# Course Outline:

 Section(s) 1. Multivariable Functions a. Definitions and notation 14.1, 15.1 b. Representations: graphs and images c. Slicing and projections 2. Vectors a. Definitions 13.1, 13.2 b. Vector operations 13.3, 13.4 c. Vector decomposition 13.3 d. Angles between vectors 13.3 3. Lines and Planes in Space a. Equations: graph, parametric, implicit 13.5, 13.6 b. Normal vectors 13.6 4. Introduction to Linear Algebra (In supplement) a. Systems of linear equations 1.1, 1.2, 1.3 b. Matrices and matrix arithmetic 1.4, 1.5 c. Inverse matrices 1.6 d. Determinants 2.1, 2.2 5. Functions of the form f: R2 -> R (Surfaces in Space as Graphs of a Funcion) a. Directional derivatives 15.6 b. Partial derivatives 15.3 c. The gradient vector 15.6 d. The normal vector 15.3 e. The tangent plane 15.3 f. Critical points and optimization problems 15.8, 15.9 g. Limits and continuity 15.2 6. Functions of the form f: R -> R3 (Parametric Curves in Space) a. Velocity and acceleration 14.2 b. Tangent and normal vectors 14.4 7. Functions of the form f: R2 -> R3 (Parametric Surfaces in Space) a. Partial derivatives 15.7 b. The normal vector and tangent plane c. The Jacobian matrix d. The multi-variable chain rule 15.5 8. Functions of the form f: R3 -> R (Implicit Surfaces in Space) a. Gradients and partial derivatives 15.1, 15.7 b. Tangent planes and normal vectors 15.7

See the course calendar for details concerning exams and quizzes. Math 15H (Fall 2002) web pages Created: 07 Sep 2002 Last modified: 07 Sep 2002 00:00:00 Comments to: `dpvc@union.edu`