> HW2 Introduction to Computer Programming

## 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 non-linear 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 high-order 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
10:00-11:50, Room 202