Section Summary: 3.4

1. Definitions

   Make a list of all definitions in the section (a few words each is fine). Summarize any lengthy definitions introduced in this section in your own words.

   The definitions here are not general, but specific to the various sciences (e.g. linear density, current).

2. Theorems

   Make a list of all theorems (lemmas, corollaries) in the section (a few words each is fine). Summarize each one introduced in this section in your own words.

   There are no new theorems presented here.

3. Properties/Tricks/Hints/Etc.

   Make a note of any especially useful properties, tricks, hints, or other materials.

   The Examples:

   1. Physics: position, velocity, distance traveled, points at which a particle is at rest.
   2. Physics: inhomogeneous mass distribution in a rod, and linear density
   3. Physics: current - time rate of change of charge.
   4. Chemistry: rates of reactions, concentrations
   5. Thermodynamics: compressibility
   6. Biology: rate of growth of a population
   7. Biology: blood flow in a blood vessel
   8. Economics: cost function, marginal cost

4. Summary

   Summarize the section in two or three sentences.

   ``Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them.'' Joseph Fourier (1768-1830)

   ``A single abstract mathematical concept (such as the derivative can have different interpretations in each of the sciences.'' (p. 167)

   In this section we examine 8 examples of the use of the derivative in the sciences. This is no doubt intended to impress the student with the breadth of application of this fundamental idea - and it should!

Problems:

Problems pp. 167-170, #9, 14, 21, 26; In groups: 2, 3, 4, 5; 18

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