MAT 3380

INTRODUCTION TO NUMERICAL METHODS

WINTER TERM: 4 January - 7 April 2006 (3 hours per week for 12.5 weeks - 3 cr.)

UNDER CONSTRUCTION

COURSE DESCRIPTION:
Roots of equations. Iterative methods for systems of equations (Gauss-Seidel, Gauss-Jacobi, SOR, Newton and Quasi-Newton methods). Condition number, discrete dynamical systems, interpolation and polynomial approximation, numerical differentiation and integration. Prerequisites: (MAT2141(2541) or MAT2341(2741)), MAT2122(2522), (MAT2331(2731) or MAT2324(2724)). (This course cannot be combined for credit with CSI3150(3550).)

PROFESSOR: Rémi VAILLANCOURT


COURSE SCHEDULE:


NOTES and REFERENCE TEXT:

  • Numerical Methods by Rémi Vaillancourt, notes for the course, dowwnloadable in pdf Notes pdf . Paper copy on sale for XX$ at MRN 0028. These notes are sufficient for the course. The contents of these notes can also be found in the notes for MAT2731, MAT2331, CSI 3150 and CSI 3550 (see these courses for a pdf version).
  • Numerical Analysis , R.L. Burden, J.D. Faires, 7th edition, PWS-Kent Publishing Company, Boston. Useful reference but not necessary for the course.

    GRADE FORMULA:


    AIMS OF THE COURSE:
    Dans ce cours, l'étudiant(e) apprend à reconnaître les types de problèmes dont la solution requiert une technique numérique. L'étudiant(e) rencontre des exemples de propagation d'erreurs inhérantes aux méthodes numériques et approxime avec précision des solutions de problèmes qu'on ne peut résoudre exactement.

    COURSE CONTENTS:

  • Préliminaires mathématiques;
  • Solutions d'équations en une variable;
  • Interpolation et approximation polynômiales;
  • Dérivation and intégration numériques;
  • Méthodes pour la résolution des systèmes linéaires;
  • Techniques itératives en algèbre matricielle;
  • Problèmes de valeurs initiales pour les équations différentielles.

    APPROXIMATE PLAN OF THE COURSE:

  • 6-13 Jan.: Solution of nonlinear equations. Download old handwritten pdf notes : Notes on Chap. 1.
  • 17-20 Jan.: Interpolation. Download old handwritten pdf notes : Notes on Chap. 2,
  • 20 Jan.: Splines. Download : Four sheets on spline.
  • 27 Jan.- 7 Feb.: Differentiation and integration. Download old handwritten pdf notes : Notes on Chap. 3.
  • 17 Feb.: MID-TERM 1 (80 min), on assignments 1 to 3. Closed book. All types of calculators allowed. Download Typical questions pdf , Mi-session1 pdf , Mid-term1 pdf , Mid-term1 sol. 1 pdf , Mid-term1 sol. 2 pdf .
  • 20-24 Feb: STUDY BREAK.
  • 11 fév.-5 mars:Élimination gaussienne, pivotage, affinage de la solution par récurrence.
  • 10-12 mars: Résolution de systèmes linénaires
  • 17-19 mars: Valeurs propres, estimation de l'erreur, décomposition QR et en valeurs singulières Télécharger fichier pdf Notes de cours 00.07.06,
  • 17 March: MID-TERM 2 (80 min), on assigments 4 to 6. Download Typical questions pdf Closed book. All types of calculators allowed. Download Mi-session2 pdf , Mid-term2 pdf , Mid-term2 sol. pdf.
  • 21-28 March: Initial value problems for ordinary differential equations. Runge--Kutta and multistep methods Download pdf file: Notes sur le ch. 5,
  • 31st Mach-4 April: Newton's method in n dimensions, conjugate gradient method. Download Conjugate gradient.pdf Download IterImprandSOR.pdf
  • 27 April, 14:00, GYM C: Final exam. Closed book. All types of calculators allowed. Download Contents for final 2001.txt, Final exam 2001.pdf.

    ASSIGNMENTS (LISTS OF PROBLEMS MAY CHANGE):
    Ten points per problem. Each bonus problem is worth 10 extra points. Assignments are due at the beginning of the course. Graded assignments will be brought to class. Unclaimed assigments will be put in the MAT 3380 box at 585 King Edward Ave. The FIRST page must have the course number, the date, the assignment number, your name and your student number. Please staple the FILLED-IN control sheet in landcape position (horizontal position) AFTER THE LAST SHEET OF YOUR ASSIGNEMENT. The control sheet will be kept as a record. Download a model of the control sheet: controlsheet.pdf

  • Assignment 1 : issued 05.12.26, due 06.01.20 at 10:00, sol. 06.01.23. In the Notes, pages 159-160, Exercises 1.5, 1,6, 1.9, 1.10, 1.16, 1.17, bonus problem : 1.18. Download Solution 1 pdf
  • Assignment 2 : issued 05.12.26, due 06.01.27 at 10:00, sol. 06.01.30. In the Notes, pages 160-162, Exercises 1.20, 2.2, 2.5, 2.6, 2.11, 2.13. Download Solution 2 pdf
  • Assignment 3 : issued 06.01.23, due 06.02.03 at 10:00, sol. 06.02.06. On distributed sheets, page 153, Exercises 7 and 8, page 154, Exercises 15, 22 and 23. Download pp. 153-154: Assignement3 pdf Download Solution 3 pdf
  • Assignment 4 : issued 06.01.31, due 06.02.10 at 10:00, sol. 06.02.13. In the Notes, pages 162-164, Exercises 3.1 for (4.5) only, 3.2, 3.7, 3.8, 3.11, 3.13. Download Solution 4 pdf
  • Assignment 5 : issued 06.02.09, due 06.03.03 at 10:00, sol. 06.03.07. In the Notes, pages 164-165, Exercises 4.1, 4.5, 4.8, 4.9, 4.12, 4.16. Download Solution 5 pdf
  • Assignment 6 : issued 06.03.01, due 06.03.10 at 10:00, sol. 06.03.14. In the Notes, pages 165-166, Exercises 4.16, 4.17 (use th. 4.6, not 4.3), 4.19, 4.21 (power method), 4.20 with the inverse power method; prove that the LU decomposition of a nonsingular matrix is unique, where L is unit lower triangular. Download Solution 6 pdf
  • Assignment 7 : issued 06.03.17, due Tuesday 06.03.28 at 08:30, sol. 06.03.30. In the Notes, pages 166-167, Exercises 5.2, 5.7, 5.12, 5.18; in each case, take h=0.1 and do 5 steps up to x = 0.5; plot the solution only for Ex. 5.12. Page 164, Exercise 4.3. Download Solution 7 pdf
  • Assignment 8 : issued 06.03.29, due Tuesday 06.04.04 at 08:30, sol. 06.04.06. In the Notes, pages 167, Exercises 5.21 up to x=0.5 and 5.24 up to x=0.6 (use starting values from Ex. 5.12); no need to plot the solutions. In Conjugate gradient.pdf, p. 530, P10.2.1 and P10.2.3. For P10.2.3 download P10.2.3.pdf Download Solution 8 pdf

    Last update : 2006.04.29. Will be frequently updated.