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Master Higher Order Partial Derivatives: Advanced Calculus

Calculus 3: Master Advanced Mathematical Concepts

Three Dimensions

3-D coordinate system

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3-Dimensional vectors

Dot product

Cross product

3-Dimensional lines

3-Dimensional planes

Cylindrical coordinates

Spherical coordinates 

Spherical-coordinates

Vector Functions

Calculus for vector functions

Tangent, normal, and binormal vectors

Arc length with vector functions

Curvature with vector functions

Tangential and normal components of acceleration

Partial Derivatives

Functions of several variables

Limits and continuity of multivariable functions

Partial derivatives

Higher order partial derivatives

Differentials of multivariable functions 

Chain rule for multivariable functions

Directional derivatives 

Partial Derivative Applications

Linear approximations and tangent planes

Absolute minimum and maximum of multivariable functions 

Gradient vectors

Local minima and maxima of multivariable functions

Langrage multipliers

Lagrange multipliers

Multiple Integrals

Double integrals over a rectangular region

Double integrals over a general region

Double integrals in polar coordinates

Triple integrals

Triple integrals in cylindrical coordinates

Triple integrals in spherical coordinates

Multiple Integral Applications

Change in variables

Moment and center of mass

Surface area with double integrals

Parent Assignments

Challenge Zone

Foundation Review

Calculus 3

sample

math

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Intro.

Ex 4.

Fourth order partial derivative of a three-variable radical function

Ex 3. 

Fifth order partial derivative of e^(st) + sin(s²)

Ex 2.

Finding f_xx and f_xy for an exponential and trig function

Ex 5.

Verifying Clairaut's Theorem for u = ln(x² - y)

Ex 1. 

Finding all four second order partial derivatives of a multivariable function

Ex 6.

Verifying Clairaut's Theorem for a complex function with trig and exponential terms

Intro to second-order and higher order partial derivatives

Clairaut's theorem and verifying equality of mixed partial derivatives

Computing a third-order mixed partial derivative example

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