/cpsc303

CPSC 303: Numerical Approximation and Discretization (2015W T2)

Primary LanguageMATLAB

cpsc303

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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