MATH 320:Calculus III
Fall 1999, 4 Credits, MWF: 9:00-9:50 am, T: 11:00-11:50 am, FC-B22
Instructor: Rich Maresh, Associate Professor & Chair, Mathematics Department
Office: MC 522 Hrs: MWF 9-10, W 2-3, or by appt, Ph: 796-3655, 526-4988 (home)
Final Exam: Thursday, 16 Dec 99, 3:00-5:00 pm
Catalog Description: Partial differentiation; multiple integrals; L’Hopital’s rules; infinite sequences and series. Prerequisite: grade of C or higher in 221.
Text: Calculus - Early Transcendentals, 3rd Edition, by James Stewart (Brooks Cole, 1995)
CORE SKILL OBJECTIVES
1. Thinking Skills:
Uses reasoned standards in solving problems and presenting arguments
2. Communication Skills:
Reads with comprehension and the ability to analyze and evaluate.
Listens with an open mind and responds with respect.
Accesses information and communicates using current technology.
3. Life Values:
Analyzes, evaluates and responds to ethical issues from an informed personal value system.
4. Cultural Skills:
Understands culture as an evolving set of world views with diverse historical roots that provides a framework for guiding, expressing, and interpreting human behavior.
Demonstrates knowledge of the signs and symbols of another culture.
Participates in activity that broadens the student’s customary way of thinking.
5. Aesthetic Skills:
Develops an aesthetic sensitivity
Further Course Goals:
From the perspective of mathematical content, this course should allow the student to expand and apply skills and knowledge gained in the first two semesters of Calculus to the topics of infinite sequences and series and to three-dimensional space.
The student will gain knowledge and skills, and the ability to apply these, to a variety of situations which might be encountered in the world of mathematics, science, or engineering.
The student will further improve his/her ability to communicate mathematical ideas and solutions to problems.
The student will improve her/his problem-solving ability.
From a most general perspective, the student should see growth in his/her mathematical maturity. The three-semester sequence of calculus courses form the foundation of any serious study of mathematics or other mathematically-oriented disciplines and this course is the capstone of that sequence.
COURSE OBJECTIVES
1. Thinking Skills:
Explores infinite sequences and series, and the concept of convergence and divergence.
Investigates applications of series.
Explores functions of more than one variable.
Develops an ability to construct 3-dimensional graphs of these functions, especially with an appropriate use of technology.
Learns the meaning and applications of partial differentiation.
Explores the use of multiple integration to find volumes and surface areas of 3-dimensional surfaces.
2. Communication Skills:
Collects a portfolio of one’s work during the course and write a reflection paper.
Does group work (labs and practice exams) throughout the course, involving both written and oral communication.
Uses technology - graphing calculators and Maple V in the computer lab - to solve problems and to be able to communication solutions and explore options.
Uses technology to construct and appropriately manipulate 3-dimensional graphs.
Improves one’s ability to write logically valid and precise mathematical proofs and solutions.
3. Life Value Skills:
Develops an appreciation for the intellectual honesty of deductive reasoning.
Understands the need to do one’s own work, to honestly challenge oneself to master the material.
4. Cultural Skills:
Develops and appreciation of the history of calculus and the role it has played in mathematics and in other disciplines.
Learns to use the symbolic notation correctly and appropriately.
Explores how people living in a pre-calculator/computer culture used convergent infinite series and sequences to evaluate expressions we take for granted because we get them at the push of a button (e.g., e, p, ln(2), ...).
5. Aesthetic Skills:
Develops an appreciation for the austere intellectual beauty of deductive reasoning.
Develops an appreciation for mathematical elegance.
Course Outline:
The student will study infinite sequences and series, exploring specifically the questions of divergence and convergence, and studying the use of such series to find the value of certain functions and certain numbers.
The student will study three-dimensional space and vectors, lines, planes and general surfaces in R
3.
The student will study derivatives and partial derivatives of functions in 3D space.
The student will study the concept and process of multiple integration, and explore a variety of applications of such processes.
Course Philosophy and Procedures:
I am a firm believer in the notion that you as the student must be actively engaged in the learning process and that this is best accomplished by your DOING mathematics. My job here is not to somehow convince you that I know how to do the mathematics included in the course, but to help guide YOU through the material; I am to be a "guide on the side, NOT a sage on the stage". I may not always say things in the way which best leads to your full comprehension, but I will try to do so and I ask that you try to see your learning as something YOU DO rather than as something I do to you. PLEASE feel free to come see me to discuss questions or concerns you may have during the course; I will not bite! PLEASE ask questions in class if you have them; the only dumb question is the one you fail to ask!
Let me therefore urge you to make it a regular part of your day to try working the homework problems. There will never be enough time for us to go through every listed problem in class, and it is unrealistic to think that you will be able to find the time to work through every listed problem, but you should at least spend some time thinking about virtually every problem, and working the more interesting or challenging to completion. The daily Homework assignments will not generally be collected or graded. They are intended to structure your learning so that you regularly challenge yourself to see that you understand the material we are looking at. The important thing is that you at least look at all the assigned problems. You should also feel free to work other problems if you deem it necessary for your comprehension of the content.
In general, I think students can benefit greatly by working together on problems. While there is some danger of the "blind leading the blind" syndrome, or of students deceiving themselves into thinking they understand the material better than they actually do, for the most part grappling with ideas and trying to explain them to another student or learning to listen to others explain an idea is a wonderful way to see that you really do understand the material. In class we will spend an occasional day working on a group "lab", and we sill also typically have a group "practice exam" before the individual exams, and I also encourage you to find a "learning group" outside of class.
I will be asking you to keep a JOURNAL and a PORTFOLIO. Each second Monday (Sep 13 and 27, Oct 11 and 25, Nov 8 and 22) morning I will collect a one-page journal entry; you should write about the concepts we are encountering and about your efforts, successes and failures in the learning process. These are intended to be personal reflections, and the 10 points for each entry is meant to demonstrate that I am placing value on this reflective writing; as long as you put obvious adequate effort into your journaling, you will get the 10 points.
The Portfolio will be collected at the end of the semester, on Friday 10 December. This "portfolio" should be a representative collection of your work during the semester, and should include 5 problems, written up in a finished form, along with a brief discussion of why you chose to include that particular problem. These problems should represent work you are proud of, or problems which brought you to a breakthrough point. This portfolio of your work will be worth 40 points, 8 points per problem. Presumably you will hand in 5 sheets of paper, each of which will include a nicely organized solution to the problem, which might be from homework, or from a lab or worksheet, of from an exam, along with that reflection mentioned above.
I am making a conscious decision here to cover a little less material (specifically, chapter 14) for the sake of greater depth and, I hope, comprehension. If I eliminated the group labs and practice exams we could "zip along" a little faster, but I want the pace kept at a level which allows us to ask interesting questions and try working interesting problems, and which allows you to master better the material we do cover. If you feel a need to learn the material in chapter 14 (the calculus of vectors), you are certainly permitted to do so.
I use a rather traditional Grading Scale: A = 90% (or better), AB = 87%, B = 80%, BC = 77%, C = 70%, CD = 67%, D = 60%. I do try to come up with a mix of points so that exams are not weighted too heavily; about half the points during the semester will come from individual, in-class exams - the rest will come from group labs, take-home problems, group practice exams, journals, and portfolios.
It is rarely much of a problem at the level of a calculus course, but it remains important that students turn work in in a timely manner, so that they do not get behind. Consequently, Late Assignments will be penalized 20% of the possible points for each class period late, up to a maximum of three periods.
Americans with Disability Act:
If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see me or Wayne Wojciechowski in MC 320 (796-3085) within 10 days to discuss your accommodation needs.
MATH 320 Course Schedule, Fall 1999:
30 Aug <10.1> Sequences p 586 # 1,3,9,11,15,19,21,27,45
31 Aug <10.2> Series p 586 # 57,59,61; p 596 # 1,3,5,7,11,13,15
1 Sep ... more on <10.1>, <10.2> p 596 # 19,21,25,27,33,39,43,45,51,57
3 Sep Lab #1 Lab #1 Take-Home Problems
7 Sep <10.3> Integral Test for Convergence, Estimates of Sums p 603 # 1,3,7,11,13,19,26
8 Sep <10.4> Comparisons Tests for Convergence p 608 # 1,3,7,9,13,17,25,29,35
10 Sep <10.5> Alternating Series p 613 # 1,3,5,9,13,19,25,27
13 Sep <10.6> Absolute Convergence, Ratio and Root Tests p 619 # 1,3,7,11,15,19,29,31
14 Sep <10.7> Strategies for Testing Series for Convergence p 622 # 1,5,7,9,13,15,17,25,31
15 Sep Lab #2 Lab #2 Take-Home Problems
17 Sep <10.8> Power Series p 627 # 3,5,7,9,13,19,25,29
20 Sep <10.9> Functions as Power Series p 632 # 1,3,5,11,15,21,23,25
21 Sep <10.10> Taylor Series and Maclaurin Series p 643 # 1,3,7,9,11,13,17,19,33,37,39
22 Sep <10.11> Binomial Series p 647 # 1,3,5,11,13,17
24 Sep Lab #3 Lab #3 Take-Home Problems
27 Sep <10.12> Applications of Taylor Polynomials p 653 # 1,5,9,13,19,23
28 Sep
Group Practice Exam #1
29 Sep
EXAM #1
1 Oct <11.1> 3D Coordinate System p 668 # 1,3,5,9,13,17,29,31,33,35
4 Oct <11.2> Vectors p 675 # 3,5,9,13,17,21,27,31
5 Oct <11.3> The Dot Product p 680 # 3,5,9,13,15,17,23,31,37,39,49
6 Oct <11.4> The Cross Product p 687 # 3,5,7,9,13,19,21,25
8 Oct Lab #4 Lab #4 Take-Home Problems
11 Oct <11.5> Equations of Lines and Planes in R
3 p 696 # 3,7,11,15,19,23,29,31,35
12 Oct <11.6> Quadric Surfaces p 702 # 1,3,5,7,17,18,19,20,21,22,23,24,25,35,37
13 Oct <11.7> Vector-Valued Functions p 711 # 1,2,3,4,5,6,9,17,19
15 Oct <11.8> Arc Length and Curvature p 719 # 1,3,5,7,11,15,21,23
18 Oct Lab #5
19 Oct <11.9> Motion in Space, Velocity, Acceleration p 727 # 1,5,7,11,19,21,23
20 Oct <11.10> Cylindrical and Spherical Coordinates p 733 # 1-55 odd
25 Oct
Group Practice Exam #2
26 Oct
EXAM #2
27 Oct <12.1> Functions of Several Variables p 748 # 1,7,9,11,31,35,39,41,43,47,59,60,61,62,63,64
29 Oct <12.2> Limits and Continuity p 757 # 1,3,7,13,19,21,27,29,47,49
1 Nov <12.3> Partial Derivatives p 764 # 1,3,5,7,9,13,17,21,35,49
2 Nov Lab #6 Lab #6 Take-Home Problems
3 Nov <12.4> Tangent Planes and Differentials p 773 # 3,5,7,11,13,19,21,25,29,31,33
5 Nov <12.5> The Chain Rule p 780 # 1,3,5,7,9,11,13,19,23,27,29,33,35
8 Nov <12.6> Directional Derivatives and the Gradient Vector p 790 # 1,3,5,7,9,11,13,17,23,25
9 Nov <12.7> Maximum and Minimum Values p 799 # 1,5,9,11,13,17,21,25,33,37,41,45,49
10 Nov Lab #7 Lab #7 Take-Home Problems
12 Nov
Group Practice Exam #3
15 Nov
EXAM #3
16 Nov <13.1> Double Integrals over Rectangles p 817 # 1,3,5,9,11
17 Nov <13.2> Iterated Integrals p 822 # 1,3,5,7,9,11,15,17,21,23,25,27,29
19 Nov <13.3> Double Integrals over General Regions p 830 # 1,3,5,7,9,11,13,19,21,29,31
22 Nov <13.4> Double Integrals in Polar Coordinates p 836 # 1,3,5,7,9,11,13,15,19,25,27,29,31
23 Nov <13.5> Applications of Double Integrals p 844 # 1,3,5,7,11,13
29 Nov <13.6> Triple Integrals p 852 # 1,3,5,7,9,17,19,25
30 Nov <13.7> Triple Integrals in Cylindrical and Spherical Coords p 858 # 1,3,5,7,9,11,13,15,19,21
1 Dec <13.8> Change of Variables in Multiple Integrals p 866 # 1,3,5,7,9,11,13
3 Dec Lab #8 Lab #8 Take-Home Problems
6 Dec
Group Practice Exam #4
7 Dec
EXAM #4
8 Dec Review ...
10 Dec Group Practice Final Exam
16 Dec
FINAL EXAM, Thursday, 3:00-5:00 pm