#  Date  Topic 

1  Wednesday, January 4  Course Information and Tentative Outline. 
2  Wednesday, January 4  AG Table of Contents and Preface. 
3  Wednesday, January 4  AG Bibliography and Index. 
4  Wednesday, January 4  AG Chapter 1: Numerical Algorithms & Errors. 
5  Friday, January 6  AG Chapter 2: Roundoff Errors. 
6  Monday, January 9  AG Chapter 10: Polynomial Interpolation. 
7  Monday, January 16  Linear algebra facts particularly useful to interpolation. More details of numerical linear algebra can be found in Heath chapter 2. 
8  Monday, January 16  Review of Linear Algebra: AG Chapter 4: Linear Systems Introduction. CPSC 302 students already have this chapter. 
9  Wednesday, January 18  AG Chapter 11: Piecewise Polynomial Interpolation. 
10  Friday, February 3  AG Chapter 12: Best Approximation. 
11  Wednesday, February 22  AG Chapter 13: Fourier & Wavelet Transforms. 
12  Monday February 27  AG Chapter 14: Numerical Differentiation. 
13  Wednesday March 8  AG Chapter 16: Initial Value Ordinary Differential Equations 
14  Wednesday March 8  AG Chapter 15: Numerical Integration. 
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. You may never share executable code (including Matlab mfiles) for homework questions.
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  Assignment  Other Assignment Files  Solution  Other Solution Files 

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

TA: Kangkang Yin

TA: Jelena Sirovljevic

Course Communication:
Lectures: 11:00  12:00, Monday / Wednesday / Friday, Dempster 110
Grades: Your final grade will be based on a combination of:
Textbook:
Other References:
#  Date  Topic  Links  Required Readings  Optional Readings 

1  Jan 4  Course Syllabus and administration. Collaboration guidelines. Professor introduction.  Ian Mitchell's research slides. Ian Mitchell's homepage.  None.  H Preface; AG Preface; BF Preface 
2  Jan 6  Introduction to Scientific Computing. Sources (Types) of Error. Problem sensitivity.  Scientific Computing overview slides. Nick Trefethen's essay on the definition of numerical analysis.  H 1.11.2; AG 1.1  H 1.41.5 
3  Jan 9  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 11  Floating Point: Properties & Arithmetic. Sources (Types) of Error during Computation: Truncation and Rounding.  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 13  Interpolation: Background, Problem Formulation, Monomial Basis.  An example of polynomial interpolation in Matlab: interpolateSine.m  H 7.07.3.1; AG 10.010.1  BF 3.0 
6  Jan 16  Lagrange Basis.  None.  H 7.3.2; AG 10.2  BF 3.1 
7  Jan 18  Newton Basis & Divided Differences.  None.  H 7.3.3; AG 10.3  BF 3.2 
8  Jan 20  Interpolation Error.  None.  H 7.3.5; AG 10.4  AG 10.7 
9  Jan 23  Osculating Interpolation.  None.  AG 10.5  BF 3.3 
10  Jan 25  Piecewise Polynomial Interpolation.  None.  H 7.4.1; AG 11.011.1  BF 3.4 
11  Jan 27  Cubic Splines. Piecewise Hermite.  Example and the code piecewiseCubic.m  H 7.4.2; AG 11.2  BF 3.4 
12  Jan 30  Polynomial Interpolant Review.  None.  None.  H 7.57.6; AG 11.7; BF 3.6 
Feb 1  Midterm 1.  
13  Feb 3  Bspines & Parameteric Curves.  None.  H 7.4.3; AG 11.311.4  BF 3.5 
14  Feb 6  Best Approximation. Problem Formulation.  None.  AG 12.0  None. 
15  Feb 8  Discrete Least Squares Data Fitting.  bestFitNormChoice.m computes the best linear fit under various norms for the data from class. Results  AG 12.1; H 3.1  H 3.2; BF 8.1 
16  Feb 10  More Discrete Least Squares Data Fitting.  lsExample.m computes least squares regression (best fits) for two model functions from class. Results  H 3.4.1  H 3.3 (or even H 3) 
Feb 1317  Midterm Break.  
17  Feb 20  Continuous Least Squares Approximation.  None.  AG 12.2; H 7.3.5  BF 8.2 
18  Feb 22  Orthogonal Polynomials.  lsContinuous.m computes continuous least squares best fit polynomial to f(x) = 4 x^3.  AG 12.3; H 7.3.4  AG 12.4; BF 8.2 
19  Feb 24  GramSchmidt Orthogonalization. Chebyshev Approximation. Fourier Transform.  GramSchmidt Algorithm Slide  AG 12.5, 13.1; H 3.5.3  AG 12.7; BF 8.3 
20  Feb 27  Discrete Fourier Transform. Wavelets mentioned.  dft.m computes the best fit trigonometric approximant or discrete Fourier Transform.  AG 13.2, 13.4; H 12.1  H 12.3; BF 8.5 
21  March 1  Complex Exponential Basis of the Fast Fourier Transform. Review of Interpolation and Best Approximation.  None.  AG 13.3 (ha!); H 12.2  AG 13.6; H 12.412.6; BF 8.6 
22  March 3  Numerical Differentiation. Symbolic & Automatic Differentiation. Taylor Series Methods.  None.  AG 14.0  14.1; H 8.6  BF 4.1 
22  March 3  Interpolate & Differentiate. Lagrange Basis Formulae.  None.  AG 14.2; H 8.6  None 
March 8  Midterm 2.  
24  March 10  Errors in Numerical Differentiation. Richardson Extrapolation.  None.  AG 14.4, 14.6; H 8.7  BF 4.2 
25  March 13  Ordinary Differential Equations Introduction.  None.  AG 16.0; H 9.1  BF 5.1 
26  March 15  High order ODE Reformulation. Lipschitz continuity.  None.  H 9.1  BF 5.9 
27  March 17  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 
28  March 20  Integrator Error Analysis. Backward Euler, Implicit Trapezoidal & Explicit Midpoint.  None.  H 9.3.3  None. 
29  March 22  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 
30  March 24  Error Estimation and Control.  None.  AG 16.3  BF 5.5 
31  March 27  Stiffness & Stability  stiff.m demonstrates a stiff system.  H 9.3.2, 9.3.4  AG 16.7; H 9.49.5; BF 5.105.11 
32  March 29  Introduction to Numerical Integration. Basic Quadrature.  Examples  AG 15.0  15.1; H 8.18.3.2  BF 4.3 
33  March 31  Composite Quadrature  None.  AG 15.2; H 8.3.5  BF 4.4 
34  April 3  Review Basic & Composite Quadrature. Composite Quadrature Example.  None.  None.  None. 
35  April 5  Gaussian Quadrature.  None.  AG 15.3; H 8.3.38.3.4  BF 4.7 
36  April 7  Adaptive Quadrature and (Brief) Review.  None.  AG 15.4; H 8.3.6  AG 15.515.8; H 8.4, 8.88.9; BF 4.6 
April 12  Final Exam: April 12, 3:30pm, DMP 110 (the regular classroom) 