MATH 238 Differential Equations • 5 Cr.
Uses tools from algebra and calculus in solving first- and second-order linear differential equations. Students focus on applying differential equations in modeling physical situations, and using power series methods and numerical techniques when explicit solutions are unavailable. May include work with Laplace Transforms and systems of differential equations. Fulfills the quantitative or symbolic reasoning course requirement at BC. Recommended: MATH& 153.
After completing this class, students should be able to:
- Use symbolic methods to find general and particular solutions of separable differential equations and first order linear differential equations.
- Construct direction fields and phase lines, and use them, along with the existence-uniqueness theorem, to perform qualitative analysis of first order autonomous differential equations.
- Use Euler's Method to construct approximate solutions for first order differential equations.
- Use first order techniques to analyze applied situations (such as velocity-acceleration models, population models, mixing models, etc.), and construct simple models from rate-data.
- Find explicit general and particular solutions of second order, linear, homogeneous differential equations with constant coefficients.
- Use the superposition principle and the method of undetermined coefficients to find general and particular solutions of second order linear, nonhomogeneous differential equations with constant coefficients.
- Use second order techniques to analyze classical applications (such as mechanical vibrations, electrical circuits, etc.).
- Extract qualitative properties of the solutions of a second order autonomous system of first order differential equations from the phase portrait of the system, and construct the phase portrait of a second order linear autonomous system.
- Use systems techniques to analyze predator-prey models, models for competition, mechanical applications, etc.
- Use Laplace transforms to solve first and second order initial value problems.
- Use power series to construct the approximate solution of a simple nonlinear differential equation near an ordinary point.
- Distinguish between an ordinary and a partial differential equation; verify a solution of a partial differential equation; and use the separation of variables technique to solve the one dimensional wave equation or the heat equation.