CPSC 303: Numerical Approximation and Discretization (2015W T2) assignments
| Assignment | |
|---|---|
| 0 | Speed of matrix multiplication |
| 1 | Numerical errors in forward and backward recursive integral computation; errors in CDF series |
| 2 | Polynomial interpolation with monomial and Lagrange bases |
| 3 | Piecewise polynomial interpolation (cubic splines, piecewise cubic Hermite polynomials); Bézier curves |
| 4 | Trigonometric polynomial interpolation with the discrete Fourier transform; magnitudes and phases of Fourier coefficients; lossy image compression with the discrete cosine transform |
| 5 | Numerical differentiation with finite differences; noisy numerical differentiation; automatic differentiation with Autograd (Python/NumPy) |
| 6 | Composite quadrature (trapezoidal, midpoint, Simpson, Gaussian); numerical integration with Chebfun |
| 7 | Monte Carlo approximation of pi; comparison with quadrature; multidimensional integration; quasi-Monte Carlo integration; rejection and importance sampling |
| 8 | Forward Euler, backward Euler, and implicit trapezoidal methods; stiff ODEs and stability; quadrature with ODE solvers; the Hodgkin-Huxley model of electrical activity in the squid giant axon |
| 9 | Capstone: Pollution spread simulation with the convection-diffusion PDE (finite differences for spatial derivatives; backward Euler discretization in time) and Weibull-distributed wind |
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