# Course Outline:

 Section(s) 1. Multivariable Functions a. Definitions and notation 12.1, 13.1 b. Graphs and images c. Level sets and level surfaces 13.1 d. Cylinders 11.8 e. Quadric Surfaces 11.7 2. Vectors a. Definitions 11.1, 11.2 b. Vector operations 11.3, 11.4 c. Vector decomposition 11.3 d. Angles between vectors 11.3 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 13.6 b. Partial derivatives 13.3 c. The gradient vector 13.6 d. The normal vector 13.3 e. The tangent plane 13.3, 13.7, 11.6 f. Critical points and optimization problems 13.8, 13.9 5. Functions of the form $f\colon\R^3\to\R$ (Implicit Surfaces in Space) a. Gradients and partial derivatives 13.1, 13.7 b. Tangent planes and normal vectors 13.7 6. Functions of the form $f\colon\R\to\R^3$ (Parametric Curves in Space) a. Velocity and acceleration 12.2, 12.6 b. Tangent and normal vectors 12.4, 12.6 7. Functions of the form $f\colon\R^2\to\R^3$ (Parametric Surfaces in Space) a. Partial derivatives 13.3 b. The normal vector and tangent plane 13.7 c. The multi-variable chain rule 13.5 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

See the course calendar for details concerning exams and quizzes. Math 115H (Fall 2017) web pages Created: 04 Sep 2017 Last modified: Sep 4, 2017 6:44:53 PM Comments to: dpvc@union.edu