### CME 102 ― Ordinary Differential Equations for Engineers

My twin brother

Afshine and

I created this set of cheatsheets when I was a TA for Stanford's CME 102 class in Spring 2018. They can (hopefully!) be useful to all future students taking this course as well as to anyone else interested in learning the fundamentals of Ordinary Differential Equations.

**Cheatsheet**

- • Direction field method, separation of variables, equilibrium
- • Linear first-order technique, system of linear ODEs
- • Existence and uniqueness, initial value numerical methods

- • General methods of resolution, standard form, linear dependency
- • Linear homogeneous: variable coefficients, constant coefficients
- • Linear inhomogeneous: variable coefficients, constant coefficients

- • Gravitational, spring, friction forces, Newton's second law
- • Spring-mass system: free and forced oscillation
- • Boundary value problems: direct and shooting methods

**Mathematical tools**

**Matlab tips**

- • Installation and first steps
- • Built-in functions, vectors, matrices, operators
- • Functions, plots and good practices