Vector Calculus Independent Study Path
Unit 6: Double and Triple Integrals
Single integrals, the integrals you learned all about in calculus,
find the area under the graph of a function of one variable.
Double integrals, the integrals you will learn about in this section,
find the volume under the graph of a function of two variables.
How do you calculate a double integral? You take two integrals
and call me in the morning. No, seriously, that's what you do.
And triple integrals? Well, they find the hyper-volume under the
graph of a function of three variables. I mean, duh.
In this unit, you will learn:
For more detailed instructions, see the Xdvi
or PDF pages.
- The definition of double and triple integrals in terms of a limit
of Riemann sums.
- How to calculate double and triple integrals as iterated (nested)
- How to change the order of an integration.
- How to change the variables of an integration. In particular,
you will learn how to do triple integrals in spherical and cylindrical
- How to apply double and triple integrals to calculate masses,
centers of mass, average values, and moments of inertia.
- Read and do some problems from
- Rogers Chapters 14 - 18,
- Marsden and Tromba chapters 5 and 6, or
- Simmons, chapter 20
- Take the Sample Test, Xdvi or PDF.
- Take a unit test.
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Last modified November 5, 1998