MACM 316-3
Numerical Analysis I

Fall 2013


INSTRUCTOR: John Stockie
Office: K 10518
Phone: 778-782-3553
E-mail: stockie  [at]  math.sfu.ca
Web: http://www.math.sfu.ca/~stockie/teaching/macm316/
CLASS TIMES: MWF    12:30-13:20,   AQ 3181
MY OFFICE HOURS: W    13:30-14:30
TUTORIALS: Each of you is assigned to a tutorial section which is run by one of the following TA's:

Reynaldo Arteaga (email: rarteaga [at] sfu [dot] ca)
Tuesdays - 9:30-10:20,   AQ 4140 (D101)
10:30-11:20, BLU 10031 (D102)
11:30-12:20, AQ 4120 (D103)

Mitchell Kovacic (email: mkovacic [at] sfu [dot] ca)
Thursdays - 9:30-10:20, AQ 5018 (D104)
10:30-11:20, BLU 10031 (D105)
11:30-12:20, AQ 2104 (D106)
I strongly encourage you to attend your scheduled tutorial session. Your TAs are available to provide help with homework questions or explaining material from class. They will also review homework and midterm solutions. When needed, the TAs may provide some supplementary material and additional examples that I couldn't otherwise cover in class.
PREREQUISITES: MATH 152 or MATH 155 or MATH 158, and MATH 240 or MATH 232, and knowledge of a high level computer language. Students with credit for MATH 406 may not receive further credit for MACM 316.
TEXTBOOK:
Numerical Analysis, 9th edition, by R. L. Burden and J. D. Faires (Thomson Brookes/Cole)
The authors maintain a web site that contains a list of errata, the first two chapters of the Student Study Guide, and a collection of programs that implement many algorithms from the text in a number of common languages.
NOTE: Although I will mostly follow the text, some essential material will be drawn from other sources.
HOMEWORK:
Homework will be assigned roughly every second week and you will have approximately two weeks to complete each assignment. Homework is due on Friday at 12:00 noon and should be deposited in the appropriate locked submission box on the 9000 level below the Math Department.
Some homework questions will be taken from the textbook, although some additional problems may be assigned from other sources.
Some questions will require the use of a programming language. Maple and Matlab are both available on the university computing network, as are compilers for languages such as C and Fortran. The code examples I provide in class will be written in Matlab only, although you are free to use whatever language you prefer in your assignments.
TESTS: There will be one midterm test held in class on Wednesday October 23. The midterm will cover material roughly up to the end of the section on linear equations. The final exam is scheduled for December 13 and will cover all material in the course.
ACADEMIC INTEGRITY:
Academic dishonesty has no place in a university and I have zero tolerance for it. All students must understand the meaning and consequences of cheating, plagiarism and other academic offences identified under the SFU Code of Academic Integrity and Good Conduct. Cheating includes, but is not limited to:
  • Handing in assignment solutions copied from other sources such as solution manuals, other students' work, on-line sources, etc.
  • Using calculators or unauthorized reference materials during tests or examinations, unless they are explicitly allowed.
  • Looking at the work of other students during examinations.
In all of these cases, all students involved in the act will receive a mark of zero for the entire work in question. The Chair of the Mathematics Department will be notified and a permanent note will go in your academic file. Further action may also be taken as outlined in the SFU Policies and Procedures for Student Discipline.
OUTLINE: (below is the official outline for Fall 2013, which may differ slightly from what is posted on the Math Department's web site)
  1. Number systems and errors: Ch 1 (all) -- 1.5 weeks
    • Representation of numbers
    • Error propagation and error estimation
    • Review of concepts from calculus

  2. Solution of nonlinear equations: Ch 2 (except 2.6) -- 2 weeks
    • Bisection, secant and Newton's methods
    • Fixed point iteration and acceleration
    • Rate of convergence

  3. Systems of linear equations: Chs 6 & 7 (all) -- 3 weeks
    • Elimination method: factorization, pivoting and inverse calculation
    • Norm, determinant and condition number
    • Iterative methods
    • Eigenvalue problems

  4. Interpolation and approximation: Ch 3 (except 3.3 & 3.5) plus Secs 8.1 & 8.5 -- 2 weeks
    • Interpolating polynomials: Lagrange form and error formula
    • Spline interpolation
    • Trigonometric interpolation and Fourier series
    • Least squares

  5. Differentiation and integration: Ch 4 (except 4.6, 4.8 & 4.9) -- 1.5 weeks
    • Numerical differentiation and finite differences and Richardson extrapolation
    • Numerical quadrature: rectangle rule, trapezoid rule, Romberg integration, composite rules and Gaussian quadrature

  6. Initial value problems: Ch 5 (except 5.6-5.8) -- 2 weeks
    • Euler's method
    • Taylor and Runge-Kutta methods
    • Convergence, stability and stiffness
    • Systems of equations

MARKING SCHEME:
   Assignments (bi-weekly):   25%
Midterm test (Oct. 23):   25%
Final examination (Dec. 13):    50%
Students requesting any special accommodations for religious or other reasons MUST inform me during the first week of the semester.


Last modified: Tue Sep 10 2013