MA/CSC 428 - Introduction to Numerical Analysis II

You can download the course syllabus here.
More information can be found on the course Moodle page.
Reference: [Sauer] Timothy Sauer, Numerical Analysis, 2nd/3rd Edition, Pearson (ISBN 978-0-321-78367-7).

Spring 2025 Tentative Course Schedule

Week 1

  • 01/07 Lecture 1: Welcome and Course Overview; Review of Numerical Linear Algebra
  • 01/09 Lecture 2: Singular Value Decompositions I
    • [Sauer] section 12.3

Week 2

  • 01/14 Lecture 3: Singular Value Decompositions II
    • [Sauer] section 12.3, 12.4
  • 01/16 Lecture 4: SVD for least squares problems

Week 3

  • 01/21 Lecture 5: Eigenvalue Problems
    • [Sauer] section 12.1
  • 01/23 Lecture 6: Power Methods
    • [Sauer] section 12.1.1, 12.1.2

** Homework 1 due Thursday

Week 4

  • 01/28 Lecture 7: Inverse Power Methods
    • [Sauer] section 12.1.3
  • 01/30 Lecture 8: QR Algorithm

Week 5

  • 02/04 Lecture 9: Optimization I

  • 02/06 Lecture 10: Optimization II - Newton’s iteration

** Homework 2 due Thursday

Week 6

  • 02/11 Wellness Day; No class

  • 02/13 Lecture 11: Optimization III - Convexity

Week 7

  • 02/18 Lecture 12: Optimization IV: Newton’s method, Steepest Descent
    • [Sauer] section 13.2.1 - 13.2.2
  • 02/20 Lecture 13: Optimization V - Conjugate Gradient Search
    • [Sauer] section 13.2.3

** Homework 3 due Thursday

Week 8

  • 02/25 Lecture 14: Optimization VI - Unconstrained optimization without derivatives
    • [Sauer] section 13.1
  • 02/27 Midterm Exam

Week 9

  • 03/04 Lecture 15: Shooting Method
    • [Sauer] section 7.1
  • 03/06 Lecture 16: Finite Difference Methods for linear BVPs
    • [Sauer] section 7.2.1

** Homework 4 due Thursday

Week 10

  • 03/11, 03/13 Spring Break: No Classes.

Week 11

  • 03/18 Lecture 17: Finite Difference Methods for nonlinear linear BVPs
    • [Sauer] section 7.2.2
  • 03/20 Lecture 18: Collocation
    • [Sauer] section 7.3.1

** Homework 5 due Thursday

Week 12

  • 03/25 Lecture 19: Finite Elements and the Galerkin Method
    • [Sauer] section 7.3.2
  • 03/27 Lecture 20: Finite Elements and the Galerkin Method
    • [Sauer] section 7.3.2

Week 13

  • 04/01 Lecture 21: Random Numbers
    • [Sauer] section 9.1
  • 04/03 Lecture 22: Monte Carlo Simulation
    • [Sauer] section 9.2

** Homework 6 due Thursday

Week 14

  • 04/08 Lecture 23: Monte Carlo Simulation II
    • [Sauer] section 9.2
  • 04/10 Lecture 24: Discrete and Continuous Brownian Motion I
    • [Sauer] section 9.3

Week 15

  • 04/15 Lecture 25: Discrete and Continuous Brownian Motion II
    • [Sauer] section 9.3
  • 04/17 Lecture 26: Stochastic Differential Equations
    • [Sauer] section 9.4

** Homework 7 due Thursday

Week 16

  • 04/22 Lecture 27: Review

** 04/23 Reading Day

Final Exam: Thursday, April 24, 12:00 PM - 2:30 PM