Section Summary: 3.4

1. Definitions

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

2. Theorems

   There are no new theorems presented here.

3. Properties/Tricks/Hints/Etc.

   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

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