MAT 3341
APPLIED LINEAR ALGEBRA
UNDER CONSTRUCTION:
Spring Term: 1st May - 16 July 2002 (4 hours of lecture per week, 10
weeks - 3 cr.)
COURSE DESCRIPTION:
An introductory course in the application of numerical methods using
computer oriented algorithms such as finding roots, solving systems of
equations, differentiation, integration and optimization.
Prerequisites:
MAT 1322(1722), MAT 2141(2541) or MAT 2341(2741).
INSTRUCTOR: Rémi VAILLANCOURT
LECTURES:
Tuesday 14:30-16:30 VNR 469
Thursday 14:30-16:30 MCD 120
TEXTBOOK:
Applied Linear Algebra, 3rd ed., B. Noble and J.W. Daniel, Prentice-Hall,
Englewood Cliffs NJ.
CLASS NOTES as the course progresses will be put on the web and on sale
at VCN 104
OTHER REFERENCES:
Matrix Computations, 1st and 3rd ed., G. H. Golub and C. F. Van
Loan, John Hopkins Univ. Press, Boltimore, 1983, 1996.
Numerical Linear Algebra and Applications, B. N. Datta, Brooks/Cole,
Pacific Grove, 1995.
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: 2002.07.17