MATH 4073

Numerical Analysis

OU Presidential Dream Course

Fall 2018, Sec 001: TR 1:30-2:45pm, Classroom PHSC 108

Instructor: Dr. Ying Wang

Contact info: PHSC 1119, tel: 405-325-6074, email:

Office hours: TR 2:45-3:45, and by appointment

Syllabus: Sec 001

Policy: Late homework will have no credit.

Applied Math Seminar

Tentative Schedule: updated regularly



August 21

Linear algebra review:

Matrices addition/subtraction,



Scalar multiplication,




HW 0 (Due Aug 23)

August 23


System of linear equations:

Gaussian Elimination


Quiz 1 is on Aug 30

August 28

Guest Lecture

Professor Colin Macdonald

Office: PHSC 1008

Topic: Polynomial Lagrange Interpolation

Lecture Notes

Office hour: 8/29 1:30-2:30pm


Public Lecture 5-6pm PHSC 201

Title: Numerical Computation on Curved Surfaces


HW 1 (Due Sep 11) gauss_elim.m Solution

August 30

Gaussian Elimination

Matrix Inversion

Gaussian Elimination with Partial Pivoting


Quiz 1 Solution


Aug 31: Last day to drop without a “W”

September 4

Gaussian Elimination with Partial Pivoting

Vector Norms

Matrix Norms

September 6

Matrix Norms

Eigenvalues, Eigenvectors

September 11

Error Estimate

Condition Number

Perturbation of A and b


Quiz 2 Solution

September 13

Office hours

(Due to Engineering Career Fair)

September 18

Perturbation of A and b

Existence, Uniqueness, Stability of solutions to IVPs


HW 2 (Due Oct 2) Solution

September 20

Existence, Uniqueness, Stability of solutions to IVPs

Euler Method for ODEs

Local Truncation Error of Euler’s Method


Quiz 3 is on Sep 25


September 21

Public Lecture Sep 21 3:30-4:30pm PHSC 108

Speaker: Professor Yalchin Efendiev

Title: Data Integration in Multiscale Simulations

September 25

Quiz 3 Solution

Review for Midterm I

September 27

Midterm I

October 2

Midterm 1 discussion

Taylor methods


HW 3 (Due Oct 18) Solution

October 4

Runge-Kutta Method


October 8

Public Lecture Oct 8 5:30-6:30pm Nielsen Hall 270

Speaker: Professor Chi-Wang Shu

Title: Mathematics in Scientific Computing

October 9

Guest Lecture

Professor Chi-Wang Shu

Topic: TVD(SSP) Runge-Kutta time discretization

October 11

Global error of Euler Method

October 16

Multi-step ODE solvers



HW 4 (Due Nov 13) ab4.m Solution

October 18

Multi-step ODE solvers



October 23

Multi-step ODE solvers


Consistency, Stability, and Convergence conditions for 1-step methods

October 25

Consistency, Stability, and Convergence conditions for multi-step methods


Oct 26: Last day to drop with a “W” for undergraduate students

October 30

Error control and variable step size algorithms



November 1

Guest Lecture:

Professor Alex Grigo

Topic: Programming demonstration of variable step size algorithms

November 6

Review for Midterm II

November 8

Midterm II

November 13

Discussion of Midterm II

November 15

Nonlinear equations

Bisection Method

Newton’s Method


HW 5 (Due Dec 4) Solution

November 20

Newton’s Method

Secant Method


Quiz 4 is on Nov 27

November 22

Thanksgiving break, no class

November 27

Fixed Point Iteration


Quiz 4 Solution

November 29

Fixed Point Iteration


Applied Math seminar Nov 30 2:30-3:30 PHSC 323

Speaker: Professor Xingjie Li

Title: Consistent coupling of nonlocal diffusion

December 4

Review for the Final Exam

December 6

Review for the Final Exam


MATLAB tutorials:

   The documentation available at the central MATLAB web-site, in particular Getting Started, the Function Reference, and the Examples web-sites.

   A 33-page Practical Introduction to Mathlab by Mark Gockenbach (Michigan Technological University) Introduction, in html format.

    A 16-page MATLAB Tutorial by Peter Blossey (University of Washington).

    A 8-page Introduction to Plotting with Matlab from the University of Washington.

    A very detailed (125 pages) MATLAB Overview by Ed Overman (Ohio State University).

    A 35-page MATLAB Primer by Kermit Sigmon (University of Florida).


Final Exam: Sec 001 December 12 Wednesday 1:30--3:30 PHSC 108 (classroom)