Math 550  University of South Carolina
D. Meade  Fall 1997

Math 550 (Section 1) – Vector Analysis

Instructor Professor Doug Meade

Office Hours: MWF 10:00–11:00 and by prior appointment
Office:  LeConte College 300E
Phone:  777-6183

 E-mail:  meade@math.sc.edu

WWW URL  http://www.math.sc.edu/~meade/math550-F97/

Meeting Times MWF 11:15am–12:05pm, LC 401A

Text Marsden and Tromba, Vector Calculus, (4th ed.), W.H. Freeman and Company, 1996.

Prerequisite Completion of Math 241.

Course Content Vector analysis involves the study of functions whose domain and/or range is vector-valued. Some of the main topics include: representations of curves and surfaces, derivatives and integrals. The main goal of this course is to thoroughly develop and apply the integral theorems of Green, Gauss, and Stokes. This discussion requires a solid foundation in the geometry of curves and surfaces, as well as line integrals, surface integrals, and volume integrals. These concepts should all be somewhat familiar from Math 241. The material in Chapters 1 and 2 will be reviewed very quickly. Chapters 4 and 5 will be discussed in more detail, although most of the material should still be familiar. Approximately two-thirds of the course will be devoted to understanding Chapters 6, 7, and 8. The following listing summarizes some of the main topics in each chapter.

Chapter 1 The Geometry of Euclidean Space (1 class) • vectors and vector operations

• cylindrical and spherical coordinate systems Chapter 2 Differentiation (1 class)

• limits, continuity, and differentiation

• definition and properties of gradients and directional derivatives Chapter 4 Vector-Valued Functions (4 classes)

• arclength

• vector fields, divergence and curl Chapter 5 Double and Triple Integrals (6 classes)

• iterated integrals

• changing the order of integration Chapter 6 The Change of Variable Formula and Applications of Integration (5 classes)

• Jacobians Chapter 7 Integrals over Paths and Surfaces (9 classes)

• parameterization of lines and surfaces Chapter 8 The Integral Theorems of Vector Analysis (13 classes)

• Green’s theorem

• Stokes’ theorem

• Gauss’ theorem

• applications Study Hints Before each class, you should both review your class notes and read the section to be discussed

that day. This will allow you to better understand the terminology and concepts discussed in class, to identify concepts that are not clear to you, and to identify questions that you may need to ask during class.

Math 241 is the prerequisite for this course. The review of this material will be brief. Be sure you take all necessary steps to refresh your memory and skills relating to the material in Chapters 1 and 2 of our textbook.

Grading Your grade in this course will be based on your performance on homework, two (2) mid-term exams, and a final exam. The weights assigned to each of these components will be:

Homework  10%
Mid-term exams (3) 60%
Final exam  30%

Course grades will be determined according to the following scale:

A 90 –100
B 80 – 89
C 70 – 79
D 60 – 69
F 0 – 59

Note that the deadline to drop this course with a grade of W is \underline{Thursday, October 2, 1997}.

Exams There will be two (2) exams during the semester. Tentative dates and topics for these exams are:

Wednesday, September 24  Chapters 1, 2, 4, and 5
Wednesday, October 29  Chapters 6 and 7

Make-up exams will be given only for documented reasons of illness, family emergency or participation in a University sponsored event. Excuses such as oversleeping, forgetting the time or location of the exam, and lack of studying are explicitly noted as unacceptable grounds for the administration of a make-up exam.

A comprehensive final will be given at \underline{2:00p.m.} on \underline{Wednesday, December 10, 1997}. (Do not trust exam schedules published by unofficial sources, e.g., the Mortar Board.)

Homework A minimum set of homework problems will be distributed at the beginning of each chapter. You are responsible for working these problems as we work through the book. All problems marked with an asterisk (^{∗}) will be collected and graded once each week (usually on Monday, but this may change).

Your homework average will be determined after dropping your three (3) lowest homework scores \underline{No late homework will be accepted.}

Attendance Regular class attendance is important. Consistent with the USC Undergraduate Bulletin, a grade penalty may be applied to any student missing more than four classes (10%) during the semester.

Academic Honesty Cheating and plagiarism will not be tolerated in this course. You may discuss homework problems with others, but do not copy solutions from another student or from a book. Violations of this policy will be dealt with in a matter consistent with University guidelines.