Lecture 2 (Sep 6)

Introduction to Mathematical Modeling

4 steps in doing modeling:
1. formulation of a problem: approximations and assumptions to develop, simplify and understanding the mathematical model;
2. solve the equation(s): analytically (usually with some simplification) and numerically;
3. interpretation of the mathematical results in the context of the physical problem;
4. prediction: see the limitation(s) of the mathematical model/theory.

Simple pendulum: derivation of the nonlinear ODE. small angle approximation. period for both the linear and nonlinear pendulum.