MATH 37A: Differential EquationsInstructor: Denis Patterson Prerequisites: MATH 15a or 22a and MATH 20a or 22b. Course Description: Differential equations is an essential topic in applied mathematics as many (if not most) important models in the physical and social sciences are expressed as differential equations. However, most practically useful differential equation-based models do not omit solutions that can be expressed in terms of elementary functions. Thus we typically try to classify solutions in terms of their key properties. For instance, what is the long-run behavior of the solutions to a given equation? Is there a unique solution? How does the behavior of the solution change as parameters are varied? This course will introduce students to the core techniques needed to qualitatively analyze the solutions of simple differential equations in low dimensions. Since it is often useful to compute numerical approximations to solutions we will also cover some basic techniques to numerically solve differential equations.We will illustrate our techniques by analyzing models from a variety of applied fields such as population dynamics, epidemiology (the SIR model), physics (Hooke's Law) and ecology (vegetation models from my own research).The main topics of the course will be: 1. First order DEs, 2. First order systems, 3. Linear systems, 4. Oscillations, 5. Nonlinear systems. Additionally, we will discuss and implement some simple schemes to solve differential equations numerically - these lessons will be integrated into the main topics. Session: Session II Day: M, T, W, Th Time: 11:10am - 1:10pm Credit Hours: 4 Credits Course Format: 2424 Brandeis Graduation Requirement Fulfilled: SN Enrollment Limit: Course Classification: Undergraduate Level Course Course Tuition: $3,050 (+$50 Once per summer Registration Fee) Course Fees: None Open to High School Students: No |
