# Numerical Differential Equations MAT 460 class projects: Mathematical Modeling and Numerical Simulation of Problems modeled by ODEs and PDEs

## Faculty: Andrea Dziubek

Projects of problems which can be modeled by ordinary or simple (linear or nonlinear) partial diﬀerential equations, e.g. spring-mass systems, framework, heat conduction, Bernoulli beam, wave equation, chemical reactions, data, ﬁnance.

**Course Objectives:**

Numerical methods for:

- the solution of linear equation systems (direct decomposition methods),
- the solution of nonlinear equation systems,
- polynomial interpolation,
- diﬀerentiation and integration of functions,
- discretization of ordinary and partial diﬀerential equations.

Learning how to:

- code most of these methods (in Python),
- compute the order of convergence of a method and the error between an analytic solution and the solution of the discretized problem,
- estimate the potential and limits of a method and how to choose an appropriate method for diﬀerent types of real-world problems.

A Python crash course in the ﬁrst two weeks of the semester is offered by the Learning Center and the College of Arts and Sciences.