Lecture 1 (intro, floating-point numbers, errors) Lecture 2 (numerical differentiation, interpolation, integration) Lecture 3 (integration) Lecture 4 (Fourier transform, root-finding) Lecture 5 (initial-value problems for ODEs) Lecture 6 (Verlet algorithm, molecular dynamics) Lecture 7 (nonlinear dynamics) Lecture 8 (boundary-value problems for ODEs) Lecture 9 (boundary-value problems, intro to finite-element, intro to linear algebra) Lecture 10 (solving linear systems) Lecture 11 (iterative methods for linear systems, eigenproblems) |
Lecture 12 (eigenproblems) Lecture 13 (eigenproblems) Lecture 14 (singular-value decomposition) Lecture 15 (SVD, intro to PDEs) Lecture 16 (finite-difference for elliptic PDEs) Lecture 17 (finite-difference and boundary-element for elliptic PDEs) Lecture 18 (boundary-element for elliptic PDEs; long-range interactions - Ewald etc.) Lecture 19 (finite-volume for elliptic PDEs, parabolic PDEs, Schrodinger eq.) Lecture 20 (hyperbolic PDEs) Lecture 21 (hyperbolic PDEs, FDTD for Maxwell's eqs., conservation laws) Lecture 22 (advection-diffusion eq., finite-element for PDEs, optimization of functions) Lecture 23 (optimization, summary, outlook) |