MATH 452: Numerical Analysis II (Section 1)
Welcome to the course webpage for Math 452! This course is the second
part of the Numerical Analysis sequence (Math 451-Math 452-Math 453)
offered at Cal Poly San Luis Obispo, and it complements itself the topics
covered in Math 451. In particular, the following topics (not necessarily
in the order listed) will be covered: Finite difference schemes for
steady-state boundary value problems, numerical methods for ordinary
differential equations (ODEs) as well as methods for initial and boundary
value problems (IVPs and IBVPs, respectively) containing partial differential
equations (PDEs). The use of MATLAB will be adopted in this
class where practical implementations of the methods discussed in this course
will be presented.
Course Instructor: Dr. Stathis Charalampidis
- Section 1 (MTRF) 7:10-8:00am (Zoom ID and password was sent via e-mail)
Class Material by Topic:
- Finite Difference approximations
- Steady states, i.e., time-independent solutions and BVPs
- Elliptic equations
- Iterative methods for sparse linear systems (review)
- IVPs for ordinary differential equations
- Convergence and zero as well as absolute stability for ODEs
- Diffusion equations and parabolic problems
- Advection equations and hyperbolic systems
Please click here for the complete course syllabus. Make sure you make copies of the syllabus bring it with you in class. A very tentative schedule is as follows:
- Week of 3/29: Finite Difference Approximations (Chapter 1).
- Week of 4/5: Steady States and BVPs (Chapter 2).
- Week of 4/12: Elliptic equations (Chapter 3); Iterative methods for sparse linear systems (Chapter 4, review).
- Week of 4/19: IVPs for ODEs (Chapter 5).
- Week of 4/26: Zero Stability for ODEs (Chapter 6).
- Week of 5/3: Absolute Stability for ODEs (Chapter 7).
- Week of 5/10: Stiff ODEs (Chapter 8, briefly); Diffusion equations, part I (Chapter 9).
- Week of 5/17: Diffusion equations, part II (Chapter 9).
- Week of 5/24: Advection equations, part I (Chapter 10).
- Week of 5/31: Advection equations, part II (Chapter 10).
Please visit the Canvas page for the course for a complete list of homework assignments.
MATLAB links and tutorials:
- Access to MATLAB at Cal Poly: Click here in order to download and install MATLAB.
Here are a few PDF files and links for help with MATLAB:
- MATLAB Basics Tutorial
- MATLAB Primer and its PDF version (by Kermit Sigmon)
- MATLAB Tutorial (PDF) (by Peter Turner of Clarkson University)
- MATLAB Tutorial (PDF) (by Monica Nitsche of the University of New Mexico)
- MATLAB Tutorial (PDF) (by Kendall Atkinson of Iowa State University)
- MATLAB Plotting Guide (PDF) (from MSCC, University of Washington, 1996)
- MATLAB Help Desk at the MathWorks site.
For your convenience, links for the academic calendar are included in this section: