Time: 
TuTh 1:102:25  Location:  535 Mudd 
Instructor:  Marc
Spiegelman (home page) 
Office Hours:  Tues/Thurs
4:005:00pm 211 Mudd (APAM) 
TAs:  Daisuke
Shiraki (principal TA), Yan
Yan Wenjia Jing (1/2 time) 
Office Hours: 
Daisuke: Mondays 45pm
Wenjia: Wednesdays 3:304:30 pm Yan Yan: Tuesdays 9:1010:50am All office hours in 287 Engineering Terrace 
Useful (?) Texts: 
Online
References/Resources:

Grading:  Homework 60%, Midterm 20% Final 20% All Homeworks due by 5pm on the due date in the E4300 Homework box in 200 Mudd (APAM). Homeworks can also be turned in during class. 
Matlab Resources  


Prerequisites: Calculus,
Vector Calculus, Linear Algebra and ODE's will
be used extensively. Students must also have some programming
experience to the level of COMS 1000x classes. All programming
exercises in this class will be in MATLAB and
some experience with this language will be useful.
However, I will teach most things that are necessary and try to
provide sufficient examples.


Dates  Reading/Notes  Subject  Problem Sets  Matlab Examples/Demos 
22 Jan 
Introduction and Motivation:Modeling, Methods and Matlab the fundamental tools and problems in scientific computation 

2429 Jan 

Sources of Error and Life in Floating point land:model Error, Truncation Error, Roundoff ErrorA short guide to IEEE floating point, The Nitty Gritty guide to floating point systems, An IEEE floating point calculator 
Homework #1 Due 5 Feb 

31 Jan 6 Feb 
Root finding and optimization for f(x)Fixed Point iterationBrackets and existence Basic Algorithms: Bisection, Newton, Secant, inverse interpolation Comparison and convergence rates Combined Algorithms  Brent's method and fzero Optimization of 1D functions: Basic algoriththms: golden section, Newton, parabolic interpolation 
Due 15 Feb  
714 Feb  Interpolation and
Approximation Polynomial Interpolation, Lagrange and Monomial Basis Pitfalls of large order: Chebyshev points Heath's Interpolation demos Piecewise Polynomial Interpolation: C0, C1, C2 (pchip and spline) Matlab Interp routines Data Approximation by Linear Least Squares 
Due 26 Feb 


1926
Feb 

Numerical Quadrature and DifferentiationMotivation: solution of IVPs and BVPsNewton Cotes and error estimates: Midpoint, Trapezoidal, Simpsons Arbitrary order and method of undetermined coefficients Gauss Quadrature Extended Newton Cotes Adaptive Quadrature: quad routines 
Homework #4 Due Wednesday 5 March 
Moler's NCM Quadrature Demos (quadtx, quadgui) 
28 Feb 11 March 
Solution of ODE's #1: Initial Value ProblemsInterlude:Numerical Differentiation: Finite Difference to Spectral methods ODE IVPs Motivation Linear systems and expm Application of Quadrature: Single step schemes: Euler, Midpoint, RK4 and errors Error Control and Adaptive Stepping Embedded RK schemes: ode45 (matlab ode suite) Systems of ODE's Stiff systems: Example and symptoms Implicit methods: ODE23s 
Homework #5 Due Thursday 13 March 

11 March 
Solving Nonlinear systems of EquationsMotivation:Existence and Uniqueness (Hah!) nDimensional Taylor's theorem and Newton's method Packages and Libraries (fsolve, PETSc) nD nonlinear optimization Nonlinear leastsquares: GaussNewton method 


1721 March  Spring Break!  
27 March 
Midterm 1:102:25pm 
Study Guide updated 12 March 2008 

13 March3 April 
Numerical Linear Algebra #1Motivation: Ax=b is everywhereHooray for backslash! Existence, Uniqueness and Condition #: Vector and Matrix Norms Direct Methods for NLA: Gaussian Elimination and the LU: Partial Pivoting and roundoff error Special Matrices: Symmetric, Tridiagonal, Sparse matrices Least Squares and QR Orthogonalization by Householder Transformations (Givens?) 
Homework #6 due April 10 


810 April 

Numerical Linear Algebra #2Introduction to Iterative methods for sparse matricesSplitting Methods and the Iteration Matrix (Jacobi, GaussSeidel) Eigenvalues of the iteration matrix: spectral radius, power method, inverse power method with shifts Other methods: Krylov Methods (CG, GMRES) 


1529 April 
Solution of ODE's #2: Boundary Value Problems and intro to PDE'sMotivation: Numerical PDE's Discrete vs Continuous Approximations2 point BVPs: Shooting methods, Finite Difference, Collocation and Galerkin FEM Adding time= PDE's Method of lines, Explicit FD, Newton Stability and beyond 
Homework #7 due May 2 Matlab Routine for Newton's method newton.m 

6 May 
Review Session Study Guide v1.2 

13 May 
Final Exam Tuesday
13 May, 1:104:00
PM, 535 Mudd 