Lecture 10, Wednesday, 9/17/08: Section 12.3: Partial derivatives

[Section 12.2 (limits and continuity) will be deferred till the end of the semester.]

Topics

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Section 12.3: This section is pretty tame mathematically (it's the easiest section in Chapter 12), but it has a wealth of real-world examples and applications ranging from meteorology (heat index) to thermodynamics (various gas laws), economics (production models) and sports (flight of a baseball). Some of these appear as Examples in the body of the section, and many more appear in the exercises. (In fact, most of the latter half of the exercises are such applications.) The homework assignment below includes some of these applications (I picked those that are particularly instructive and computationally not too tedious). Others will be discussed in the lecture and/or discussions.

You do not need to know the background for any of these applications or the terminology involved. However, you should be able to perform the mathematical analysis if you are given the underlying equation. The analysis typically consists of computing appropriate partial derivatives and interpreting these in the context of the application. For example, given an equation relating the pressure, volume, and temperature of a gas, a problem might ask what effect on the volume a change in the temperature has if the pressure remains constant.

Homework

Section 12.3: 3, 5, 9, 17, 19, 25, 51.
Solutions.

Notes

Differentiation techniques: Beginning with this section, and through the remainder of Chapter 12, you will have to compute lots of ordinary (one variable) derivatives. Some of these computations are moderately difficult, so you will need to know the standard differentiation rules and be proficient in using them. If you are a bit rusty on this, brush up on your own.

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Last modified Mon 22 Sep 2008 06:30:01 PM CDT