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Table of Contents
Preface
Chapter 1: Vectors, Lines and Planes
Chapter 1 - Overview
Section 1.1
Cartesian Coordinates and Vectors
Section 1.2
Vector Arithmetic
Section 1.3
Dot Product
Section 1.4
Cross Product
Section 1.5
Applications of Vector Products
Section 1.6
Lines
Section 1.7
Planes
Chapter 2: Space Curves
Chapter 2 - Overview
Section 2.1
Position-Vector Representation
Section 2.2
Arc Length as Parameter
Section 2.3
Tangent Vectors
Section 2.4
Curvature
Section 2.5
Principal Normal
Section 2.6
Binormal and Torsion
Section 2.7
Frenet-Serret Formalism
Section 2.8
Resolution of R" along T and N
Section 2.9
Applications to Dynamics
Chapter 3: Functions of Several Variables
Chapter 3 - Overview
Section 3.1
Functions and Their Graphs
Section 3.2
Limits and Continuity
Section 3.3
Quadric Surfaces
Chapter 4: Partial Differentiation
Chapter 4 - Overview
Section 4.1
First-Order Partial Derivatives
Section 4.2
Higher-Order Partial Derivatives
Section 4.3
Chain Rule
Section 4.4
Directional Derivative
Section 4.5
Gradient Vector
Section 4.6
Surface Normal and Tangent Plane
Section 4.7
Approximations
Section 4.8
Unconstrained Optimization
Section 4.9
Constrained Optimization
Section 4.10
Optimization on Closed Domains
Section 4.11
Differentiability
Chapter 5: Double Integration
Chapter 5 - Overview
Section 5.1
The Double Integral
Section 5.2
Iterated Double Integrals
Section 5.3
Regions with Curved Boundaries
Section 5.4
Changing the Order of Iteration
Section 5.5
Numeric Evaluation of Iterated Integrals
Section 5.6
Changing Variables in a Double Integral
Section 5.7
Double Integration in Polar Coordinates
Chapter 6: Applications of Double Integration
Chapter 6 - Overview
Section 6.1
Area
Section 6.2
Volume
Section 6.3
Surface Area
Section 6.4
Average Value
Section 6.5
First Moments
Section 6.6
Second Moments
Chapter 7: Triple Integration
Chapter 7 - Overview
Section 7.1
The Triple Integral
Section 7.2
Iterated Triple Integrals
Section 7.3
Section 7.4
Integration in Cylindrical Coordinates
Section 7.5
Spherical Coordinates
Section 7.6
Integration in Spherical Coordinates
Chapter 8: Applications of Triple Integration
Chapter 8 - Overview
Section 8.1
Section 8.2
Section 8.3
Section 8.4
Moments of Inertia (Second Moments)
Section 8.5
Changing Variables in a Triple Integral
Chapter 9: Vector Calculus
Chapter 9 - Overview
Section 9.1
Student VectorCalculus Package - Overview
Section 9.2
Vector Objects
Section 9.3
Differential Operators
Section 9.4
Differential Identities
Section 9.5
Line Integrals
Section 9.6
Surface Integrals
Section 9.7
Conservative and Solenoidal Fields
Section 9.8
Divergence Theorem
Section 9.9
Stokes' Theorem
Section 9.10
Green's Theorem
Appendix: All about Maple
Appendix - Overview
Section A-1
The Working Environment
Section A-2
Arithmetic Calculations
Section A-3
Referencing
Section A-4
Algebraic Expressions and Operations
Section A-5
Evaluation
Section A-6
Coordinate Geometry
Section A-7
Trigonometry
Section A-8
Functions
Section A-9
Graphing
Section A-10
Solving Equations
Section A-11
Factoring and Collecting Terms
Section A-12
Additional Resources
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