Math 211 Multivariable Calculus

Textbook: 

• Vector Calculus by Susan Jane Colley, 4th Edition.

Software:

Mathematica

Topics:

Chapter 1 Vectors

1.1 Vectors in Two and Three Dimensions
1.2 More About Vectors
1.3 The Dot Product
1.4 The Cross Product
1.5 Equations for Planes Distance Problems

Chapter 2 Differentiation in Several Variables

2.1 Functions of Several Variables Graphing Surfaces
2.2 Limits
2.3 The Derivative
2.4 Properties Higher-Order Partial Derivatives
2.5 The Chain Rule
2.6 Directional Derivatives and the Gradient

Chapter 3 Vector-Valued Functions

3.1 Parametrized Curves and Kepler's Laws
3.2 Arc Length and Differential Geometry
3.3 Vector Fields: An Introduction
3.4 Gradient, Divergence, Curl, and the Del Operator

Chapter 4 Maxima and Minima in Several Variables

4.2 Extrema of Functions
4.3 Lagrange Multipliers

Chapter 5 Multiple Integration

5.1 Introduction: Areas and Volumes
5.2 Double Integrals
5.3 Changing the Order of Integration
5.5 Change of Variables

Chapter 6 Line Integrals

6.1 Scalar and Vector Line Integrals
6.2 Green's Theorem
6.3 Conservative Vector Fields

Chapter 7 Surface Integrals and Vector Analysis

7.1 Parametrized Surfaces
7.2 Surface Integrals
7.3 Stokes' and Gauss' Theorems