Final exam

The final course grade will be computed as Homework 30% + MAX { Midterm 20% + Final 50% , Final 70% }


Lecture notes

Class schedule

Date Topics
W 1/10 Floating point numbers. Axiom 0.
F 1/12 Floating point arithmetic. Axiom 1.
W 1/17 Propagation of error. Roundoff error analysis of summation methods.
F 1/19 Products. Condition number of a function. Elementary analytic functions.
W 1/24 Roundoff error analysis of power series. Babylonian method.
F 1/26 Fixed point iterations. Newton-Raphson method.
W 1/31 Modified Newton. Reciprocal iteration. Complexity of division. Bisection.
F 2/2 Secant method. Regula falsi. Gaussian elimination.
W 2/7 LU decomposition. GEPP. Condition number of a matrix.
F 2/9 Gram-Schmidt orthogonalization. QR decomposition.
W 2/14 Householder's elimination.
F 2/16 Backward error analysis.
W 2/21 Backward stability of Housholder's elimination.
F 2/23 Some examples. Cholesky factorization.
W 2/28 Lagrange interpolation. Vandermonde matrices.
F 3/2 Newton's divided differences. Lebesgue's lemma.
3/5–3/9 Reading week
W 3/14 Peano kernel theorem. Weierstrass approximation theorem.
F 3/16 Bézier curves. Existence of minimax polynomials.
W 3/21 Oscillation theorems of de la Vallée-Poussin and Chebyshev. Chebyshev polynomials.
F 3/23 Least squares approximation. Legendre polynomials.
W 3/28 Dirichlet kernel. Chebyshev kernel. Lebesgue constants for Chebyshev truncation.
F 3/30 Good Friday
W 4/4 Newton-Cotes quadrature. Romberg integration.
F 4/6 Gauss quadrature.
W 4/11 Euler-Maclaurin formula. Bernoulli numbers.
F 4/13 Fourier series. Jackson's inequality.
R 4/19 Final exam (9am, in department)

Online resources

Numerical analysis


Recommended books

Course outline

Instructor: Dr. Gantumur Tsogtgerel

Prerequisite: MATH 325 (Honours ODE) or MATH 315 (ODE), COMP 202 or permission of instructor.

Corequisite: MATH 255 (Honours Analysis 2) or MATH 243 (Analysis 2).

Restriction: Intended primarily for Honours students.

Calendar description: Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.

Topics to be covered:

Homework: We will have 3–4 homework assignments. Each assignment will consist of theoretical and programming components.

Exams: A midterm exam and a final exam. The midterm will be a take-home exam, and the final will consist of a theory exam in class, and a programming ("lab") exam to be done at home.

Grading: Homework 30% + MAX { Midterm 20% + Final 50% , Final 70% }.