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Introducing the double integral

Defining the double integral

Iterated integrals and Fubini's theorem

Examples of integrals over rectangles

Integrals over general regions

Example: integral over a general region

Reversing the order of integration: Example 1

Reversing the order of integration: Example 2

Double integrals in polar coordinates

Polar coordinates: Examples 1 and 2

Polar coordinates: Example 3

Example: volume of a tetrahedron

Example: volume using polar coordinates

Introduction to triple integrals

Tetrahedron volume, as a triple integral

Changing order of integration in a triple integral

Volume problem leading to cylindrical coordinates

The cylindrical coordinate system

Cylindrical coordinates and volume of a cone

Introducing spherical coordinates

Integration in spherical coordinates

Volume of a spherical wedge

Volume of a conical cup

The spherical coordinate Jacobian

Transformations and change of variables

Change of variables example: parallelogram

Working with the inverse transformation (a shortcut!)

Another change of variables example

Description:

Explore a comprehensive series of video lectures on multiple integration, covering double and triple integrals, coordinate systems, and change of variables. Learn to define and evaluate double integrals, apply Fubini's theorem, and integrate over general regions. Master integration techniques in polar, cylindrical, and spherical coordinates. Dive into practical examples, including volume calculations for various geometric shapes. Understand the Jacobian and its role in coordinate transformations. Enhance your understanding of advanced calculus concepts through clear explanations and diverse problem-solving approaches.

APEX Calculus - Multiple Integration

Sean Fitzpatrick

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#Mathematics #Calculus #Multivariable Calculus #Double Integrals #Polar Coordinates #Triple Integrals