An introduction to the theory of ordinary differential equation and their applications. Topics will include analytical and qualitative methods for analyzing first-order differential equations, second-order differential equations, and systems of differential equations. Examples of analytical methods for finding solutions to differential equations include separation of variables, variation of parameters, and Laplace transforms. Examples of qualitative methods include equilibria, stability analysis, and bifurcation analysis, as well as phase portraits of both linear and nonlinear equations and systems.
Theory, development, and evaluation of algorithms for mathematical problem solving by computation. Topics will be chosen from the following: interpolation, function approximation, numerical integration and differentiation, numerical solution of nonlinear equations, systems of linear equations, and differential equations. Treatment of each topic will involve error analysis.