Course Notes:
A First Course on Numerical Methods by Uri M. Ascher and Chen Greif. These notes are provided for the private use of students enrolled in CPSC 303 at UBC in 20062007, and are not to be redistributed.
Additional Handouts:
Date  Topic 

Omitted 
Collaboration Policy:
You may collaborate with other students in the class on homework questions prior to writing up the version that you will submit. This collaboration may include pseudocode solutions to programming components. Once you begin writing the version that you will submit, you may no longer collaborate on that question, either by discussing the solution with other students, showing your solution to other students, or looking at the solutions written by other students. Some additional prohibitions:
You may seek help from the course instructor or TA at any time while preparing your homework solutions. You may not receive help from any other person.
If you feel that you have broken this collaboration policy, you may cite in your homework solution the name of the person from whom you received help, and your grade will be suitably adjusted to take this collaboration into account. If you break this collaboration policy and fail to cite your collaborator, you will be charged with plagarism as outlined in the university calendar. If you have any questions, please contact the instructor.
More information is available from (among other sources):
Homework Submission Policy:
Homeworks:
#  Topic  Assigned  Due Date  Max Late Days  Assignment  Other Assignment Files  Solution  Other Solution Files 

Omitted 
Intended Audience: Undergraduates in
Prerequisites:
Instructor: Ian Mitchell

TA: Jelena Sirovljevic

TA: Tin Yin (Philip) Lam

Course Communication:
Lectures: 11:00  12:00, Monday / Wednesday / Friday, Dempster 110
Grades: After the adjustment to take account of the lack of pop quizzes, your final grade will be based on a combination of:
Textbooks:
Other References:
#  Date  Topic  Links  Required Readings  Optional Readings 

1  Jan 8  Course Syllabus and administration. Collaboration guidelines. Introduction to Scientific Computing.  Scientific Computing overview slides. Matlab code for the Lorenz model: butterfly.m.  None.  H Preface; AG Preface; BF Preface 
2  Jan 10  Sources (Types) of Error. Problem sensitivity.  Nick Trefethen's essay on the definition of numerical analysis (pdf format), or get the original (ps format).  H 1.11.2; AG 1.1  H 1.41.5 
3  Jan 12  Algorithm Stability. Measures of Error: Absolute & Relative. Methods of Analyzing Error: Forward and Backward.  None.  H 1.2; AG 1.2  AG 1.3; BF 1.3 
4  Jan 15  Floating Point: Properties & Arithmetic.  An interview William Kahan, "father" of IEEE floating point. Kahan's lecture notes on IEEE 754  H 1.3; AG 2  BF 1.2 
5  Jan 17  Sources (Types) of Error during Computation: Truncation and Rounding. Interpolation: Background, Problem Formulation  None.  H 7.07.2; AG 10.0  BF 3.0 
6  Jan 19  Monomial Basis.  An example of polynomial interpolation in Matlab: interpolateSine.m  H 7.3.1; AG 10.1  None 
7  Jan 22  Lagrange Basis. Newton Basis.  None.  H 7.3.27.3.3; AG 10.210.3  BF 3.13.2 
8  Jan 24  Divided Differences.  None.  AG 10.3  AG 10.7; BF 3.2 
9  Jan 26  Osculating Interpolation.  None.  AG 10.5  BF 3.3 
10  Jan 29  Interpolation Error.  interpolateRunge.m and the handout with Interpolation Error examples.  H 7.3.5; AG 10.4  None. 
11  Jan 31  Piecewise Polynomial Interpolation.  None.  H 7.4.1; AG 11.011.1  BF 3.4 
12  Feb 2  Cubic Splines. Piecewise Hermite.  Piecewise Cubic example and the code piecewiseCubic.m  H 7.4.2; AG 11.2  H 7.57.6; AG 11.7; BF 3.4 
13  Feb 5  Piecewise Polynomial Interpolation wrapup. Parametetric Interpolation Curves.  None.  AG 11.4  H 7.57.6; AG 11.7; BF 3.53.6 
14  Feb 7  Best Approximation: Problem Formulation. Discrete Least Squares Data Fitting.  bestFitNormChoice.m computes the best linear fit under various norms for the data from class. Results  AG 12.012.1; H 3.1  H 3.2; BF 8.1 
Feb 9  Midterm 1.  
15  Feb 12  More Discrete Least Squares Data Fitting.  Discrete Least Squares example and the code lsExample.m  H 3.4.1  H 3.3 (or even H 3) 
16  Feb 14  Continuous Least Squares Approximation.  Continuous Least Squares example and the code lsContinuous.m  AG 12.2; H 7.3.5  BF 8.2 
17  Feb 16  Orthogonal Polynomials.  None.  AG 12.3; H 7.3.4  AG 12.4; BF 8.2 
Feb 1923  Midterm Break.  
18  Feb 26  GramSchmidt Orthogonalization. Chebyshev Polynomials and Applications.  GramSchmidt Algorithm Slide  AG 12.5; H 3.5.3  AG 12.7; BF 8.3 
19  Feb 28  Discrete Fourier Transform: sine & cosine basis.  Discrete Fourier Transform example and the code dft.m  AG 13.113.2  H 12.312.6; BF 8.5 
20  March 2  Discrete Fourier Transform: applications & exponential basis.  Demos of filtering and the twiddle factor  AG 13.3; H 12.1, 12.3  AG 13.6; H 12.512.6; BF 8.6 
21  March 5  Fast Fourier Transform. Wavelets mentioned.  None.  H 12.2  H 12.4; BF 8.6 
22  March 7  Numerical Differentiation. Symbolic & Automatic Differentiation. Taylor Series Methods.  None.  AG 14.0  14.1; H 8.6  BF 4.1 
23  March 9  Interpolate & Differentiate. Lagrange Basis Formulae.  None.  AG 14.2, 14.4; H 8.6  AG 14.6; H 8.8, 8.9 
24  March 12  Errors in Numerical Differentiation. Richardson Extrapolation. Ordinary Differential Equations Introduction.  Richardson's Extrapolation example and the code richardson.m  AG 14.314.4; H 8.7  BF 4.2 
March 14  Class Cancelled.  
March 16  Midterm 2.  
25  March 19  ODEs: introduction, high order reformulation. Lipschitz continuity.  None.  AG 16.0; H 9.1  BF 5.1, 5.9 
26  March 21  ODE existence, uniqueness & conditioning. ODE Basic Methods: Forward Euler.  Example codes: stiff.m, circle.m, and matlabFailure.m. For more information, see the ODE links below.  AG 16.1; H 9.29.3.1  BF 5.2 
27  March 23  Integrator Error Analysis. Backward Euler, Implicit Trapezoidal & Explicit Midpoint.  None.  H 9.3.3  None. 
28  March 26  Higher Order Accuracy: RungeKutta Methods.  None.  AG 16.2; H 9.3.6  AG 16.4; H 9.3.5, 9.3.79.3.9; BF 5.4 
29  March 28  Error Estimation and Control.  None.  AG 16.3  BF 5.5 
30  March 30  Embedded schemes. Stiffness & Stability  astronomy.m demonstrates the benefits of adaptive stepsize error control (you will also need astroODE.m and rk4.m). stiff.m demonstrates a stiff system.  H 9.3.2, 9.3.4  AG 16.7; H 9.49.5; BF 5.105.11 
31  April 2  Introduction to Numerical Integration. Basic Quadrature.  None.  AG 15.0  15.1; H 8.18.3.2  BF 4.3 
32  April 4  Composite Quadrature  None.  AG 15.2; H 8.3.5  BF 4.4 
April 6 & 9  Good Friday & Easter Monday. University Holidays.  
33  April 11  Gaussian and Adaptive Quadrature.  None.  AG 15.3, 15.4; H 8.3.38.3.4, 8.3.6  AG 15.5  15.8; H 8.4, 8.8  8.9; BF 4.6  4.7 
April 26  Final Exam, 3:30 pm, DMP 301 