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Lessons
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 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

About these Lessons

The primary content for these lessons is provided courtesy of Paul's Online Math Notes and Lamar University.

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