MAT 4785 /4385

MÉTHODES NUMÉRIQUES POUR LES ÉQUATIONS DIFFÉRENTIELLES /NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS

UNDER CONSTRUCTION:

Session du printemps / Spring Term: 2003.05.05 - 2003.07.xx (lecture dirigée / reading cours, 10 sem./weeks weeks - 3 cr.)

COURSE DESCRIPTION:
Méthodes numériques pour équadif. / Numerical methods for ode's. Prerequisites: MAT 3741(3341).

INSTRUCTOR: Rémi VAILLANCOURT

READING COURSE:
  • A problem set from Lambert and other sources.


    • LECTURE NOTES:

  • Download pdf on numerical methods for ode's : MNEquadif.pdf.


    • REFERENCES:

  • Computational methods in ordinary differential equations, J.D. Lambert, Wiley, London, 1973.
  • Numerical methods in ordinary differential equations, J.D. Lambert, Wiley, Chischester, 1991.


    • MARKING SCHEME:

  • Assignments (AS) 10%
  • Midterm (MT) 30%
  • Final exam (FE) 60%
  • Marks in assignments and tests : Marks3341.html,
  • E-mail to the class : e-mail.


    • COURSE OBJECTIVES:
    In this course, algebra meets geometry. The students will learn to apply algebra to matrix computation. The core of the course will be matrix factorizations. Matlab, which stood originally for "matrix lab" is a useful software for the course.

    COURSE OUTLINE - NOT DONE YET:

  • Mathematical preliminaries
  • Solutions of equations in one variable
  • Interpolation and polynomial approximation
  • Numerical differentiation and integration
  • Download pdf or ps file on matrix computations Matrix_computation.pdf, Matrix_computation.ps,
  • Direct methods for solving linear systems
  • Iterative techniques in matrix algebra


    • APPROXIMATE ORGANIZATION OF LECTURES - DONE ONLY UP TO JULY 18:

  • May 2-7: The action of A = USV', where U and V are unitary and S is a diagonal matrix.
  • May 9-14: The factorizaton PA = LU with partial pivoting and row interchange, where P is a permutation matrix, L is unit lower triangular and U is upper triangular,
  • May 16: Vector p-norms and matrix 1-, infinity- and Frobenius norms.
  • May 21-23: Schur factorization A = UTU', where U is unitary and T is upper triangular. Normal matrices,
  • May 28-30: Gaussian elimination, pivoting strategy, iterative refinement.
  • Jun 6-18: Iterative technique for solving linear systems
  • Jun 10-14: STUDY BREAK
  • Jun 20: MIDTERM (Cosed book, all calculators allowed). On material of assignments 1, 2 and 3 and material seen in class.
  • Jun 25-27: Eigenvalues, error estimates, QR and singular value decompositions Download pdf file Example of QR factorization,
  • July 2-4: Initial value problems for ordinary differential equations, Euler, higher-order Taylor and Runge-Kutta methods.
  • Jun 9-11: Multistep methods
  • Jul 16: Review
  • FINAL EXAM Take-home part. Due Wednesday, 24, July 2002. 4 questions, each worth 5 % on your final grade.
  • FINAL EXAM Thursday, 18, July 2002, 13:00-16:00, MNT 207 (Open book, all calculators allowed but not needed). 8 questions on material seen in class, in midterm and assignments, each worth 5 % on your final grade.


    ASSIGNMENT MATERIAL - NOT DONE YET :

  • Weeks 1-2: Assignment 1 : issued 02.05:04, due 02.05.25, sol. 02.05.25
  • Weeks 3-4: Assignment 2 : issued 02.05.27, due 02.06.13, sol. 02.06.14.
  • Weeks 5-6: Assignment 3 : issued 02.06.20, due 02.07.04, sol. 02.07.09
  • Weeks 7-8: Assignment 4 : issued 02.07.04, due 02.07.11, sol. 02.07.16 Solutions will be available on the web and on paper at VCN 104.
  • Graded assignments will be returned in class.


    • Last modified: 2003.05.07