Section(s) | ||||

1. | Multivariable Functions | |||

a. | Definitions and notation | 14.1, 15.1 | ||

b. | Representations: graphs and images | |||

c. | Slicing and projections | |||

2. | Vectors | |||

a. | Definitions | 13.1, 13.2 | ||

b. | Vector operations | 13.3, 13.4 | ||

c. | Vector decomposition | 13.3 | ||

d. | Angles between vectors | 13.3 | ||

3. | Lines and Planes in Space | |||

a. | Equations: graph, parametric, implicit | 13.5, 13.6 | ||

b. | Normal vectors | 13.6 | ||

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: R^{2} -> R(Surfaces in Space as Graphs of a Funcion) | |||

a. | Directional derivatives | 15.6 | ||

b. | Partial derivatives | 15.3 | ||

c. | The gradient vector | 15.6 | ||

d. | The normal vector | 15.3 | ||

e. | The tangent plane | 15.3 | ||

f. | Critical points and optimization problems | 15.8, 15.9 | ||

g. | Limits and continuity | 15.2 | ||

^{ }6. | Functions of
the form f: R -> R^{3}(Parametric Curves in Space) | |||

a. | Velocity and acceleration | 14.2 | ||

b. | Tangent and normal vectors | 14.4 | ||

^{ }7. | Functions
of the form f: R^{2} -> R^{3}(Parametric Surfaces in Space) | |||

a. | Partial derivatives | 15.7 | ||

b. | The normal vector and tangent plane | |||

c. | The Jacobian matrix | |||

d. | The multi-variable chain rule | 15.5 | ||

^{ }8. | Functions of
the form f: R^{3} -> R(Implicit Surfaces in Space) | |||

a. | Gradients and partial derivatives | 15.1, 15.7 | ||

b. | Tangent planes and normal vectors | 15.7 |

See the course calendar for details concerning exams and quizzes.

Comments to: dpvc@union.edu

Created: Aug 31 1998 --- Last modified: Sep 1, 1998 9:14:41 AM