Section 1-1:
Vectors in Two and Three Dimensions
Section 1-2:
More About Vectors
Section 1-3:
The Dot Product
Section 1-4:
The Cross Product
Section 1-5:
Equations for Planes; Distance Problems
Section 1-6:
Some n-dimensional Geometry
Section 1-7:
New Coordinate Systems
Page 75:
Miscellaneous Exercises
Page 75:
True/False Exercises
Chapter 2: Differentiation in Several VariablesSection 2-1:
Functions of Several Variables; Graphing Surfaces
Section 2-2:
Limits
Section 2-3:
The Derivative
Section 2-4:
Properties; Higher-order Partial Derivatives
Section 2-5:
The Chain Rule
Section 2-6:
Directional Derivatives and the Gradient
Section 2-7:
Newton's Method (optional)
Page 182:
True/False Exercises
Page 183:
Miscellaneous Exercises
Chapter 3: Vector-Valued FunctionsSection 3-1:
Parametrized Curves and Kepler's Laws
Section 3-2:
Arclength and Differential Geometry
Section 3-3:
Vector Fields: An Introduction
Section 3-4:
Gradient, Divergence, Curl, and the Del Operator
Page 237:
Miscellaneous Exercises
Page 237:
True/False Exercises
Chapter 4: Maxima and Minima in Several VariablesSection 4-1:
Differentials and Taylor's Theorem
Section 4-2:
Extrema of Functions
Section 4-3:
Lagrange Multipliers
Section 4-4:
Some Applications of Extrema
Page 305:
True/False Exercises
Page 306:
Miscellaneous Exercises
Chapter 5: Multiple IntegrationSection 5-1:
Introduction: Areas and Volumes
Section 5-2:
Double Integrals
Section 5-3:
Changing the Order of Integration
Section 5-4:
Triple Integrals
Section 5-5:
Change of Variables
Section 5-6:
Applications of Integrations
Section 5-7:
Numerical Approximations of Multiple Integrals (optional)
Page 401:
True/False Exercises
Page 403:
Miscellaneous Exercises
Section 6-1:
Scalar and Vector Line Integrals
Section 6-2:
Green's Theorem
Section 6-3:
Conservative Vector Fields
Page 450:
True/False Exercises
Page 451:
Miscellaneous Exercises
Chapter 7: Surface Integrals and Vector AnalysisSection 7-1:
Parametrized Surfaces
Section 7-2:
Surface Integrals
Section 7-3:
Stoke's and Gauss's Theorems
Section 7-4:
Further Vector Analysis; Maxwell's Equations
Page 522:
True/False Exercises
Page 523:
Miscellaneous Exercises
Chapter 8: Vector Analysis in Higher DimensionsSection 8-1:
An Introduction to Differential Forms
Section 8-2:
Manifolds and Integrals of k-forms
Section 8-3:
The Generalized Stoke's Theorem
Page 561:
True/False Exercises
Page 561:
Miscellaneous Exercises
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