CS111 Topics

• Python libraries for numerical computation: numpy, scipy, matplotlib.
• Basic matrix/vector manipulation and arithmetic.
• Permutation matrices and permutation vectors.
• Systems of linear equations.
• Solving linear systems by LU factorization with pivoting.
• Solving symmetric positive definite linear systems by conjugate gradients.
• Least squares data fitting, QR factorization.
• Sparse matrices and graphs.
• Eigenvalues and eigenvectors.
• Matrix condition number.
• Floating-point arithmetic.
• Standard form of ordinary differential equations (ODEs).
• Forward and backward Euler and BS23 algorithms for ODEs.
• Basic elliptic partial differential equations (PDEs): Poisson / Laplacian / heat equation.
• Finite difference methods for PDEs: the 2D heat equation.