This course will cover the theory of ordinary differential equations, using qualitative, analytical and numerical methods, and the textbook Differential Equations by Blanchard, Devaney, and Hall, 4th Ed. We will begin with the study of single variable equations, introducing slope fields, stability theory, separation of variables, Euler's method, and solving initial value problems. We will then develop the theory of linear systems in two dimensions, covering vector fields, fixed point stability analysis, eigenvalues and eigenvectors, and analytical solutions, with discussions of how this theory extends to n dimensions. Nonlinear dynamics, including chaotic systems, will be discussed using qualitative techniques such as phase plane analysis and linearization of fixed points via Jacobian matrices. There will be 2 hours of lecture and 2 hours of computer lab per week, with an expectation that students supplement face-to-face instruction with readings in the book, online videos, and web-based simulators.
This course is built as a supplement to the program F.U.N., Fractals Underlying Networks, as an upper-division replacement to the algebra component, but it is open to all students. It is recommended that students take this course with F.U.N. to enhance learning. Please contact the instructor for details on how to register for both programs.
Anticipated Credit Equivalencies:
4* - Differential Equations
Registration
Demonstrated success in Calculus 1 and 2
Academic Details
Preparatory for further studies in differential equations such as mathematical modeling, nonlinear dynamics, partial differential equations and numerical analysis.
Upper division science credit may be awarded in differential equations upon satisfactory completion of all assignments and demonstrated understanding of all topics covered