M15911: Numerical Methods: Solving Equations w/ Computers
Most problems cannot be computed exactly, and even those that can might be very expensive. Numerical methods try to find good enough approximations efficiently.
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Tentative Schedule:
1. The derivative, fixed point iteration, Newton’s method, Euler, Runge-Kutta, and multistep methods.
2. Quadrature a.k.a. numerical integration, finite difference methods and correctors.
3. Linear differential equations, matrix fundamentals, the QR algorithm, Newton-like methods, stiffness.
4. Finite element methods, various bases, Fourier/DCT transforms, Fourier analysis (faster solvers), Fourier analysis (stability).
5. Optimization: Binary and golden-section search, the simplex method, gradient descent, conjugate gradient descent, and Adam.
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Class website: https://programjames.github.io/hssp-spring-numerical-methods/
Class Style
Lecture
Prerequisites
At a minimum, you should know middle school math such as algebra and sines/cosines. If you wish to do homework (it's optional) you should know Python or MATLAB.
We will rederive anything more advanced, such as calculus or linear algebra, but some background in them will make it easier to follow.