| 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 (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 (Parametric Curves in Space) | |||
| a. | Velocity and acceleration | 15.2 | ||
| b. | Tangent and normal vectors | 15.4 | ||
| 7. | Functions
of the form (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 (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.