Math 300: Overview of Numerical Methods (Spring 2006)


Department of Mathematics
Drexel University


The primary goal of the course is to highlight the essential concepts in numerical methods: convergence, stability, and efficiency. A particular emphasis is placed on implementation and visualization with in-depth discussions of good coding practices. The main topics include numerical integration, optimization, the FFT and spectral methods, boundary element method, an introduction to the finite element method and an introduction to numerical linear algebra.

Lecturer: Pavel Grinfeld, Korman-275, e-mail: "My Initials"@math.drexel.edu

o Lectures: MWTR @Noon; Korman-247

Teaching Assistant: None

o Syllabus: (doc, pdf)

Flash Recordings of Lectures

  • Tue, April 4th - Intro to Matlab I
  • Wed, April 5th - Intro to Matlab II
  • Thu, April 6th - Rate of Convergence
  • Tue, April 11th - Richardson Extrapoltion
  • Wed, April 12th - Vectorization
  • Wed, April 12th - Plots in 3D
  • Mon, April 17th - The Left End Rule and the Trapezoid Rule
  • Tue, April 18th - Simpson's Rule
  • Thur, April 20th - Introduction to Gaussian Quadrature - Legendre Polynomials.
  • Tue, May 2nd - Gaussian Elimination, LU and LDU decompositions, Cholesky decomposition, Legendre and Chebyshev Polynomials
  • Wed, May 3nd - Gaussian Quadrature - outline of the method
  • Thur, May 4nd - Lecture on misc topics in numerical integration. Recording did not work, sorry.
  • Mon, May 8th - IEEE Doubles, Lecture I
  • Tue, May 9th - IEEE Doubles, Lecture II
  • Wed, May 10th - Finite Differences
  • Mon, May 15th - High order Finite Differences
  • Tue, May 16th - Laplace's equation (Not recorded)
  • Wed, May 17th - IEEE Review
  • Thur, May 18th - IEEE + Finite Differences Review
  • Tue, May 23rd - Laplace/Poisson in 1D
  • Tue, May 23rd - Laplace/Poisson in 2D

  • plotter.m
  • gauss.m
  • Laplace1D.m

    Problem Sets

  • Homework 1, Matlab project due Thursday, April 13th. (doc, pdf)
  • Homework 2, Matlab project due Friday, April 21st. (doc, pdf)
  • Homework 3, due Wed, April 26th. (pdf)
  • Homework 4, Matlab project due Wed, May 10th. (doc, pdf)
  • Homework 5 due Wed, May 24th. (pdf)
  • Homework 6, due Last Day of Class (pdf)

    Past Exams

  • Fall 2005, Midterm 1
  • Fall 2005, Midterm 2

    Class resources

    Matlab Tutorials
  • http://www.math.utah.edu/lab/ms/matlab/matlab.html
  • http://www.math.ufl.edu/help/matlab-tutorial/
  • http://www.cyclismo.org/tutorial/matlab/
  • http://www.mathworks.com/academia/student_center/tutorials/launchpad.html
  • http://amath.colorado.edu/computing/Matlab/Tutorial/
  • http://www.engin.umich.edu/group/ctm/basic/basic.html

    Cygwin instructions
  • Instructions for Cygwin installation
  • Open a cygwin shell. Type "startx". In the new window, type the ssh command: ssh -X yourid@dunx1.irt.drexel.edu Once in, type "matlab".

    Lectures of past quarters
  • Matlab Intro - Tuesday, September 27th, 2005
  • Matlab Intro - Wednesday, September 28th, 2005 (Matrices, Loops, Scripts/Functions) | OurFirstScript.m | sqr.m | multiply.m
  • Monday, October 3rd, 2005 | integrateLeftEnd.m | integrateTrapezoid.m
  • Tuesday, October 4th, 2005 | integrateLeftEndVectorized.m | integrateTrapezoidVectorized.m | determineRateOfConvergence.m
  • Thursday, October 6th, 2005 | integrateMidPointVectorized.m | integrateSimpsonsRuleVectorized.m | HowToDetermineCoefficients
  • Wed, October 12th, 2005 | integrateGaussian10.m | rateOfConvergenceExercise.m
  • Thu, October 13th, 2005 | intGauss10Plus.m
  • Tue, October 18th, 2005 | 2D in Matlab + Gaussian Integration on Rectangle | intGauss10Rect.m
  • Tue, October 25th, 2005 | HowToObtainSimpsonCoefficients.pdf
  • Tue, November 14th-ish, 2005 | PoissonOnSquareByFD.m
  • Tue, November 28th, 2005 | ft.m
  • Tue, December 6th, 2005 | ComplexNumbers.pdf