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:
- 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)
integrals.
- 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
coordinates.
- How to apply double and triple integrals to calculate masses,
centers of mass, average values, and moments of inertia.
For more detailed instructions, see the Xdvi
or PDF pages.
Suggested Procedure
- 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