Harvard AM205: Course schedule

Home Material Group Activities Office Hours Homework Archive

Home Material Group Activities Office Hours Homework Archive

Unit 0: Overview of Scientific Computing

Lecture	Date	Topics & videos	Handouts
–		0. Course logistics	Logistics Unit 0 slides Condition number notes
1	Sep 1	1. Introduction 2. Sources of error 3. Numerical sensitivity 4. Finite-precision arithmetic	Logistics Unit 0 slides Condition number notes

Unit 1: Data fitting

Lecture	Date	Topics & videos	Handouts
2	Sep 8	1. Data fitting introduction 2. Interpolating discrete data	Unit 1 slides Spline notes Spline ball movie
3	Sep 13	3. Function approximation 4. Lebesgue constant
4	Sep 15	5. Piecewise polynomial interpolation 6. Linear least squares
5	Sep 20	7. Underdetermined least squares 8. Nonlinear least squares

Unit 2: Numerical Linear Algebra

Lecture	Date	Topics & videos	Handouts
6	Sep 22	1. Introduction 2. Norms 3. The residual	Unit 2 slides Superellipsoids PCA example
7	Sep 27	4. LU factorization 5. LU pivoting and Cholesky factorization 6. Timing algorithms
8	Sep 29	7. QR decomposition 8. Gram–Schmidt orthogonalization 9. Householder triangularization 10. Givens rotations
9	Oct 4	11. Singular value decomposition 12. Low-rank approximation 13. PCA example

Unit 3: Numerical Calculus

Lecture	Date	Topics & videos	Handouts
–		0. Final project organization	Final project slides Slides (part 1) Slides (part 2) Gaussian quadrature notes FD stencil notes Additional derivations
10	Oct 6	1. Introduction 2. Numerical integration 3. Composite quadrature rules 4. Gauss quadrature
	Oct 11	University holiday
11	Oct 13	5. Finite-difference approximations 6. Differentiation matrices 7. ODE initial value problems 8. One-step integration methods
12	Oct 18	9. ODE convergence 10. ODE stability 11. Runge–Kutta methods
13	Oct 20	12. ODE error estimation 13. Stiff systems 14. Multistep methods
14	Oct 25	15. ODE boundary value problems 16. Partial differential equations 17. Advection equation & characteristics
15	Oct 27	18. CFL condition & upwinding 19. Accuracy and stability for FD schemes 20. Semi-discretizations & the wave equation
16	Nov 1	21. Parabolic PDEs: the heat equation 22. Elliptic PDEs: the Poisson equation

Unit 4: Root-finding and Optimization

Lecture	Date	Topics & videos	Handouts
17	Nov 3	1. Introduction 2. Root finding: fixed point iteration 3. Newton and secant methods 4. Multivariate root-finding	Slides Lagrange multiplier notes
18	Nov 8	5. Conditions for global minimum 6. Optimality conditions and the Hessian 7. Equality-constrained optimization
19	Nov 10	8. Steepest descent and Newton method 9. Quasi-Newton methods 10. Sequential quadratic programming
20	Nov 15	11. Penalty methods and linear programming 12. PDE-constrained optimization

Unit 5: Eigenvalue Problems and Iterative Methods

Lecture	Date	Topics & videos	Handouts
21	Nov 17	1. Introduction 2. Eigenvalue definitions 3. Gershgorin theorem & eigenvalue sensitivity 4. Power method & inverse iteration 5. Rayleigh quotient	Slides Iterative method notes
	Nov 22	No lecture
	Nov 24	No lecture
22	Nov 29	6. QR algorithm 7. Iterative methods for linear systems
23	Dec 1	8. The multigrid method 9. Krylov methods; Arnoldi iteration 10. Lanczos iteration
–	–	11. Conjugate gradient method