Overview of engineering mathematics and example weather model in Matlab.

Notes: faculty.washington.edu/sbrunton/me564/pdf/L01.pdf
Matlab code: faculty.washington.edu/sbrunton/me564/matlab/L01_weather.m

1. Overview of engineering mathematics
2. Review of calculus and first order linear ODEs
3. Taylor series and solutions to first and second order linear ODEs
4. Second order harmonic oscillator, characteristic equation, ode45 in Matlab
5. Higher-order ODEs, characteristic equation, matrix systems of first order ODEs
6. Matrix systems of first order equations using eigenvectors and eigenvalues
7. Eigenvalues, eigenvectors, and dynamical systems
8. 2x2 systems of ODEs (with eigenvalues and eigenvectors), phase portraits
9. Linearization of nonlinear ODEs, 2x2 systems, phase portraits
10. Examples of nonlinear systems: particle in a potential well
11. Degenerate systems of equations and non-normal energy growth
12. ODEs with external forcing (inhomogeneous ODEs)
13. ODEs with external forcing (inhomogeneous ODEs) and the convolution integral
14. Numerical differentiation using finite difference
15. Numerical differentiation and numerical integration
16. Numerical integration and numerical solutions to ODEs
17. Numerical solutions to ODEs (Forward and Backward Euler)
18. Runge-Kutta integration of ODEs and the Lorenz equation
19. Vectorized integration and the Lorenz equation
20. Chaos in ODEs (Lorenz and the double pendulum)
21. Linear algebra in 2D and 3D: inner product, norm of a vector, and cross product
22. Div, Grad, and Curl
23. Gauss's Divergence Theorem
24. Directional derivative, continuity equation, and examples of vector fields
25. Stokes' theorem and conservative vector fields
26. Potential flow and Laplace's equation
27. Potential flow, stream functions, and examples
28. ODE for particle trajectories in a time-varying vector field

This course by Prof. Steve Brunton will provide an in-depth overview of powerful mathematical techniques for the analysis of engineering systems. In addition to developing core analytical capabilities, students will gain proficiency with various computational approaches used to solve these problems. Applications will be emphasized, including fluid mechanics, elasticity and vibrations, weather and climate systems, epidemiology, space mission design, and applications in control.

In this course, we will develop many powerful analytic tools. Equally important is the ability to implement these tools on a computer. The instructor and TAs use Matlab, and all examples in class will be in Matlab.