#### 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.

In this web page and associated links, you will find important information about Math 452 including (but not limited to) syllabus, MATLAB tutorials and important dates, among others. Note that homework problems will be uploaded on Canvas!

Course Instructor: Dr. Stathis Charalampidis

SC's Office Hours: MW: 10:30-11:30am, or by appointment
Class Meetings:

• MW: 8:10-10:00am (10-111)
Main Textbook: Finite difference methods for ordinary and partial differential equations, Authors: Randall J. LeVeque, Publisher: Society of Industrial and Applied Mathematics (SIAM), 2007.

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
Syllabus and Tentative Schedule:

• Week of 4/3: Finite Difference Approximations (Chapter 1).
• Week of 4/10: Steady States and BVPs (Chapter 2).
• Week of 4/17: Elliptic equations (Chapter 3); Iterative methods for sparse linear systems (Chapter 4, review).
• Week of 4/24: IVPs for ODEs (Chapter 5).
• Week of 5/1: Zero Stability for ODEs (Chapter 6).
• Week of 5/8: Absolute Stability for ODEs (Chapter 7).
• Week of 5/15: Stiff ODEs (Chapter 8, briefly); Diffusion equations, part I (Chapter 9).
• Week of 5/22: Diffusion equations, part II (Chapter 9).
• Week of 5/29: Advection equations, part I (Chapter 10).
• Week of 6/5: Advection equations, part II (Chapter 10).
Homework Assignments:

Please visit the Canvas page for the course for a complete list of homework assignments.