Conquer Multivariable Calculus

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Multivariable Calculus Topics

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1. Three Dimensions

1.1

3-D coordinate system

1.2

3-Dimensional vectors

1.3

1.4

1.5

3-Dimensional lines

1.6

3-Dimensional planes

1.7

Cylindrical coordinates

1.8

Spherical coordinates

2. Vector Functions

2.1

Calculus for vector functions

2.2

Tangent, normal, and binormal vectors

2.3

Arc length with vector functions

2.4

Curvature with vector functions

2.5

Tangential and normal components of acceleration

3. Partial Derivatives

3.1

Functions of several variables

3.2

Limits and continuity of multivariable functions

3.3

Partial derivatives

3.4

Higher order partial derivatives

3.5

Differentials of multivariable functions

3.6

Chain rule for multivariable functions

3.7

Directional derivatives

4. Partial Derivative Applications

4.1

Linear approximations and tangent planes

4.2

Gradient vectors

4.3

Local minima and maxima of multivariable functions

4.4

Absolute minimum and maximum of multivariable functions

4.5

Langrage multipliers

5. Multiple Integrals

5.1

Double integrals over a rectangular region

5.2

Double integrals over a general region

5.3

Double integrals in polar coordinates

5.4

Triple integrals

5.5

Triple integrals in cylindrical coordinates

5.6

Triple integrals in spherical coordinates

6. Multiple Integral Applications

6.1

Change in variables

6.2

Moment and center of mass

6.3

Surface area with double integrals

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