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