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 |
See the course calendar for details concerning exams and quizzes.
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