MATH 323(3230) Introduction to Differential Equations (MQR)
Fall. 4 credits. Prerequisites: multivariable calculus and linear algebra (e.g., MATH 221 222, 223 224, or 192 and 294), or permission of instructor.
Intended for students who want a one-semester introduction to the theory and techniques of both ordinary and partial differential equations. Topics for ordinary differential equations include initial-value and two-point boundary value problems, the basic existence and uniqueness theorems, continuous dependence on data, stability of fix-points, numerical methods, special functions. Topics for partial differential equations include the Poisson, heat and wave equations, boundary and initial-boundary value problems, maximum principles, continuous dependence on data, separation of variables, Fourier series, Green's functions, numerical methods, transform methods.
MATH 293(2930) Differential Equations for Engineers (MQR)
Fall, spring, summer. 4 credits. Prerequisite: MATH 192. Taking MATH 293 and 294 simultaneously is not recommended.
Introduction to ordinary and partial differential equations. Topics include: first-order equations (separable, linear, homogeneous, exact); mathematical modeling (e.g., population growth, terminal velocity); qualitative methods (slope fields, phase plots, equilibria, and stability); numerical methods; second-order equations (method of undetermined coefficients, application to oscillations and resonance, boundary-value problems and eigenvalues); Fourier series; linear partial differential equations (heat flow, waves, the Laplace equation); and linear systems of ordinary differential equations.
MATH 4200 Differential Equations and Dynamical Systems (MQR)
Fall. 4 credits. Prerequisite: high level of performance in MATH 2210–2220, 2230–2240, 1920 and 2940, or permission of instructor.
Covers ordinary differential equations in one and higher dimensions: qualitative, analytic, and numerical methods. Emphasis is on differential equations as models and the implications of the theory for the behavior of the system being modeled and includes an introduction to bifurcations.
MATH 428(4280) Introduction to Partial Differential Equations (MQR)
Spring. 4 credits. Prerequisite: MATH 221 222, 223 224, or 192 and 294, or permission of instructor.
Topics are selected from first-order quasilinear equations, classification of second-order equations, with emphasis on maximum principles, existence, uniqueness, stability, Fourier series methods, approximation methods.