Differentiation Rules: Rates of Change in the Natural and Social Sciences

Vocabulary

linear density, current, charge, Boyle's Law, isothermal compressibility, Law of Laminar Flow, average productivity

Objectives

• 1. Recognize derivatives in the context of mathematical models of natural phenomena.
• 2. Find the rate of change of a dependent quantity with respect to an independent quantity given a relationship between those quantities.
• 3. Interpret the meaning of the derivative in discrete and continuous contexts.

Lecture Outline

Examples from Physics

Particle motion in one dimension

Linear density

Electrical current

Examples from Chemistry

Reaction rates

Boyle's Law

An example from Biology

Poiseuille's Law

Laminar Blood Flow

An example from Economics

Average and Marginal Productivity