cs/math 257
Numerical
Methods
Fall 2007
The authors of the textbook have many materials available on their website. Please also take a look at the interactive JAVA applets on numerical analysis ( Interactive Educational Modules in Scientific Computing) which allow you to explore many of the important concepts of this class.
Lecture notes below are only available from uiuc.edu domain. Downloading from any computer on campus should work. For downloading from off-campus, use VPN.
The section numbers in parenthesis are only an approximate indication of what was covered in lecture, since the lectures do not follow the book strictly. For exams you will be expected to know the material covered in the lectures, the readings assigned from the book, and material covered in homeworks.
Combined class lecture notes ( 2 slides per page, 8 slides per page)
LectureDateTopic/SectionMaterial
1August 24, 2007 Introduction, Unexpected results, Numerical representation (2.1) [PDF]
2August 29, 2007 Floating point (2.2) [PDF]
3August 31, 2007 Floating point (2.2) [PDF]
4September 05, 2007 Floating point (2.2) [PDF]
5September 07, 2007 Floating point (2.2), Bisection method (3.1) [PDF]
6September 12, 2007 Bisection method (3.1), Taylor series (1.2) [PDF]
7September 14, 2007 Bisection method (3.1), Newton's method (3.2) [PDF]
8September 19, 2007 Fixed point iterations, Newton's method (3.2) [PDF]
9September 21, 2007 Polynomial interpolation [PDF]
10September 26, 2007 Polynomial interpolation (4.1), Interpolation error (4.2) [PDF]
11September 28, 2007 Polynomial interpolation (4.1), Interpolation error (4.2) [PDF]
12October 3, 2007 Exam 1
13October 5, 2007 Exam 1 solutions
14October 10, 2007 Barycentric Lagrange interpolation, Interpolation summary [PDF]
15October 12, 2007 Numerical differentiation (4.3), Function value errors vs. truncation errors [PDF]
16October 17, 2007 Function value error vs. truncation error, Richardson extrapolation (4.3) [PDF]
17October 19, 2007 Richardson extrapolation (4.3), Trapezoid rule (5.2), Mean Value theorems (1.2 and 5.2) [PDF]
18October 24, 2007 Trapezoid rule (5.2), Newton-Cotes error, Method of undetermined coefficients (6.2) [PDF]
19October 26, 2007 Newton-Cotes rules (6.1), Method of undetermined coefficients (6.2), Midpoint rule [PDF]
20October 31, 2007 Composite rules (6.1), Improper integrals [PDF]
21November 2, 2007 Gaussian quadrature (6.2), Orthogonal polynomials : definition and use [PDF]
22November 7, 2007 Orthogonal polynomials : properties [PDF]
23November 9, 2007 Exam 2
24November 14, 2007 Orthogonal polynomials : examples, existence and three term recurrence, Exam 2 solutions [PDF]
25November 16, 2007 Introudction to systems of linear equations [PDF]
26November 28, 2007 Triangular systems, Gaussian elimination [PDF]
27November 30, 2007 Gaussian elimination, Pivoting [PDF]
28December 5, 2007 Vector and matrix norms, Condition number, Sensitivity analysis for Ax=b [PDF]
29December 7, 2007 Sensitivity analysis for Ax=b, Gaussian elimination and LU decomposition [PDF]
--Monday December 10, 2007, 7-10pm Final Exam
TEST