Analytic Geometry & Calculus C (Math 243 sec. 010) Spring 2002
EWG 205 - Monday, Wednesday, Thursday & Friday 0800-0850
SHL 105 - Tuesday 0800-0850 (discussion)
©2002 L. F. Rossi All rights reserved.

Prof. L. F. Rossi
Office: Ewing 524
Telephone: x1880
Email: rossi@math.udel.edu
WWW: http://math.udel.edu/$\sim$rossi
Computer project number: 2096

Course description: The main topics of Calculus C involve the differentiation and integration of functions of many variables. As you may have noticed, life is multidimensional, and so, Calculus III forms the foundation for most, if not all, of the physical sciences in addition to most social sciences.

Prerequisites: Math 241 and Math 242 (Calculus A and B), or equivalent are prerequisites for this course.

Your objectives:

I hope everyone will hone their mathematical abilities to reason quantitatively, logically, confidently and eventually correctly. In this course, everyone will master the following skills:

• Visualize and sketch parametrized curves. Also, given a sketch or a description of a curve, be able to parametrize curves.

• Calculate and interpret partial derivatives of functions of many variables.

• Understand the gradient and the directional derivative and be able to use them in applications such as optimization problems.

• Understand continuity and differentiability in functions of many variables.

• Calculate double and triple integrals over non-rectangular regions.

• Understand vector fields, line integrals and their applications.

• Parametrize curves and compute line integrals.

• Use the three fundamental vector calculus theorems (Divergence Theorem, Stokes' Theorem and Green's Theorem) to convert integrals from one form into another.

Your resources: All of the following will help you achieve your objectives:

$\bullet$

Time: The best way to learn mathematics is to spend time with it. It is your responsibility to come to class each day, and it is unlikely that you will pass if you miss more than a day or two, regardless of the reason. Attendance is crucial to success in this course.

$\bullet$

Textbook: Calculus, 4$^{\rm th}$ ed. by James Stewart.

$\bullet$

Office hours: Monday 0900-1000, Thursday 0900-1000, Friday 1030-1130 or by appointment. This is time that I have set aside especially for you. Office hours are one of the most valuable and least used resources at the University, and I hope you will take advantage of them. I want to help you learn this material, so do not be shy about seeing me outside of class. Your exams will only be distributed during office hours. If you need to see me at a time other than an office hour, feel free to ``drop in'' or make an appointment.

$\bullet$

Computer Algebra Systems: Maple will be used both in and out of class, and is an integral part of the curriculum. If used properly, it can function as both an interactive textbook and a powerful tool that you can use to explore different concepts.

$\bullet$

Calculator: I expect everyone to have at least a scientific calculator. You will not be allowed to use calculators with symbolic mathematical capabilities on exams.

$\bullet$

Your classmates: Math is not a competitive sport. There are many obvious reasons to work together. Even if you end up helping others most of the time, teaching is one of the best ways to gain a deeper understanding of a subject.

Grading policy: Your grade is determined solely by your understanding of mathematics and your ability to communicate this knowledge to me on exams and other assignments.

Discussion section (includes homework)	15%
Maple problems	10%
Report problems	10%
Exams (15% each)	45%
Final exam	20%

Final letter grades will be assigned strictly based on the following percentages of your total point score:
100 $\leftarrow$ A $\rightarrow$ 93 $\leftarrow$ A- $\rightarrow$ 90 $\leftarrow$ B+ $\rightarrow$ 87 $\leftarrow$ B $\rightarrow$ 83 $\leftarrow$ B- $\rightarrow$ 80 $\leftarrow$ C+ $\rightarrow$ 77 $\leftarrow$ C
C $\rightarrow$ 73 $\leftarrow$ C- $\rightarrow$ 70 $\leftarrow$ D+ $\rightarrow$ 67 $\leftarrow$ D $\rightarrow$ 63 $\leftarrow$ D- $\rightarrow$ 60 $\leftarrow$ F $\rightarrow$ 0



I reserve the right to adjust this scale to improve grades if the course material proves to be unreasonably demanding.

Exams: All exams will occur in class on the days listed on the syllabus. There are no makeup exams without prior notification and a valid, documented reason. Graded exams will be handed back in person in office hours only.

Homework and quizzes: Homework will be collected in your discussion section, and graded homework will be returned in your discussion section. Your discussion instructor may or may not give quizzes at his discretion. I will drop your lowest three homework or quiz scores during the semester. I do not accept late homework, so do not squander these three assignments. You might be sick sometime and not be able to do your homework on time. Each assignment is worth 10 points, 5 for completeness and 5 for the accuracy of several randomly selected problems.

Student conduct: To provide the best learning environment for all my students, I expect all my students to conduct all their scholarly activities with honesty and integrity. Students should note that in certain situations doing nothing can be dishonest. Though I hope there will never be a need to address academic dishonesty, I will strongly enforce all provisions noted in the Academic Regulations for Undergraduates. See The University of Delaware Undergraduate and Graduate Catalog

http://www.udel.edu/catalog/current/ugacadregs.html#acadhonesty

for further discussion on basic responsibilities.

Tentative schedule:

Week of	Section(s)	Topic(s)
Feb 6	13.1-13.3	3D rectangular coordinates, vectors.
Feb 11	13.4-13.6	Dot products, cross products, lines, planes, quadratic surfaces.
Feb 18	13.7, 14.2, 14.2	Cylindrical & spherical coordinates, vector functions, space curves.
Feb 25	14.3, 14.4	Arc length, curvature, review, Exam 1.
Mar 4	15.1-15.3	Multivariate functions, limits, continuity & differentiability, partial derivatives.
Mar 11	15.4-15.6	Tangent planes, multivariate chain rule, directional derivatives, gradients.
Mar 18	15.7, 15.8, 16.1	Min/max problems, Lagrange multipliers, double integrals.
Mar 25	16.2-16.3	Iterated integrals, double integrals over general regions, review, Exam 2.
Apr 8	16.4, 16.7, 16.8	Double integrals (polar), triple integrals (spherical & cylindrical).
Apr 15	17.1-17.3	Vector fields, line integrals, exact vector fields.
Apr 22	17.4-17.6	Green's Theorem, curl, divergence, parametric surfaces.
Apr 29	17.6, 17.7	Parametric surfaces (cont'd), surface integrals, review, Exam 3.
May 6	17.7, 17.9	Divergence (Gauss') Theorem, Stokes' Theorem.
May 13		Catch-up day, review.

Important dates:

Feb 18	Last day to drop without record.
Mar 1	Report Problem #1 due. Exam 1.
Mar 29	Report Problem #2 due. Exam 2.
Apr 22	Last day to drop with a ``W''.
Apr 26	Exam 3.
May 3	Report Problem #3 due.
May 22 (1030-1230)	Final exam.

Problem sets: The best way to learn and understand mathematics is by trying problems. An excellent way to prepare for an exam is to make sure you can solve these and other non-assigned problems without referring to your book or notes. To receive credit, you must show your work. Below are problem assignments from the book that you must hand in.

Assignment	Problems
1	13.1: 5, 7, 9; 13.2: 4, 14, 15, 29; 13.3: 5, 6, 16, 19, 25.
2	13.1: 18, 35; 13.2: 32; 13.3: 40, 46; 13.4: 4, 5, 9, 30; 13.5: 8, 9, 14; 13.6: 3, 4, 21-28.
3	13.1: 40; 13.2: 34; 13.6: 44; 13.7: 7, 8, 25, 26, 50; 14.1: 2, 8, 11; 14.2: 3, 6, 14.
4	14.1: 32; 14.2: 50; 14.3: 2, 3, 8; 14.4: 4. 7, 19.
5	14.3: 5; 14.4: 16; 15.1: 6, 13, 14; 15.2: 1, 6-8; 15.3: 12, 16, 19.
6	15.2: 15; 15.3: 60; 15.4: 3, 5, 12; 15.5: 9, 10, 19; 15.6: 4, 5, 8.
7	15.4: 32; 15.5: 38; 15.6: 32; 15.7: 3, 4, 12 (M)1; 15.8: 3, 4, 19; 16.1: 11, 12, 17.
8	15.7: 28; 15.8: 39; 16.2: 3, 4, 10, 21, 28; 16.3: 7, 10, 15, 16, 22.
9	16.2: 30 (M); 16.3: 36; 16.4: 3, 4, 6, 26; 16.7: 3, 4, 5, 12.
10	16.3: 46; 16.4: 32; 16.7: 34; 16.8: 5, 6, 9, 10, 26; 17.1: 11, 12, 17; 17.2: 5, 6, 14.
11	17.2: 22; 17.3: 3, 4, 6, 33; 17.4: 3, 4, 11, 14; 17.5: 7, 8, 13, 14, 20.
12	17.4: 22, 24; 17.5: 35; 17.6: 11-14, 18, 24, 29 (M), 32 (M), 37, 40.
13	17.7: 3, 4, 8, 11, 12, 28, 39-42; 17.9: 7-9, 12, 20, 29, 30.

Report problems: A special component of this course called report problems are designed to augment the textbook's approach. They will focus on problem solving, abstract reasoning and applications. The guidelines for reports are:

$\bullet$

Reports must be handed in by the due date.

$\bullet$

The intended audience of the report is your fellow classmates. You must explain each step you take clearly, neatly and accurately. A report should not exceed five pages.

$\bullet$

A single report may be submitted by teams of up to three people. Each team member must contribute roughly one third to the content of the report.

$\bullet$

Reports either receive full credit or a ``REDO.'' Full credit is awarded for a clear, concise and correct solution. REDO's are awarded otherwise.

$\bullet$

One can resubmit a corrected REDO for full credit for up to two weeks after reports are returned.

$\bullet$

Periodically, you may be asked to submit a progress report to help to make steady progress toward completing your reports. To receive credit for a report problem, you must hand in all the progress reports.

I have excellent examples of report problems available in my office for you to look at if you are unsure of what I expect.