Lecture 18: Change of variables
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Lesson Description:
Learn about the change of variables method for difficult integral calculations.
Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (Accessed March 21, 2009). License: Creative Commons Attribution-Noncommercial-Share Alike.
Additional Resources:
- Problem Set - A problem set with some problems from this lecture.
- Transcript of Lesson - Written transcript from this lesson.
- Lecture Notes - Lecture Notes from this lesson.
Questions answered by this video:
- How do you change variables in double integrals?
- How do you use u and v substitution with a double integral?
- How do you find the area scaling factor when changing from dxdy to dudv?
- What is the Jacobian of a change of variables and how do you find it?
- How do you find the double integral of x^2y dxdy from 0 to 1 for x and y using a change of variables?
- How do you find the new bounds when you change variables in a double integral?
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Staff Review
Change of variables in double integrals is discussed. This can really simplify a double integral, but it has to be done carefully. This process is described very well with some great example problems. The Jacobian is also discussed and examples are shown. The strength of this lecture is its useful example problems that are computed. -
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