
Lecture Description
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
Course Index
- Overview of engineering mathematics
- Review of calculus and first order linear ODEs
- Taylor series and solutions to first and second order linear ODEs
- Second order harmonic oscillator, characteristic equation, ode45 in Matlab
- Higher-order ODEs, characteristic equation, matrix systems of first order ODEs
- Matrix systems of first order equations using eigenvectors and eigenvalues
- Eigenvalues, eigenvectors, and dynamical systems
- 2x2 systems of ODEs (with eigenvalues and eigenvectors), phase portraits
- Linearization of nonlinear ODEs, 2x2 systems, phase portraits
- Examples of nonlinear systems: particle in a potential well
- Degenerate systems of equations and non-normal energy growth
- ODEs with external forcing (inhomogeneous ODEs)
- ODEs with external forcing (inhomogeneous ODEs) and the convolution integral
- Numerical differentiation using finite difference
- Numerical differentiation and numerical integration
- Numerical integration and numerical solutions to ODEs
- Numerical solutions to ODEs (Forward and Backward Euler)
- Runge-Kutta integration of ODEs and the Lorenz equation
- Vectorized integration and the Lorenz equation
- Chaos in ODEs (Lorenz and the double pendulum)
- Linear algebra in 2D and 3D: inner product, norm of a vector, and cross product
- Div, Grad, and Curl
- Gauss's Divergence Theorem
- Directional derivative, continuity equation, and examples of vector fields
- Stokes' theorem and conservative vector fields
- Potential flow and Laplace's equation
- Potential flow, stream functions, and examples
- ODE for particle trajectories in a time-varying vector field
Course Description
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.