Section(s) 1. Multivariable Functions a. Definitions and notation 13.1, 14.1 b. Graphs and images c. Level sets and level surfaces 14.1 d. Cylinders 12.8 e. Quadric Surfaces 12.7 2. Vectors a. Definitions 12.1, 12.2 b. Vector operations 12.3, 12.4 c. Vector decomposition 12.3 d. Angles between vectors 12.3 3. Lines and Planes in Space a. Equations: graph, parametric, implicit 12.5, 12.6 b. Normal vectors 12.6 4. Functions of the form $f\colon\R^2\to\R$ (Surfaces in Space as Graphs of a Funcion) a. Directional derivatives 14.6 b. Partial derivatives 14.3 c. The gradient vector 14.6 d. The normal vector 14.3 e. The tangent plane 14.3 f. Critical points and optimization problems 14.8, 14.9 5. Functions of the form $f\colon\R^3\to\R$ (Implicit Surfaces in Space) a. Gradients and partial derivatives 14.1, 14.7 b. Tangent planes and normal vectors 14.7 6. Functions of the form $f\colon\R\to\R^3$ (Parametric Curves in Space) a. Velocity and acceleration 13.2, 13.6 b. Tangent and normal vectors 13.4, 13.6 7. Functions of the form $f\colon\R^2\to\R^3$ (Parametric Surfaces in Space) a. Partial derivatives 14.7 b. The normal vector and tangent plane c. The multi-variable chain rule 14.5 8. 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
 Math 115 (Fall 2013) web pages Created: 05 Sep 2013 Last modified: 05 Sep 2013 00:00:00 Comments to: dpvc@union.edu