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# Math 15 Course Outline:

 Section(s) 1. Multivariable Functions a. Definitions and notation 15.1, 16.1 b. Representations: graphs and images c. Slicing and projections 2. Vectors a. Definitions 14.1, 14.2 b. Vector operations 14.3, 14.4 c. Vector decomposition 14.3 d. Angles between vectors 14.3 3. Lines and Planes in Space a. Equations: graph, parametric, implicit 14.5, 14.6 b. Normal vectors 14.6 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 16.6 b. Partial derivatives 16.3 c. The gradient vector 16.6 d. The normal vector 16.3 e. The tangent plane 16.3 f. Critical points and optimization problems 16.9, 16.10 g. Limits and continuity 16.2 6. Functions of the form f: R -> R3 (Parametric Curves in Space) a. Velocity and acceleration 15.2 b. Tangent and normal vectors 15.4 7. Functions of the form f: R2 -> R3 (Parametric Surfaces in Space) a. Partial derivatives 16.7 b. The normal vector and tangent plane c. The Jacobian matrix d. The multi-variable chain rule 16.8, 16.4 8. Functions of the form f: R3 -> R (Implicit Surfaces in Space) a. Gradients and partial derivatives 16.1, 16,7 b. Tangent planes and normal vectors 16.7

See the course calendar for details concerning exams and quizzes.

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Comments to: dpvc@union.edu
Created: Jan 4 1998 --- Last modified: Jan 4, 1998 9:42:47 PM