Class Progress
This page tracks the class, giving a description of the lecture, the associated reading, and the homework assigned that day.
Date  Topics Covered  Reading  Demos  Homework 

Tues, Jan 29  Course Overview, intro. to matlab  Chap. 1, skim Chap. 2, read to learn Matlab 
whiledemo.m  HW1 
Thurs, Jan 31  Solving nonlinear eq., Bisection Alg., Newton's method  Chap. 4  bisection.m f.m 

Tues, Feb 5  Review of Taylor series. Linear, Superlinear, and Quadratic Convergence. Convergence Rate of Newton's method.  Chap. 4  newtonsetup.m newtonstep.m 
HW2 
Thurs, Feb 7  Secant method, Derivation of Error estimate and Conv. Rate  Chap. 4 theorem review sheet 
newtonsteploop.m  
Tues, Feb 12  Fixed Pt. Iteration, Existence and Uniqueness of Fixed Pt., Conv. rate, interpretation of Newton's method as a fixed pt. iteration  Chap. 4 (plus more)  fixedpoint.m  HW3 
Thurs, Feb 14  Floating pt. number representation; subnormal numbers, Inf, Nan  Chap. 5  
Tues, Feb 19  Floating pt. arithmetic, Sources of error Return HW 2 
Chap. 5, 6  
Thurs, Feb 21  Sources of Error (cont), conditioning and stability  Chap. 6  HW4  
Tues, Feb 26  Optimal h for first order finite diff. Linear Algebra Review 
Chap. 7  
Thurs, Feb 28  Gaussian elimination, op. counts, LU factorization  Chap. 7  HW5  
Tues, March 5  finish LU factorization; elementary matrices, pivoting  Chap. 7  
Thurs, March 7  vector and matrix norms, conditioning of linear systems 
Chap. 7.4  
Tues, March 12  cond. number examples, sensitivity to changes in rhs b and matrix A, computing det using LU factors, start of Cholesky decomp.  Chap. 7.2.4, 7.3  HW6  
Thurs, March 14  least squares problems, normal equations; QR decomposition.  Chap. 7.6  
Tues, March 19  Spring Break  
Thurs, March 21  Spring Break  
Tues, March 26  Least Squares and QR decomp., Householder reflections  I am preparing notes for this material ...  
Thurs, March 28  Householder examples, SVD  ...check back for posting  QRdemo.m svdExperiments 
HW7 
Tues, April 2  Midterm  
Thurs, April 4  Return and go over Midterm  
Tues, April 9  Interpolation: existence,uniqueness,vanderMonde matrix, Lagrange form  Chap. 8  HW8 nonoise.dat noise.dat  
Thurs, April 11  highorder poly demo, Newton Form, divided differences and their recursive def.  polyEx.m  
Tues, April 16  divided difference table, nth divided diff/nth deriv, error in poly interp.  
Thurs, April 18  error in poly interp., error polynomial, upper error bounds, Chebyshev points  poly2.m poly3.m 
HW9  
Tues, April 23  piecewise poly interp., cubic splines. Derivative approximations.  Chap. 9  
Thurs, April 25  Method of Undetermined Coefficients, Richard Extrapolation  richEx.m  
Tues, April 30  Numerical Quadrature: Trap. Rule, Midpoint Rule, Simpson's Rule  Chap. 10  
Thurs, May 2  Error in quadrature formulas, Composite rules. (Skip orthogonal polynomials).  
Tues, May 7  Trap Rule, Error in Trap. Rule, Corrected Trap. Rule, Trap. for periodic functions, Gauss quadrature  trapEx.m  
Thurs, May 9  Last Class  Newton's method for multidimensional problems; Euler's method and trapezoid rule for ODEs. (This material will not be on the final exam)  Practice HW 10  
Thurs, May 16  Final Exam 10:0011:50, Room 202 