Unit: School of Engineering and Applied Science
Department: Department of Engineering and Society
Office location and address
156 Engineer's WayCharlottesville, Virginia 22903
First order differential equations, second order and higher order linear differential equations, reduction of order, undetermined coefficients, variation of parameters, series solutions, Laplace transforms, linear systems of first order differential equations and the associated matrix theory, numerical methods. Applications. Prerequisite: APMA 2120 or equivalent.
The focus will be on solving systems of ordinary differential equations using basic linear algebra. Techniques for both homogeneous and nonhomogenous systems will be introduced. Time permitting, solving differential equations with the unit step and unit impulse functions will also be covered. Prerequisite: Differential Equations from Virginia Community College or equivalent
Examines variability and its impact on decision-making. Introduces students to basic concepts of probability, such as random variables, probability distribution functions, and the central limit theorem. Based on this foundation, the course then emphasizes applied statistics covering topics such as descriptive statistics, statistical inference, confidence intervals, hypothesis testing, correlation, regression modeling, statistical quality control. Students cannot receive credit for both this course and APMA 3120. Prerequisite: APMA 2120 or equivalent.
Partial differential equations that govern physical phenomena in science and engineering. Separation of variables, superposition, Fourier series, Sturm-Liouville eigenvalue problems, eigenfunction expansion techniques. Particular focus on the heat, wave, and Laplace partial differential equations in rectangular, cylindrical, and spherical coordinates. Prerequisites: APMA 2120 and 2130 or equivalents.
Applications of the theory presented in MATH 7310, 7320, and 7340 to specific examples in real and complex analysis. The course emphasizes problem-solving and preparation for the General Examination in Analysis. Problems are based on those from past General Exams. This course is offered in the summer and restricted to Mathematics and Graduate Arts and Science students.
For master's students.
For doctoral students.