[SFU] [Math] [CECM]
Course Web Site
- http://wayback.cecm.sfu.ca/~hle/teaching/MACM316/
Textbook
- R.L. Burden, J.D. Faires. Numerical Analysis, seventh edition. ITP Nelson, 2001.
Course Outline
The course covers the first seven chapters of the text book.- Floating number systems (1-1/2weeks)
- Representation of numbers; error propagation and error estimation.
- Interpolation and polynomial approximation (2 weeks)
- Interpolating polynomial, Lagrange form, error formular; spline interpolation; parametric curve.
- Systems of linear equations (3 weeks)
- Elimination method - factorization, pivoting, inverse calculation; iterative methods; eigenvalue problems.
- Solutions of equations in one variable (2 weeks)
- Bisection, secant methods, Newton's method; fixed point iteration and acceleration.
- Numerical differentiation and integration (1-1/2 weeks)
- Numerical differentiation; numerical quadrature-Romberg scheme, composite rules, Gaussian quadrature.
- Intial-value problems for ordinary differential equations (2 weeks)
- Euler's method, Taylor and Runge-Kutta methods; convergence, stability, trapezoid method; stiff equations.
Grading schemes
- Assignments: 20%
- Midterm: 30%
- Final Exam: 50%
- Midterm: 30%
Assignments
Assignments are due in class.- Assignment 1: .ps, .pdf - Due: Monday, January 24.
- Assignment 2: .ps, .pdf - Due: Monday, February 7.
- Assignment 3: .ps, .pdf - Due: Monday, February 28.
- Assignment 4: .ps, .pdf - Due: Monday, March 21.
- Assignment 5: .ps, .pdf - Due: Monday, April 4.
Midterm
- March 9th, 1:00pm -- 2:20pm, Room 540.
- Aids allowed:
- Lecture notes
- Text book
- Hand calculator
Final Exam
- April 20th, 8:30am -- 11:20am, Room 540.
- Aids allowed: One two-sided cheat sheet.
Tutorials
Maple
- Maple Application Center (Mathematics, Numerical Analysis)
Matlab
- Matlab Primer (postscript file documenting many of Matlab's features)
- Matlab tutorial, examples, resources (at Indiana University )
- Another tutorial (in pdf format, from Texas Tech)
Additional Materials
Lecture Notes
(including Maple worksheets used during lectures)- Floating number systems .ps, .pdf, Maple worksheet .mws.
- Interpolation (part I)
.ps,
.pdf,
Interpolation (part II) .ps, .pdf,
Maple worksheet .mws. - Direct methods for solving linear systems .ps, .pdf.
- Iterative techniques in matrix algebra .ps, .pdf.
- Solutions of equations in one variable .ps, .pdf.
- Numerical differentiation and integration .ps, .pdf.
- Initial-value problems for ordinary differential equations .ps, .pdf.
Maple Worksheets
The following Maple worksheets are downloaded from the Maple Application Center:- An Example Of Round-Off Error - Bruno Guerrieri - Maple 7
- Bisection algorithm for root finding - D. Chamberlain-Long - Maple 7
- Higher Order Interpolation is a Bad Idea - Autar Kaw, Jai Paul, Nathan Collier - Maple 8
- Comparison of Polynomial Interpolation and Cubic Splines - Mohamed Moutadayne - Maple 7
- EM Section 40.5: Bezier Curves - Robert Lopez - Maple 8
- AEM Section 43.4: Adaptive Quadrature - Robert Lopez - Maple 8
- AEM Section 39.6: Relaxation and SOR - Robert Lopez - Maple 8
- Numerical linear algebra and the NAG Libraries - Maplesoft - Maple 6
Internet Resources
- Numerical Mathematical Systems:
- Computer Algebra Systems:
Entertainment
Maintainer: hle@cecm.sfu.ca