Systems of ordinary and/or partial differential equations form the basis for nearly all mathematical models used in the physical, social and engineering sciences. Most of the equations that arise cannot be solved "by hand" and require the use of numerical (computational) methods to obtain solutions. The focus of the Math 269 series of courses is on the numerical methods used to create approximate solutions of systems of ordinary and partial differential equations.

In 269A, the principle goals consist of identifying, analyzing, and implementing the most commonly used numerical techniques to construct approximate solutions of systems of ordinary differential equations (ODE's). A variety of single step and multistep methods will be covered as well as general theoretical aspects that, when understood, help with the tasks of method selection and implementation. Methods for "stiff systems" and adaptive timestepping methods will be covered in the latter part of the quarter.

As a practicing numerical analyst, one often doesn't get to choose the software environment where an ODE solution technique is needed. To help prepare students for situations where Matlab is not the software environment in use, C++ and object oriented software techniques will be used for the computational component of this course.