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Multivariable Calculus topics

1Three Dimensions

1.13-D coordinate system
1.23-Dimensional vectors
1.3Dot product
1.4Cross product
1.53-Dimensional lines
1.63-Dimensional planes
1.7Cylindrical coordinates
1.8Spherical coordinates

2Vector Functions

2.1Calculus for vector functions
2.2Tangent, normal, and binormal vectors
2.3Arc length with vector functions
2.4Curvature with vector functions
2.5Tangential and normal components of acceleration

3Partial Derivatives

3.1Functions of several variables
3.2Limits and continuity of multivariable functions
3.3Partial derivatives
3.4Higher order partial derivatives
3.5Differentials of multivariable functions
3.6Chain rule for multivariable functions
3.7Directional derivatives

4Partial Derivative Applications

4.1Linear approximations and tangent planes
4.2Gradient vectors
4.3Local minima and maxima of multivariable functions
4.4Absolute minimum and maximum of multivariable functions
4.5Langrage multipliers

5Multiple Integrals

5.1Double integrals over a rectangular region
5.2Double integrals over a general region
5.3Double integrals in polar coordinates
5.4Triple integrals
5.5Triple integrals in cylindrical coordinates
5.6Triple integrals in spherical coordinates

6Multiple Integral Applications

6.1Change in variables
6.2Moment and center of mass
6.3Surface area with double integrals
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