MA/CSC 780 - Numerical Analysis II

You can download the course information here.
More information can be found on the course Moodle page.

Textbook:

W. Gautschi, Numerical analysis, 2nd edition, 2011.

Spring 2023 Tentative Course Schedule

Week 1

01/09 Lecture 1: Welcome and Course Overview; Review of key concepts
01/11 Lecture 2: Polynomial Interpolation
01/13 Lecture 3: Lagrange Interpolation

Week 2

01/16 Martin Luther King Jr. Day; No class
01/18 Lecture 4: Polynomial Interpolation II
01/20 Lecture 5: Polynomial Interpolation III

Week 3

01/23 Lecture 6: Error Analysis of Polynomial Interpolation
01/25 Lecture 7: Convergence of Polynomial Interpolation
01/27 Lecture 8: Hermite Interpolation

** Homework 1 due Friday

Week 4

01/30 Lecture 9: Piecewise Polynomial Interpolation
02/01 Lecture 10: Piecewise Polynomial Interpolation II
02/03 Lecture 11: Cubic spline

Week 5

02/06 Lecture 12: Fourier Interpolation
02/08 Lecture 13: Fourier Interpolation II
02/10 Lecture 14: Least Squares Approximation

** Homework 2 due Friday

Week 6

02/13 Lecture 15: Least Squares Approximation II
02/15 Lecture 16: Least Squares Approximation III
02/17 Lecture 17: Orthogonal polynomials

Week 7

02/20 Lecture 18: Orthogonal polynomials II
02/22 Lecture 19: Numerical Differentiation
02/24 Lecture 20: Review

Week 8

02/27 Midterm Exam
03/01 Lecture 21: Numerical Integration I
03/03 Lecture 22: Numerical Integration II

** Homework 3 due Monday

Week 9

03/06 Lecture 23: Gauss Quadrature I
03/08 Lecture 24: Gauss Quadrature II
03/10 Lecture 25: Quadrature in multi-dimensions

Week 10

Spring break: 03/13 - 03/17

Week 11

03/20 Lecture 26: Richardson Extrapolation
03/22 Lecture 27: Ordinary Differential Equations
03/24 Lecture 28: One Step Methods I

** Homework 4 due Friday

Week 12

03/27 Lecture 29: One Step Methods II
03/29 Lecture 30: Improved Euler Method
03/31 Lecture 31: Two-stage methods; Runge-Kutta Methods

Week 13

04/03 Lecture 32: Stability and Convergence
04/05 Lecture 33: Stiff systems and A-stability I
04/07 Lecture 34: Stiff system and A-stability II

** Homework 5 due Friday

Week 14

04/10 Lecture 35: Method of lines methods for heat equation
04/12 Lecture 36: Multistep Methods I
04/14 Lecture 37: Multistep Methods II

Week 15

04/17 Lecture 38: Special Topic
04/19 Lecture 39: Special Topic
04/21 Lecture 40: Special Topic

Week 16

04/24 Lecture 41: Review
04/25 - 04/26: Reading Days

** Homework 6 due Monday