Part 1: 3-Dimensional Space

1-1 The 3-D Coordinate System
1-2 Equations of Lines
1-3 Equations of Planes
1-4 Quadric Surfaces
1-5 Functions of Several Variables
1-6 Vector Functions
1-7  Calculus with Vector Functions
1-8 Tangent, Normal and Binormal Vectors
1-9 Arc Length with Vector Functions
1-10 Velocity and Acceleration
1-11 Curvature
1-12 Cylindrical Coordinates
1-13 Spherical Coordinates

Part 2: Partial Derivatives

2-1 Limits
2-2 Parital Derivatives
2-3 Interpretations of Partial Derivatives
2-4 Higher Order Partial Derivatives
2-5 Differentials
2-6 Chain Rule
2-7  Directional Derivatives

Part 3: Applications of Partial Derivatives

3-1 Tangent Planes and Linear Approximations
3-2 Gradient Vector, Tangent Planes and Normal Lingfgfes
3-3 Relative Minimums and Maximums
3-4 Absolute Minimums and Maximums
3-5 Lagrange Multipliers

Part 4: Multiple Integrals

4-1 Double Integrals
4-2 Iterated Integrals
4-3 Double Integrals over General Regions
4-4 Double Integrals in Polar Coordinates
4-5 Triple Integrals
4-6 Triple Integrals in Cylindrical Coordinates
4-7 Triple Integrals in Spherical Coordinates
4-8 Change of Variables
4-9 Surface Area
4-10 Area and Volume Revisited

Part 5: Line Integrals

5-1 Vector Fields
5-2 Line Integrals - Part I
5-3 Line Integrals - Part II
5-4 Line Integrals of Vector Fields
5-5 Fundamental Theorem for Line Integrals
5-6 Conservative Vector Fields
5-7 Green`s Theorem
5-8 Curl and Divergence

Part 6: Surface Integrals

6-1 Parametric Surfaces
6-2 Surface Integrals
6-3 Surface Integrals of Vector Fields
6-4 Stokes' Theorem
6-5 Divergence Theorem

David L. Heiserman, Editor

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All Rights Reserved

Revised: June 06, 2015