may use a 'crib sheet', consisting of a 5x8 card of notes in your own handwriting.
I will post homewrok assiagnment every Thursday (night). Each week's assignment will consist of: *The relevant core problems, *Problems from past final exams, and *A Maple assignment. In addition, I will occasionally assign some extra credit work from the text, the MAPLE/CALCULUS LAB MANUAL, and other sources. You are welcome to work on the homework together with a study group; but you MUST HAND IN YOUR OWN, INDIVIDUAL WORK, explained in your own words. Solutions must be written LEGIBLY. (Please be considerate to your poor, overworked TA who has to read your assignment. ) Homework is due each Friday at 5pm in Dragos' office. You may instead hand it in to Dragos during any recitation before the deadline, or in class at the end of the lecture. IT IS STRONGLY RECOMMENDED THAT YOU TRY TO FINISH THE HOMEWORK A FEW DAYS AHEAD OF TIME. Then, if you encounter difficulties, you will still have time to obtain help from the instructor, the TA, or a tutor. No late homework assignments will be accepted UNDER ANY CIRCUMSTANCES, (again, please be considerate to your poor, overworked TA), but the two lowest homework grades will be dropped. CORE PROBLEMS, PROBLEMS FROM PAST FINALS: Since there is much material to cover in math 115 and more problems to work through than we have time to cover in lecture or recitation, we have chosen some core problems to help define the course. The core problems are listed on page 12 of the LAB MANUAL. A copy of the list can also be found here. ) In addition you will find problems from past final exams in the Lab Manual. Together, the core problems and past finals define both the material of the course and the level of difficulty expected. Your objective is to understand thoroughly how to solve them and to develop some facility with the underlying mathematics. Because of the limited time available to the TA, only a couple of problems chosen at random from each assignment will be graded. If at the end of the semester you feel that you have been consistently unlucky in that we always happened to grade the only two problems you did not do, talk to one of us and we'll see whether we can make some adjustment.QUIZZES:
There will be a brief quiz given at the end of each recitation. Missed quizzes cannot be made up, but the two lowest (or missed) quizzes will be dropped. The material for each quiz will be taken from the previous homework assignment, giving you added incentive to do all the homework problems.MIDTERM EXAMS:
There will be two midterm exams, during usual class times: (1) Friday, October 6th (2) Friday, November 17th. The midterms will be multiple choice, closed book, no calculators, but you may use a 5"x8" cheat sheet in your own hand writing. NO MAKE UP EXAMS WILL BE GIVEN. If you have to miss a midterm exam due to illness (with a doctor's note) or another certified emergency, we will use some other way to assign you a grade for that exam. Normally this will be based on your performance on the corresponding problems of the final exam.FINAL:
All sections of Math 115 will have a common final exam on. The final will be multiple choice, closed book, no calculators, but you may use a 5"x8" cheat sheet in your own hand writing. If you miss the final or perform poorly for any reason, you may choose to take the makeup final, which will be given in the beginning of next Fall Term. In order to do this, you will (of course!) have to agree (in writing, in advance) to give up the grade you received on the original exam. So your score on the makeup exam may bring your course grade either up or down.Some useful links:
I am a new calculus teacher in a high school for gifted students. I am the youngest teacher, I am not in my home country, and this country particularly values age and experience, so I have little room to discuss syllabi and homework assignments.
The level of maths is quite high (senior students deal with vector calculus and Stokes' theorem) and the class requires a large amount of weekly homework (to give an idea: about 15 exercises for each section in Stewart's Calculus, about 3 sections a week). Deadlines for these homework assignments are very strict (new assignment every week, none accepted after the deadline).
I know that practice is important, especially in calculus, but this leads to unintended outcomes:
Grading takes a lot of time, so many teachers don't grade seriously (little feedback; just checking that students did the homework) and instead distribute a solutions printout from the textbook to the students.
Students don't spend a lot of time thinking about or engaged with the problems; they just rephrase the solutions. Good students will try to understand the solutions, but other will not really care.
Even if I don't give them the solutions printout, then they will find the answers online.
Many students don't enjoy calculus and few of them would take an optional class related to calculus (say analysis or differential geometry). Freshmen are really afraid of their future calculus class.
I have seen this with a couple of students: they believe that they will be successful if they copy the solutions for all homework problems (including non-assigned ones) from the textbook (at least 60 per section!). This has led to very poor results.
What can I do? I like teaching in the school, but the general philosophy of education in this country is:
If a student has unsatisfying grades, give him more homework and extra classes.
So far, I have just decided to relax the deadlines, and not to care too much about late homework, but the outcome is still not satisfying. I am also not comfortable with having different rules for homework than other classes.
Is there an efficient way to manage a huge load of homework?
What are the alternatives to the "practice, practice, practice" method to gain good skills in computations?
The ideal solution would be to completely change the homework list in accordance with the philosophy of "less but better," but my colleagues will be hurt if I change the school's habits. How can I discuss this problem with them without hurting their sense of hierarchy?
Thank you in advance, and sorry if my questions are imprecise. To sum up, it could be changed to "What are the most efficient methods to teach Calculus, with respect to the ratio (computation skills)/(homework load)?"
In addition to having an online homework system if possible, you might also consider asking the students present a few problems in class. This would make the students at the very least care more about the homework and the subsequent class discussion would help you identify some of the difficulties with the assignment. Often this helps a great deal with the computational practice many calc students seem to need. Doing algebra in front of your classmates will certainly inspire to get every step right and will ensure that you are able to explain the validity of each step.
Online homework combined with presentations seems ideal. Lots of practice, instantaneous feedback on all problems, detailed feedback on several problems.
answered Jun 1 '14 at 19:22
P.8 (2 dim'l data)1-21 odd; 26-28; 31,32; 35,36;46-48
1.1 (graphs/eq'ns)(i) 1-7odd; 9-12; 92(a,b)
(symm./circles) (ii) 23-27 odd;29,30;33-38; 39-45odd; 69-71;*75,79,81
1.3 (functions) (i)1-9, 23, 24, 25-33 odd, 37-40 also draw mapping figure for 37-40 (see handout)
(ii) 43- 60 odd; 61- 64; 71, 72, 74,76; 79, 81, 85
1.4 (more) 1-11 odd, 19-22 (a only);47-53 odd; 57-59
P.2 1,4,7,10. 70, 107
3.1 (298-300) (i) 1-6, 15-20
(301-304) (ii) 21-26 (we will discuss these further in lab on Tuesday)
(iii) 29, 37
(iv) 47-49, 51; 35, 36; 57, 61
3.2 (310-311) (i) 1-6; 9-14; 19-27; 31-34
(ii) 7,8,15-17, 29,30,35-39;45-50; 71, 72, 78
3.3 (i) 19, 22, 25. 37; 41, 44, 47, 59
(ii) 3-17odd; 49-58; 69-79 odd; 89
3.4 (i) 1- 9 odd
(ii) 11-19 odd; 27,30. 45; 55-61 odd
3.5 (i) 7-13,21; 25-27; 31-37 odd, 45; 57, 59; 74
4.3 (i) 1-8( sin. cos, tan only); 37;57-60
(ii) 1-8( csc, sec, cot only); 9-11; 19,20; 38-42; 61-64; 65, 67,69
4.4 (i) 1-7 odd; 13-15, 19; 35-38; 43-45;53-55;75-77,83
4.1 5-14; 25-32;39-46; 71-73
6.1 (i) 1-4,7,8,26
(ii) 5,6, 13,14,17-20; 29,33,39,40
6.2 (i) 1-5, 8, 9,10,23,26,31,33
(ii) 7, 14,15, 17, 28, 37
4.2 1-21 odd; 31-35; 45- 51; 59, 60
4.5 1-21 odd; 31-37 odd; 49, 51
4.6 1-8; 55-58
9-17,21,27,31-35,65, 67, 69, 79, 80
1-25 odd; 35-39; 45-57 odd,83
4.8 3,13, 19,25, 27,49, 51
5.3 5-27 odd, 65
5.1 Read p 458 2,5,7,8; warmup 1-4; 19-24;31-39 odd; 71,73,75
5.4 7-19 odd;21-24; 31-34;47-52; *78
5.5 read 493-498 1-4;9,11,23,35-37,45,47,103
2.1 1-8; 9-21 odd;37-41 odd,43-45;47;51;53
2.5 1,4,7,10,13. 49; 65-71 odd
2.2 1-8, 9; 27-36;43,47-52;*78
Back to Martin Flashman's Home Page :)
Back to HSU Math. Department :>
Spring, 1999 COURSE INFORMATION M.FLASHMAN
MATH 115: ALG. AND ELEM. FUNCTIONS
OFFICE: Library 48 E-MAIL: firstname.lastname@example.org PHONE:826-4950
Hours AND BY APPOINTMENT or by CHANCE!
PREREQUISITE: Math code 40 (or better) or permission.
TEXT: Precalculus Mathematics, 4 th Ed. by Larson & Hostetler (Houghton Mifflin, 1997)
SCOPE: We will cover topics primarily from the preliminaries and chapters 1-6 in L/H. Supplementary materials will be provided as appropriate.
TESTS and ASSIGNMENTS: Homework assignments are made regularly and should be passed in on the due date. Work is graded Acceptable/Unacceptable with problems to be redone.
Redone work should be returned for grading promptly. These assignments will be discussed in class on a daily basis and the quizzes will have similar problems.
During the semester there will be two special "team" assignments which I will grade (numerically).
There will be eight quizzes (15-30 minutes) usually given on Thursdays.
The final examination for the course will be comprehensive and will be held Tursday, August 13th during class time.
Students wishing to schedule an earlier final examination may request an alternate time no later than Monday, May 3rd.
MAKE-UP TESTS WILL NOT BE GIVEN EXCEPT FOR VERY SPECIAL CIRCUMSTANCES!
It is the student's responsibility to request a makeup promptly, especially for especially for unauthorized absence. *** DAILY ATTENDANCE SHOULD BE A HABIT***
------------------------------------------------------- GRADES: Final grades will be determined from the total number of points accumulated as follows:
Quizzes 1-7 best 6 scores 600
Quiz 8 100
Team Assignments 100
Final Exam 250
Total Available Points 1100 MORE THAN 4 ABSENCES MAY RESULT
IN A LOWER FINAL GRADE FOR POOR ATTENDENCE. ** Students wishing to be graded with either CR or NC should make this request to the Adm & Rec office in writing.
See the Summer Session course list for a full list of relevant days.
COMPUTERS: During this course the computer will be used for some problems. For this purpose, we will meet in Science D 017, a PC-computer lab, when announced, at the regularly scheduled hours. We will use WinPlot, X(PLORE), a powerful and friendly system designed to help learn calculus with the computer, and Geometer's Sketchpad. You will need one 3 1/2" disc on which you can keep your own work. WinPlot is freeware and can be obtained from me or over the internet. A version of X(PLORE) is available at the bookstore for MAC based PC's along with the PC version we will use.Graphing Calculators. Graphing calculators are welcome and highly recommended. If you would like to purchase one or have one already, let me know. I try to help those with their own technology when possible during office hours or by appointment (not in class). I will use the HPG for some in-class work though most graphing calculators will be able to do much of this work. Supplementary materials will be distributed if needed. [HP48G's will be available for students to borrow for the term by arrangement with the Math department.]
Description of course: This course is about integral calculus and infinite series. You should already be familiar with differential calculus. The derivative measures the instantaneous rate of change of a function. The definite integral measures the total accumulation of a function over an interval. These two objects form the basis for nearly all mathematical formulas in science. The rules by which we can compute derivatives and integrals of any function are called a calculus. The Fundamental Theorem of Calculus links the two processes of differentiation and integration in a beautiful way. Using calculus, we want you to learn how to model situations in order to solve problems. The second half of the course is a careful investigation of infinite sequences and series, culminating with Taylor's theorem and applications to physics.
Midterm exam 1 (03 Oct)
Midterm exam 2 (13 Nov)
Grades: Your final grades will be based on weekly homework, two midterm exams, and a final exam. Notice that more emphasis is placed on exams than on weekly homework assignments in computing your final grade. On the other hand, completing your homework on a weekly basis is the most sure way to success on the exams.
Group work, honestly: Working with other people on mathematics is highly encouraged and fun. You may work with anyone (e.g. other students in your section, in the course, not in the course, tutors, bums on the street. ) on your homework problems. If done right, you'll learn the material better and more efficiently working in groups. The golden rule is: Work with anyone on solving your homework problems,
but write up your final draft by yourself. Writing up the final draft is as important a process as figuring out the problems on scratch paper with your friends, see the guidelines below. Mathematical writing is very idiosyncratic - we will be able to tell if papers have been copied - just don't do it! You will not learn by copying solutions from others! Also, if you work with people on a particular assignment, you must list your collaborators on the top of the first page. This makes the process fun, transparent, and honest.
(or otherwise the small print)
Homework: Weekly homework will be due at the beginning of lecture on Friday. The assignment will be posted on Classes*v2 the week before it's due.
Consider the pieces of paper you turn in as a final copy: written neatly and straight across the page, on clean paper, with nice margins and lots of space, and well organized.
Your lowest homework score from the semester will be dropped.
Exams/quizzes: Both mid-terms will take place 7:00 - 8:30 pm at a location to be decided. The final exam will be take place 7:00 - 10:30 pm on Sunday, December 15th, 2013 in Davies Auditorium. For official policies concerning make-ups, see the Classes*v2 "Exams" page.
Homework guidelines: Generally, a homework problem in any math course will consist of two parts: the creative part and the write-up.
The creative part: This is when you "solve" the problem. You stare at it, poke at it, and work on it until you understand what's being asked, and then try different ideas until you find something that works. This part is fun to do with your friends; you can do it on the back of a napkin. If you're having trouble, even in understanding what the problem's asking, use the resources available to you: my office hours, teaching assistants' office hours, weekly tutoring sessions, etc. Ask for help as early as you can! This part should all be done on "scratch paper."
The write-up: Now that everything about the problem is clear in your mind, you go off by yourself and write up a coherent, succinct, and nicely written solution on clean sheets of paper. Consider this your final draft. just as in any other course. This part you should definitely NOT do with your friends.
A survey of mathematical techniques used in the managerial, social and life sciences. Topics include systems of linear equations and matrices, linear programming, differential calculus, and applications of the derivative. Prerequisite: A grade of “C” or better in MATH-110 or MATH-105, or placement exam.
Required Text: Brief Calculus: An Applied Approach, Eighth Edition, by Larson.
You will also need a calculator (scientific or graphing). Bring your textbook, calculator, pen or pencil, and paper to each class meeting.
Benedictine University is dedicated to the education of undergraduate and graduate students from diverse ethnic, racial and religious backgrounds. As an academic community committed to liberal arts and professional education distinguished and guided by our Roman Catholic tradition and Benedictine heritage, we prepare our students for a lifetime as active, informed and responsible citizens and leaders in the world community.
Goals, Objectives, and Outcomes
Goals: Students will develop an appreciation for the basic concepts of differential and integral calculus and their applications to other areas, particularly in business and social science.
Common Student Learning Objectives:
Know and apply the central concepts of the subject matter.
Use technology to enhance learning.
Use inquiry and collaboration to solve problems.
Course-Based Student Learning Objectives: Upon completion of the course:
1. Students will become familiar with, be able to evaluate, and understand the significance and applications of mathematical functions, their limits, and their continuity.
2. Students will learn to evaluate derivatives, and to use them in various applications,
including those involving rates of change and optimization.
3. Students will be able to evaluate definite and indefinite integrals and to use them in solving problems.
4. Students will become familiar with exponential and logarithmic functions—their properties, limits, derivatives, integrals, and uses in modeling situations in business and social science.
Lecture, discussion, demonstration, individual and group problem solving
Attendance: A lot of material will be covered every week, so it is mandatory that you be present for the entirety of every class session. If, due to unavoidable circumstances, you have to miss part or all of a class, it is your responsibility to find out what you missed, learn the material covered, and make me aware of the reasons for your absence. my cell: 217-473-1783. If any class activities are missed due to an unexcused absence, the grade for that activity will be zero.
Due to the accelerated nature of the course, should you experience a medical condition which prevents you from attending any class(es), appropriate medical documentation must e provided immediately so it may be determined what, if any, accommodations are reasonable or possible.
Homework: A listing of the homework assigned for each testing unit will be distributed at the beginning of the unit. It will be turned in on the day of the test for that unit. When doing the homework assignments, you are allowed, and even encouraged, to work together, compare answers, or seek outside help, if this helps you in learning the material. You are not allowed, however, to merely copy someone else’s answers. This defeats the purposes of doing the homework: to give you practice and help you learn by doing, and to let me and you both know how well you understand.
In addition to handing in the assigned homework, you are also expected to read each section of the book as it is covered in class, and do as many additional exercises, other than those assigned to be turned in, as you need to for extra practice.
In class, there will be review quizzes, practice exercises, or individual or group problems.
Tests: There will be two unit tests, and a comprehensive final exam which focuses primarily on Chapters 4 and 5. The testing schedule listed in the course outline will be followed as closely as possible. Tests must be taken when scheduled. In case of emergency, other arrangements can be made, but you must contact me before or very soon after the test—do not wait until the following week. Otherwise, you get a score of 0 for the missed test.
Means of Evaluation
Homework: 15%; Quiz: 15%; Tests (including final exam): 70%
Grade: 90-100% = A; 80-89% = B; 70-79% = C; 60-69% = D; under 60% = F
The following outline is approximate and subject to alteration.
Week 1 – January 8
A quick review of some preliminary topics from Chapter 0
1.1 The Cartesian Plane and the Distance Formula
1.2 Graphs of Equations
1.3 Lines in the Plane and Slope
Week 2 – January 15
2.1 The Derivative and the Slope of a Graph
2.2 Some Rules for Differentiation
Week 3 – January 22
TEST over Chapter 1
2.3 Rates of Change: Velocity and Marginals
2.4 The Product and Quotient Rules
2.5 The Chain Rule
Week 4 – January 29
2.6 Higher Order Derivatives
2.7 Implicit Differentiation
2.8 Related Rates
3.1 Increasing and Decreasing Functions
Week 5 – February 5
3.2 Extrema and the First-Derivative Test
3.3 Concavity and the Second Derivative Test
3.4 Optimization Problems
Week 6 – February 12
3.5 Business and Economics Applications
3.7 Curve Sketching: A Summary
3.8 Differentials and Marginal Analysis
Week 7 – February 19
TEST over Chapter 2, 3
4.1 Exponential Functions
4.2 Natural Exponential Functions
4.3 Derivatives of Exponential Functions
Week 8 – February 26
4.4 Logarithmic Functions
4.5 Derivatives of Logarithmic Functions
4.6 Exponential Growth and Decay
5.1 Antiderivatives and Indefinite Integrals
Week 9 – March 5
5.2 The General Power Rule
5.3 Exponential and Logarithmic Integrals
5.4 Area and the Fundamental Theorem of Calculus
5.5 The Area of a Region Bounded by Two Graphs
Week 10 – March 12
First Class Session:
Students should prepare for the first class session by looking over Chapter 0 in the textbook, paying particular attention to pages 0-2, 0-3, 0-13, 0-14, 0-15, 0-19, and 0-21. Also, since we will be covering the first three or four sections of Chapter 1 in the first class session, students may find it helpful to read over these sections before class begins.
Academic Integrity Statement
Academic and professional environments require honesty and integrity, and these qualities are expected of every student at Springfield College-Benedictine University. In accordance with such expectations, academic integrity requires that you credit others for their ideas. Plagiarism, whether intentional or not, is a grievous offense. Any time you use words or ideas that are not your own, you must give credit to the author, whether or not you are quoting directly from that author. Failure to do so constitutes plagiarism.
Any incident of plagiarism and/or academic dishonesty may result in serious consequences. Penalties for academic dishonesty vary depending on the severity or extent of the problem but are always serious.
The following are consequences you may face for academic dishonesty:
• a failing grade or “zero” for the assignment;
• dismissal from and a failing grade for the course; or
• dismissal from the Institution.
Please refer to the Springfield College Benedictine University Catalog or the Student Handbook for a complete discussion of the Academic Integrity policy.
Grade Appeal Process
According to the Springfield College Catalog, grade appeals must be initiated 90 days prior to the end of one semester after the course in question has been completed. The process for appealing a grade is outlined below.
First, contact the Instructor.
1. A student must appeal to his/her instructor in writing (e-mail is acceptable) and provide specific reasons why his/her grade should be changed.
2. The instructor must respond to the student in writing (e-mail is acceptable) and provide a copy to the division chair.
Second, contact the Division Chair.
3. If the student wishes, he/she may then appeal to the division chair in writing (e-mail is acceptable) and provide specific reasons why his/her grade should be changed without the instructor’s permission. The student should understand that overwhelming evidence must be presented to the division chair to prove that the current grade is incorrect.
4. The division chair must respond to the student in writing (e-mail is acceptable) and provide a copy to the academic dean.
Lastly, contact the Academic Dean.
5. If the student wishes, he/she may appeal to the academic dean in writing (e-mail is acceptable) and provide specific reasons why his/her grade should be changed without the instructor’s or the division chair’s permission. The student should understand that overwhelming evidence must be presented to the academic dean to prove the grade is incorrect.
6. The academic dean must respond to the student in writing (e-mail is acceptable). The
Academic dean’s decision is final.
Last day to drop with 100% refund = 1 week from beginning of class
Last day to withdraw with 25% refund = 2 weeks from beginning of class
Last day to withdraw from class = Beginning of the 8th week of class
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Student Withdrawal Procedure
It is the student’s responsibility to officially withdraw from a course by completing the appropriate form, with appropriate signatures, and returning the completed form to the Advising Office. Please refer to the Student Handbook for important financial information related to withdrawals.
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Goals, objectives, and learning outcomes that will be assessed in the class are stated in this syllabus. Instructor will use background knowledge probes, one-minute papers, reflective essays and/or other Classroom Assessment Techniques as deemed necessary in order to provide continuous improvement of instruction.Navigation:
(1) Course introduction, expectations, and requirements. (2) School expectations. (3) An introduction to major Precalculus components.
Please complete problems 1-17 off of the Summer Review Packet that was given and begun today in class.
(1) Review of domain terminology and trouble spots while reviewing last night's homework. (2) Complete homework review. (3) Graphing translations and transformations of the families of functions. (4) Piecewise functions.
Please complete problems 24-37 from the review packet. Remember that the trig cheat sheet has been emailed to you or is available on this website!
(1) Review of homework problems from last night (including logarithmic and exponential equations). (2) Reveiw of the unit circle, exact radian values, inverse trig functions, trig equations, and the basics of trig graphing.
Please complete the remaining trig problems from page 7 of your summer packet (excluding the final three problems). Do not attempt problem 51 on the very back page, we will do that together in class on Monday. On the new worksheet that you were given, please complete (1-16 even) from Topic 1 and (1-14 even) from the Indentities WS portion.
(1) Review of homework from last night. (2) Solving trig equations. (3) Fundamental trig identities and verifying. (4) The basics of trig graphing.
Please complete from your worksheet Topic 3 problems (1-10) and the Identities (odds). Tentatively scheduled for Wednesday is Quiz 1 on Precalculus review items.
(1) Review of Topic 3 items and Identities/Equations problems from yesterday. (2) Work on Topic 2 problems in class. (3) Domain review. (4) Trig graphing review.
Please review, rework, and study material from all Precalculus review sheets in preparation for Quiz 1 that will be given in class tomorrow.
(1) Quick recap. (2) Quiz 1 on Precalculus Review Items was given today in class.
No additional homework or problems were assigned today.
(1) Review of graded Quiz 1 papers. (2) Notes 1.1: A Transition to Calculus (3) Notes 1.2: A Numerical and Graphical Approach to Evaluating Limits.
We did not cover everything that needed to be covered with limits today, hence you will complete some problems from section 1.1. Please do p. 47 (1-9 odd). If you have difficulty with the directions, don't fear. These are not items that will be formally assessed, but are merely designed to make you think about the types of problems that you may see.
(1) Review of homework from last night. (2) Notes 1.2 cont. and begin Notes 1.3: Evaluating Limits Analytically.
Please complete from your textbook p. 54-55 (2-16 even, 20) and p. 67 (1, 5-21 odd). Also, if you were not here today, I have posted a copy of the notes that were given in class under hints and solutions. Please make sure you select the one with the correct date from today. Please email me if you have any questions.
September 4, 2012
(1) Review of limits homework from Friday. (2) Clean-up from finding limits numerically and graphically. (3) Rationalizing limits and two special trig limits.
Please complete the odd problems from the limits worksheet that was given today in class. Be prepared to complete that WS in class tomorrow. If you were absent today, I have placed a copy of the notes that I did in class under the hints and solutions link on the left hand side of the page. Enjoy!
September 5, 2012
(1) Review of odd problems from last night's worksheet. (2) More on special trig limits.
Please complete the even problems from the worksheet given in class yesterday. Additionally, I hold you responsible for the following problems/types of problems from your textbook which you should also do tonight. Please complete p. 55-56 (19,25) and p. 67-69 (23,25,37,39,61,69,71, and 75). Quiz 2 on limits will be given on Friday!
September 6, 2012
(1) Review of yesterday's homework. (2) Recap of all things limits. (3) Notes 1.4: Continuity and One-Sided Limits.
No homework was given from the book this evening. You are charged with reviewing and preparing for your second quiz tomorrow on 1.1-1.3.
September 7, 2012
No new material covered today. Quiz 2 on sections 1.1-1.3 was given in class today.
No additional homework was given over the weekend.
September 10, 2012
(1) Weekend recap and round up. (2) Verifying that a function is continuous at a certain point in the domain. (3) Using the Intermediate Value Theorem to find values of 'c' for a given k or such that f(c) = 0. (4) Outlook for the immediate future in Calculus.
Please complete from your textbook p. 78-79 (1-6,7,11,16,27,29,79,81,83-85). Please plan accordingly to finish Chapter 1 tomorrow in class, have a brief recap on Wednesday, and a Chapter 1 test on Thursday.
September 11, 2012
(1) Review of homework from last night. (2) Pass back and discuss graded Quiz 2 papers. (3) Notes 1.5: Infinite Limits.
Please complete from your textbook p. 88-89 (1-4,9-21 odd,33-43 odd, 49). This covers infinite limits. Please begin preparing for Test 1 on Chapter 1 which will be given in class on Thursday of this week and will cover all material taught and/or practiced at some point during this chapter.
September 12, 2012
(1) Review of homework from last night. (2) Q&A session on Chapter 1 material in preparation for tomorrow's test.
From your book, p.91-92 (5,6,11,13,15,19,26,33,49,57,63,65) are good review exercises and should be completed if you do not understand the concepts that these problems cover. This will not be formally checked and is totally optional for you to complete. Remember, anything that I have taught, assigned, quizzed, or otherwise mentioned or discussed in class is fair game for tomorrow's test. Remember, the best way to prepare for a math test is to practice problems. Merely reading over your notes will not suffice and guarantee your success, though I am not sure anything can really do that! Good luck!
September 13, 2012
Test 1 on Chapter 1
No additional homework was assigned tonight. Sit back, relax, and relish in the fact that you just completed your first college level math test!
September 14, 2012
(1) Review of the Unit Circle worksheets and extra practice.
Please complete the two in-class activities that you received today in my absence. Please bring them to class with you on Monday.
September 17, 2012
(1) Review of homework from last night. (2) Notes 2.1: The Derivative and the Tangent Line Problem. (3) Rates of change for functions. (4) The secant line as an estimate for the tangent line.
From your book please complete p. 103-104 (1,2,5-23 EOO,37-40).
September 18, 2012
(1) Review of homework from last night. (2) More on finding derivatives via the limit process. (3) Derivative of a function using the alternate form. (4) One-sided derivative example.
Please complete from your book p. 104-106 (20,24,28,32,72-78 even,81-86).
September 19, 2012
(1) Pass back and thorough review of graded Chapter 1 test papers. (2) Review of homework from last night (first part). (3) Senior class guidance meetings so no new material was taught today.
Enjoy a night off! This is not an excuse to not do any math, but to look back over things that you have previously had difficulty with for your own understanding!
September 20, 2012
(1) Review of homework from the night before last and clean-up. (2) Work out problems 24 and 31 from page 104-106. (3) Notes 2.2: Basic Differentiation Rules and Rates of Change.
Please complete from your textbook p. 115 (1-37 EOO) (That's every other even!)
September 21, 2012
(1) Check homework for completion. (2) Last minute questions on the Unit Circle. (3) Quiz 3: The Unit Circle.
Review the homework problems that you completed on Thursday once again. Since class was abbreviated today, no new material was covered. We will continue our discussion on derivatives on Monday to include postion, velocity, and acceleration function!
September 24, 2012
(1) Review of homework problems assigned from Thursday. (2) Notes 2.2 (continued): Expanding and Dealing with Quotients; Position and Velocity Functions.
Please complete p. 115-117 (47,48,53,55,57,62,89,93-96).
September 25, 2012
(1) Review of homework from last night. (2) Return graded quizzes on the Unit Circle. (3) Notes 2.3: The Product and Quotient Rules.
Please complete from your textbook p. 126 (1,3,5,7,11,16,18,22,24,63,65)
September 26, 2012
(1) Review of homework from last night. (2) Notes 2.3 (cont): Derivatives of cscx, cotx, and secx.; more on motion; higher order derivatives.
Please complete from your book p.126-127 (26,27,36,41,47,51,53,73,76,89c,96).
September 27, 2012
(1) Review of homework from last night. (2) Practice with derivatives (everything except the chain rule)!
A worksheet was given today in class. You are charged with completing the EVEN problems from homework this evening. Since I will be out on a field trip tomorrow, I am leaving a solution key with the sub for him to hand out to you. Use this to only check your answers. Get as far as you possibly can before going to the solution sheet. You will need to finish this WS in class tomorrow and use it to study for Quiz 3 which will be given in class on Monday!
September 28, 2012
I am out of the building today. You are to complete the ODD problems from the WS that was given in class yesterday. I have left behind a copy of the solutions for you to check your work since I am not in class. You should attempt every problem before checking the solution sheet.
You should finish all problems on the derivative practice WS if you have not already done so and study remaining notes and homework in preparation for Monday's quiz on 2.1-2.3!
(1) Quiz 3 (2.1-2.3) given in class today.
No addtional homework was given this evening. My hope is to start the chain rule tomorrow but I highly doubt that I will finish in time to have a test on Wednesday. We will discuss this in class tomorrow so please come prepared with your thoughts on this!
(1) Return and review graded Quiz 4 papers from yesterday. (2) Discussion about the upcoming test on Chapter 2 and the options for it. (3) Notes 2.4: The Chain Rule.
Please check out your grade on ParentPortal sometime this evening and formulate your own thoughts as to when you think the Section 2.1-2.4 Test will best suit you. We will discuss this in-class tomorrow. You need to complete from your textbook p. 137 (8-28 even, 41,45).
(1) Review of homework from last night. (2) Examples of turning a division into a Power Rule. (3) Chain Rule that includes a quotient and/or product.
Please complete the odd problems from both sides of the Chain Rule practice WS that was given to you in class today.
(1) Review of homework from last night. (2) More examples with products/quotients inside of the Chain Rule. (3) Trig Chain Problems!
You were given another WS today in class on Trigonometric Chain Rule problems. You need to complete the odd problems from this page!
(1) Please complete the EVEN problems on BOTH of the worksheets that you have received on the chain rule. The first was on basic functions the second was explicitly on trigonometry. I am providing you with an answer sheet to the first WS and the solutions to the trig WS are under the hints/solutions link to the left. We will go over these problems on Tuesday and you will have a test on Wednesday.
Complete the problems as described above.
(1) Review of WS problems from Friday. (2) Test 1 overview. (3) Q&A session.
Please study for Test 1 on 2.1-2.4 that will be given in class tomorrow.
October 10, 2012
Test 1 on Sections 2.1-2.4
No additional homework was given this evening. Relax and enjoy the evening off!
October 11, 2012
(1) A couple of troublesome points from yesterday's test were recapped on the board. (2) Notes 2.5: Implicit Differentiation.
Please complete from your book p. 146-147/ 2,4,6,10,16,21,23,26,27,45, and 49. Show all work that leads to your solution.
October 12, 2012
(1) Review of homework from last night. (2) More on implicity differentiation, tangent lines, and normal lines.
An implicit differentiation practice WS was given to you today in class. Please complete problems 1-13 from this paper! Have a wonderful weekend!
October 15, 2012
(1) Review of homework from last night. (2) Discussion of plans for the week. (3) More on implicit differentiation, horizontal and vertical tangent lines, equations of normal lines.
Please complete problems 14 and 15 from your WS from Friday as well as p. 146-148 (9,11,15,24,28,48, and 54) from your textbook. Quiz 1 on sections 2.4 and 2.5 will be given on Wednesday of this week!
October 16, 2012
Unfortunately, a good number of students were out today due to the Monticello US History field trip. Because of that, I elected to not teach any new material today in class. We went over homework from last night and looked at a cool 2nd derivative problem (3rd block only). We WILL still have Quiz 1 on sections 2.4 and 2.5 tomorrow regardless if you were in class or not today. This was announced yesterday and should serve as no surprise to you. Please plan accordingly.
No additional homework was assigned this evening. Since the quiz tomorrow also covers section 2.4, please review any missed derivative problems from your test on 2.1-2.4. Good luck!
October 17, 2012
Quiz 1 on sections 2.4-2.5. (First block)
No additional homework was given.
October 18, 2012
Quiz 1 on sections 2.4-2.5. Earthquake drill during first block.
No additional homework was given this evening. We will begin related rates tomorrow in class.
October 19, 2012
(1) Review of selected quiz problems from yesterday's quiz. (2) Notes 2.6: Related Rates (a). Please note that these notes have been posted under the hints and solutions page of my website should you want to reference those for any reason.
Please complete from your textbook p. 154-155 problems 1,3,4,15,16,18. We will be doing a lot more with these next week! Get ready and get pumped.
October 22, 2012
(1) Review of homework from last night. (2) More problems on related rates/examples.
A related rates WS packet was given in class today. We will continue to work these throughout the next several class periods. You need complete problems 1-6 and 22 off of this packet this evening. Also, please check to the left under "Hints and Solutions" for two links to video clips of worked out solutions to two more problems! Enjoy!
October 23, 2012
(1) Review of Related Rates homework from last night. (2) 3 or 4 more example problems from the packet. (3) Trig related rate problems!
Please complete from your textbook p.155/22,23,27,30, and 45. Please stay tuned to my website for some new video clips updates on some of these problems that may be of use to you.
October 24, 2012
(1) Review of homework problems from last night. (2) Related Rate problem involving the Law of Cosines!
You should be working towards really grasping and completing these problems at this point in time, particularly ones that involve right triangles, cylinders, spheres, and cones. Please complete from your packet of related rate problems numbers 8,14,15,16,21, and 25. Number 8 involves the Law of Cosines and the others should be totally workable at this point in time. Check my website for more worked out solutions!
October 25, 2012
(1) Review of homework from last night. (2) Class time for a few more practice problems. (3) The quiz on related rates that was originally scheduled for tomorrow has been postponed. We will discuss when it will be taken tomorrow in class.
Please complete from the related rates packet problems 11,13,17,19, and 23.
October 26, 2012
(1) Review of homework problems from last night. (2) Recap and summary of related rates in preparation for Monday's quiz.
No homework was given tonight. Quiz 3 on section 2.6 will be given on Monday! Please prepare accordingly!
October 29, 2012
(1) Quiz 3 on 2.6 - Related Rates (2) Notes 3.1: Extrema on an Interval
No homework tonight. Section 3.1 was not hypothetically started today, but it makes me feel better to include it on the material covered!
October 30, 2012
No School (Hurricane Sandy)
October 31, 2012
(1) Review of graded quiz papers from Monday. (2) Notes 3.1: Extrema on an Interval, Relative and Absolute Max/Min Values.
Please complete from your book p. 169 (1-29 EOO, 39, and 46).
November 1, 2012
(1) Review of homework from last night. (2) Notes 3.2: The Mean Value Theorem for Derivatives.
Please complete from your textbook p. 169/ 2,3,16,20,24, and 28 and from p. 177/ 39,41,43, and 44. We will finish section 3.2 tomorrow and have a brief review for the Chapter 2 test that will be given on Monday!
November 2, 2012
(1) Review of homework from last night. (2) More on the MVT for derivatives. (3) Quick recap of items to review for Monday's test on Chapter 2.
No homeowrk given. Please prepare for the test on Monday.
November 5, 2012
Test 2 on Chapter 2 given in class today.
No homework given. Enjoy your day off tomorrow!
November 6, 2012
No School! Election Day!
Please exercise your right to vote if you are able.
November 7, 2012
(1) Notes 3.2 (cont) and 3.3: Rolle's Theorem/Increasing, Decreasing Fuctions and The First Derivative Test.
Please complete from your book p. 176 (11,14,19) and p. 186-187 (1-37 EOO).
November 8, 2012
(1) Review of homework from last night. (2) What happens when the derivative is not defined at a point? (3) What can't happen when a derivative is undefined in terms of a discontinuity or an asypmptote? (4) More practice with the First Derivative Test.
Please complete from your book p. 186-187 (2-16 even, 20,22,26,36,61, and 63).
November 9, 2012
(1) Review of homework from last night. (2) Wrap-Up of the first derivative test. (3) A picture of f'(x) and the relationship to f(x). (4) Relating f'(x) to another tangent line, namely f''(x). (5) The Second Derivative Test and Concavity.
Please complete from your textbook p. 195 (1-25 odd).
November 12, 2012
(1) Begin with problem that was written down on Friday (rational function) and do all analysis work involved with it. (2) Review of homework from last night. (3) More on 3.4: The Second Derivative Test. (4) The Second Derivative Test as a redundancy to the First Derivative Test.
Please complete from your book p. 195 (12,14,16,24,26,27,31,35,49, and 53). Please note that if you were absent, I have put the notes up under hints and solutions and they are titled Calc Notes_3.4(b). I hope that you will find these useful.
November 13, 2012
(1) Review of homework from last night. (2) Trig examples of the 2nd Derivative Test and Concavity. (3) Notes: An Introduction to Curve Sketching. (4) Notes 3.5: Limits at Infinity. (5) Shortcuts and the analytical method.
Please complete from your textbook p. 205 (3-8, 15-33 odd).
November 14, 2012
(1) Review of homework from last night. (2) More on limits at infinity. (3) Notes 8.7: L'Hopital's Rule for the Indeterminate Form. (4) Quick recap of material that will be covered on tomorrow quiz.
Please complete from your textbook p. 574 (5,7,9,11,13,19,23,25, and 31). Quiz 3 on sections 3.1-3.4 will be given in class tomorrow. Please prepare accordingly!
November 15, 2012
Quiz 3 on 3.1-3.4 was given in class today!
No addtional homework was given for this evening. If you have not completed the assignment on L'Hopital's Rule for Indeterminate Forms from last night, you should do that this evening and be ready to discuss tomorrow. We will proceed with curve sketching tomorrow in class!
November 16, 2012
(1) Review of graded quiz papers from yesterday. (2) Review of homework assigned from Wednesday night. (3) An example on how L'Hopital's Rule fails when used in recursive form and how to use algebraic techniques to overcome that insufficiency. (4) An introduction to formal curve sketching!
Please complete the entire reverse side of the WS that was given in class today. Remember that these are possible sketches of f(x) and everyone's could look slightly different. Remember that it is very important to capture EVERYTHING you can from the graph of f'(x). and this includes what the concavity looks like!
November 19, 2012
(1) Review of homework from last night. (2) More examples on curve sketching given f'(x). (3) Sketching a curve with given conditions only!
Please complete both sides of the second curve sketching WS that was given to you in class today!
November 20, 2012
(1) Review of homework from last night. (2) Notes 3.6: An Introduction to Function Analysis and Curve Sketching.
Please complete from your textbook p. 215 (1-4,6,7,15, and 17). Please note that if you have been out, I have uploaded some notes and discussion points from class from the last two days to the "Hints and Solutions" link on the left side of this page. Please check those out. Remember, if you aren't studying Calculus, you will forget Calculus. Please make sure that you are looking at this material at some point over your break!
November 26, 2012
(1) Review of problems that were assigned last Tuesday before break. (2) A function analysis problem that was NOT a rational function.
Please complete from your book p. 215 (5,8,16,22,47-52). Quiz 1 on sections 3.5-3.6 will be given in class on WEDNESDAY of this week! Please start to prepare accordingly!
November 27, 2012
(1) Review of homework problems from last night. (2) Q&A from curve sketching, function analysis, L'Hopital's Rule, and limits at infinity. (3) Practice WS packet on curve sketching with conditions given.
Please complete the practice packet that was given in class should you feel it necessary for your own practice. Quiz 1 on sections 3.5 and 3.6 will be given in class tomorrow!
November 28, 2012
Quiz 1 on sections 3.5,3.6, and 8.7 was given in class today. No new material was covered.
No homework was assigned tonight. Please enjoy the night off!
November 29, 2012
(1) Briefly discuss the grading situation on yesterday's quizzes. (2) Notes 3.7: Applied Optimization Problems. (3) Class examples included finding two numbers with a given sum to maximize their product, a rectangular fence, and the Alpo can.
Please complete from the packet of problems given to you today in class numbers 1-4,6, and 8. Please note that I am posting a new ShowMe video with problem number 6 completed under the Hints and Solutions page on my website. Hope this helps you a bit. Good luck!
November 30, 2012
(1) Review of graded quiz papers from Wednesday (first block only). (2) Review of homework problems from last night and take notice of the new ShowMe video posted on my website. (3) Two more example problems on applied optimization.
Please complete from the packet that was given yesterday problems 7,9,12, and 13.
December 3, 2012
(1) Review of homework from last night. (2) The Norman Window problem. (3) Review of potential problems that will be seen on Wednesday's quiz. (4) In-class practice time.
Please complete for homework tonight from your packet problems 5 and 11 and from your textbook p. 223 (8, 19, and 30).
December 4, 2012
(1) Review of homework problems from last night. (2) Reveiw of the types of optimizaton problems that may be seen on tomorrow's quiz. (3) One more Optimization Practice WS to be started in class and completed for homework.
Please complete the practice WS that was given today in class omitting problems 7 and 8. Quiz 2 on Section 3.7 will be given in class tomorrow!
December 5, 2012
(1) Review of important problems from the practice WS that was given in class yesterday. (2) Quiz 2 on section 8.1 was given in class today.
No homework was assigned after the quiz was given in class today.
December 6, 2012
(1) Hand back graded quiz papers. (2) Discussion about when the Chapter 3 test will be given. This will not happen tomorrow, but has been postponed to the beginning of next week. (3) Notes 3.9: Linear Approximations Using Differentials/Propogated Error vs. Actual Error.
Please complete from your textbook p. 240 (7-10,15,18,20,31, and 32).
December 7, 2012
Club Day! (1) Review of all necessary homework problems on differentials from last night. (2) Practice WS on differentials and linear approximations given in class and assigned to be completed for homework.
Please complete the problems from the WS assigned today in class. Please begin studying over the weekend for your Chapter 3 Test which will be given in class on Tuesday of next week! You do NOT want to wait until Monday night to begin your preparations. Begin early and often. Good luck!
December 10, 2012
Review of problems off of the differentials classwork/homework WS that was given in class on Friday. Please note that those solutions have been posted to my website. Q&A session on Chapter 3 material in preparation for the test that will be given tomorrow.
No additional homework was given today. Please be prepared for the Chapter 3 test that will be given tomorrow.
December 11, 2012
Test 1 on Chapter 3.
No homework given in class. Enjoy your night off and be ready to start antiderivatives tomorrow!
December 12, 2012
(1) Notes 4.1: The Basic Concepts of Antidifferentiation and Properties.
A WS was given today in class. Please complete problems 1-21 odd off of this WS this evening.
December 13, 2012
(1) Review of homework from last night. (2) Review of graded Test papers from Tuesday. (3) Notes 4.1 (cont): Solving IVP's for Integration.
Please complete ALL even problems from the WS that was given to you in class yesterday. This includes the even problems at the bottom of the 2nd page using IVP's. Please note that the notes given in class (including worked out problems from last night's homework) can be found under the hints and solutions page of my website.
December 14, 2012
Continuation of the discussion of particular solutions to a differential equation.
Please complete from your textbook p. 255-256 (15-39 odd,55,61,62).
December 17, 2012
(1) Review of homework from Friday night. (2) Notes 4.2: Summation Notation and Area Approximations Under a Curve.
Please complete from your textbook p. 267 (15,17,19,21,22,23,26,28). Remember which endpoints have to be used for upper and lower sums and how they change when the function is increasing or decreasing.
(1) Welcome back! (2) The NFC Playoff Picture. (3) Review of sections 4.1 and 4.2 with an example problem from each of those sections. (4) Notes 4.3: Riemann Sums and the Definite Integral.
We will have a quiz on sections 4.1 and 4.2 this Friday. Please complete from your textbook p. 278-279 (13-21 odd, 25, 27, and 33-43 odd). Your final exam is tentatively scheduled for January 14th and 15th! Please plan accordingly!
(1) Review of homework from last night. (2) A review problem on finding particular solutions to a differential equation. (3) Notes 4.3 cont: The Definite Integral as Area Under a Curve and the x-axis. (4) WS on definite integrals, graphing, and finding area under the bounded region.
Please complete the Homework side of the WS that was given today in class. Please prepare for your quiz that will be given tomorrow on sections 4.1-4.2.
Quiz 3 on Sections 4.1-4.2 was given today in class.
No addtional homework was given this evening. Please make sure that the definite integral WS from Thursday is complete for me to go over with you on Monday. Additionally, you should use some time this weekend to begin preparing for your final exam which will be given on Monday and Tuesday of the last week of the semester!
(1) Review of homework from Thursday night. (2) Quizzes from Friday will be distributed on Tuesday rather than today. (3) Notes 4.4. The Fundamental Theorems of Calculus and Definite Integration
Please complete from your textbook p. 292-292 (5-25 odd, 29,31,32,34,81, and 85). Please do NOT put off studying for your final exam to the last minute. This will cost you dearly!
(1) Review of homework from last night. (2) Notes 4.4 (cont.): The Mean Value Theorem for Integrals.
Please complete from your textbook p. 291-292 (12-22 even,28,30,43,44,47,48, and 76).
(1) Review of homework from last night. (2) More on the average value of a function and finding the value of "c" that is guaranteed by the MVT for integrals. (3) Introduction to review material for the Calculus Final Exam.
Please come to class tomorrow prepared to ask me questions pertaining to Chapters 1 and 2 of this course. The first installment of your final exam will be given on Monday of next week!
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