Simon Fraser University
Engaging the World

Course Outlines

Fall 2018 - MACM 416 D100

Numerical Analysis II (3)

Class Number: 4343

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 4 – Dec 3, 2018: Mon, Wed, Fri, 10:30–11:20 a.m.
    Burnaby

  • Exam Times + Location:

    Dec 5, 2018
    Wed, 8:30–11:30 a.m.
    Burnaby

  • Prerequisites:

    MATH 310 and MACM 316.

Description

CALENDAR DESCRIPTION:

The numerical solution of ordinary differential equations and elliptic, hyperbolic and parabolic partial differential equations will be considered. Quantitative.

COURSE DETAILS:

ODEs - Initial Value Problems

  • Runge Kutta methods
  • Stability
  • Euler's method, Taylor methods
  • Linear Multistep methods
  • Predictor-corrector methods
  • Systems of ODEs

ODEs - Two point boundary value problems
  • Initial value methods (shooting)
  • Finite Differences
  • Collocation methods

Fourier Analysis
  • Fourier transform
  • Discrete Fourier transform

Time-dependent PDEs
  • Finite difference formulae
  • Method of lines
  • Finite differences and Fourier analysis

Accuracy, stability and convergence
  • Lax equivalence
  • The CFL condition
  • The von Neumann condition

Spectral Methods
  • Periodic boundary conditions
  • Polynomial spectral methods

Elliptic PDEs
  • Laplace equation
  • Finite Differences
  • Iterative Methods
  • Multigrid Methods

Introduction to finite elements

Grading

  • Homework Zero 10%
  • Biweekly Homework 20%
  • Best 3 of 4 quizzes 45%
  • Course Project 25%

NOTES:

Homework:
You will notice that your homework and project grades are worth a substantial proportion of your final grade. It is in your best interest to do your homework carefully. Any programming that you do must be clearly commented. On occasion, you may be required to hand in your programs. While you are encouraged to work in groups, I must be convinced that the work you hand in is your own.  In cases of academic dishonesty, you will receive zero for the work in question, and an academic dishonesty report will be filed.

Course Project:
The course project will consist of a written report, short oral presentation and computed examples on a topic that may not been directly covered in class but is within the scope of this course. Presentations will be in class., the report will be handed in before our presentations.

Materials

REQUIRED READING:

There is no required textbook for this course.
Typed lecture notes will be made available to the class via Canvas

RECOMMENDED READING:

Numerical Analysis
Burden and Faires
10/E, NELCA

Registrar Notes:

SFU’s Academic Integrity web site http://students.sfu.ca/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating.  Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the University community.  Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s10-01.html

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS