MATH 320: Calculus III
Fall 2001, 4 Credits, MTWF: 8:00-8:50 am, NC 121
Instructor: Rich Maresh, Associate Professor & Chair, Mathematics Department
Office: MC 522 Hrs: MWF 12-1, TW 2-3 or by appt, Ph: 796-3655, 526-4988 (home)
Final Exam: Tuesday, 11 Dec 01, 12:50-2:50 pm
Infinite sequences and series; partial differentiation; multiple integrals. Prerequisite: grade of C or higher in 221.
Text: Multivariable Calculus, From Graphical, Numerical, and Symbolic Points of View (Revised Preliminary Edition), by Ostebee and Zorn (Saunders College Publishing, 1998).
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 that 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.
1. Thinking Skills:
a) Explores infinite sequences and series, and the concept of convergence and divergence.
b) Investigates applications of series.
c) Explores functions of more than one variable.
d) Develops an ability to construct 3-dimensional graphs of these functions, especially with an appropriate use of technology.
e) Learns the meaning and applications of partial differentiation.
f) Explores the use of multiple integration to find volumes and surface areas of 3-dimensional surfaces.
2. Communication Skills:
a) Collects a portfolio of one’s work during the course and write a reflection paper.
b) Does group work (labs and practice exams) throughout the course, involving both written and oral communication.
c) Uses technology - graphing calculators and Maple V in the computer lab - to solve problems and to be able to communication solutions and explore options.
d) Uses technology to construct and appropriately manipulate 3-dimensional graphs.
e) Improves one’s ability to write logically valid and precise mathematical proofs and solutions.
3. Life Value Skills:
a) Develops an appreciation for the intellectual honesty of deductive reasoning.
b) Understands the need to do one’s own work, to honestly challenge oneself to master the material.
4. Cultural Skills:
a) Develops and appreciation of the history of calculus and the role it has played in mathematics and in other disciplines.
b) Learns to use the symbolic notation correctly and appropriately.
c) 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, π, ln(2), ...).
5. Aesthetic Skills:
a) Develops an appreciation for the austere intellectual beauty of deductive reasoning.
b) Develops an appreciation for mathematical elegance.
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.
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. Every other Monday (Sep 10, Sep 24, Oct 8, Oct 22, Nov 5, Nov 19, and Dec 3) 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 5 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 5 points. I would like you to type up your journal entries and leave the files in your Blackboard “Drop Box”.
The PORTFOLIO will be collected at the end of the semester, on Friday 15 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 that 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 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 in work 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 Fall 200 Course Schedule
27 Aug <11.1> Sequences and Limits p 309 # 1-15 odd, 21-39 odd, 47, 51
28 Aug <11.2> Infinite Series, Convergence p 320 # 1, 2, 5, 9-21 odd, 27, 29, 33, 41-47 odd
29 Aug <11.3> Testing for Convergence p 333 # 1-23 odd, 27, 39-47 odd
31 Aug <11.4> Absolute Convergence, Alternating Series p 343 # 1-21 odd
4 Sep Lab #1
5 Sep <11.5> Power Series p 350 # 1-17 odd, 21, 23, 27
7 Sep <11.6> Power Series as Functions p 357 # 1-11 odd, 17-21 odd, 27-33 odd, 47, 63
10 Sep <11.7> Maclaurin and Taylor Series p 364 # 1-15 odd
11 Sep Lab #2
12 Sep Group Practice Exam #1
14 Sep EXAM #1
17 Sep <1.1> Three-Dimensional Space p 11 # 1-11 odd
18 Sep <1.2> Curves and Parametric Equations p 25 # 1-7 odd, 10, 13
19 Sep Lab #3
21 Sep <1.3> Vectors p 35 # 1-9 odd
24 Sep <1.4> Vector-Valued Functions, Derivative, Integral p 46 # 1, 3
25 Sep <1.5> Derivative, Anti-Derivative, Notation p 55 # 1-15 odd, 25, 29
26 Sep Lab #4
28 Sep <1.6> The Dot Product p 69 # 1-17 odd
1 Oct <1.7> Lines and Planes in Three-Space p 82 # 1, 5-19 odd
2 Oct Lab #5
3 Oct <1.8> Cross Products p 90 # 1-13 odd
5 Oct Review …
8 Oct Group Practice Exam #2
9 Oct EXAM #2
10 Oct <2.1> Functions of Several Variables p 103 # 1-9 odd
12 Oct <2.2> Partial Derivatives p 115 # 1, 2, 5-11 odd
15 Oct <2.3> Partial Derivatives and Linear Approximation p 124 # 1, 3, 7, 11, 13
16 Oct <2.4> Gradients and Directional Derivatives p 134 # 1-7 odd
17 Oct <2.5> Local Linearity p 139 # 1, 3
22 Oct <2.6> Higher-Order Derivatives, Quadratic Approx. p 145 # 1, 3
23 Oct <2.7> Maximum/Minimum Values p 156 # 1-11 odd
24 Oct Lab #6
26 Oct <2.8> Chain Rule for Multi-variable Functions p 168 # 1, 5, 7
29 Oct Group Practice Exam #3
30 Oct EXAM #3
31 Oct <3.1> Multiple Integration p 179 # 1-11 odd
2 Nov <3.2> Calculating Integrals by Iterations p 191 # 1, 5-11 odd
5 Nov Lab #7
6 Nov <3.3> Double Integration in Polar Coordinates p 199 # 1-7 odd
7 Nov <3.4> Triple Integrals in Cylind. and Spher. Coord. p 208 # 1-11 odd
9 Nov <3.5> Multiple Integration Overview p 217 # 1, 5, 7
12 Nov Lab #8
13 Nov <4.1> Linear, Circular, and Combined Motion p 226 # 1-7 odd
14 Nov <4.2> Using the Dot Product on Curves p 232 # 1, 3
16 Nov <4.3> Curvature p 238 # 1-7 odd
19 Nov <4.4> Lagrange Multipliers p 245 # 1, 3, 5
20 Nov Lab #9
26 Nov Group Practice Exam #4
27 Nov EXAM #4
28 Nov <5.1> Line Integrals p 254 # 1, 3, 5
30 Nov <5.2> Fundamental Theorem for Line Integrals p 263 # 1-7 odd
3 Dec <5.3> Green’s Theorem p 273 # 1, 3, 5
4 Dec Lab # 10
5 Dec Review …
7 Dec Group Practice Final Exam
Final Exam: Tuesday, 11 Dec 2001, 12:50-2:50 pm