From Syllabus:
This course is aimed at those who want to gain a practical knowledge of modern computing techniques for the numerical solution of differential equations and basic inverse problems that arise in scientific engineering applications. We will cover issues in the use and development of mathematical software when addressing initial value and boundary value problems in ODEs and PDEs. Multistep methods as well as Runge-Kutta and finite-difference methods for time-dependent problems will be examined. Convergence, order, stability and stiffness properties will be analyzed. Fixed-point iteration and Newton's method will be covered in order to solve nonlinear systems, along with a discussion of their convergence properties. A basic level of philosophical and methodological understanding of parameter estimation and inverse problems will be covered, specifically regarding such key issues as uncertainty, ill-posedness, regularization, bias, and resolution.
After taking this course students will gain:
- Knowledge in state-of-the-art numerical methods addressing problems from scientific applications.
- An understanding of the concept of stiff differential equations, stability and accuracy.
- An understanding of convergence conditions for different methods.
- An understanding of limitations and possibilities related to inverse problems.
- An understanding of the reasons why existing software succeeds or fails, while advancing skills in programming.
Taught by Prof. Brittany Erickson at University of Oregon