Math 304, Vector Analysis

Office: Bldg 25, Rm 329, telephone: 6-1684
Web site: http://www.calpoly.edu/~dhartig

Course Objectives

1. Review the geometry of 2- and 3-space: vectors, inner products and length, determinants, cross-products, and volume; cylindrical and spherical coordinates; vector-valued functions of a real variable, derivatives.
2. Learn about vector-valued functions of a vector variable and the derivative as a linear map. Review gradients and directional derivatives. Study higher-order derivatives, Taylor's Theorem and max/min, constrained extrema. Learn about the implicit function theorem and the inverse function theorem.
3. Review Arc Length, Vector Fields, and divergence and curl. Review Double and Triple Integrals.
4. Investigate non-linear transformations and the Change of Variable Theorem for double and triple integrals.
5. Review line and surface integrals and develop the relations between them; selected applications.
6. Formalize the important integral theorems of vector analysis: Green, Stokes, and Gauss Theorems; selected applications.
7. Develop the fundamentals of differential forms as both a unifying and a generalizing tool for applications to vector fields.

Marsden and Tromba, Vector Calculus, 6th Edition, Freeman, 2012

Coverage in Text

1. Chapter 1. The Geometry of Euclidean Space
2. Chapter 2. Differentiation
3. Chapter 3. Higher-Order Derivatives: Maxima and Minima
4. Chapter 4. Vector-Valued Functions
5. Chapter 5. Double and Triple Integrals
6. Chapter 6. The Change of Variables Formula and Applications of Integration
7. Chapter 7. Integrals over Paths and Surfaces
8. Chapter 8. The Integral Theorems of Vector Analysis

Homework, Exams, etc.

• Homework will be assigned and collected regularly.
• There will be two quizzes.
• There will be two midterms and a comprehensive final exam on Monday, June 10, 1 - 4.

Grades

Office Hours (subject to change)