Linear constant coefficient equations can describe several types of mathematical behaviors, including simple periodicity, which we often refer to as harmonic motion. Models of harmonic motion might be most familiar from the spring-mass problems you've seen in physics classes. But the same simple ideas are used to model things as complicated as biological macromolecules like proteins, ribosomes, and viruses.
By the end of this lesson, you should be able to:
- Identify linear equations.
- Determine if given solutions to a homogenous linear equation form a fundamental set.
- Construct a general solution from a fundamental set of solutions.
- Solve linear, homogeneous differential equations with constant coefficients via the characteristic equation.
- Construct, analyze, and interpret models of harmonic motion.
- Read Polking, Boggess and Arnold, Sections 4.1, 4.3, 4.4.
- To reinforce some concepts, read Stewart excerpt, pages 1 - 4.
- Watch pencasts (linked above).
- Check yourself before you wreck yourself.
- Do post-class problems.