MR

Unit: School of Engineering and Applied Science

Department: Department of Engineering and Society

##### Office location and address

Small Hall, 112

156 Engineer's Way

Charlottesville,
Virginia
22903
##### Biography

Megan Ryals joined the Applied Mathematics faculty in 2017 as an Assistant Professor. She received her masters degree in mathematics (2003) and Ph.D. in mathematics education (2014) from North Carolina State University. Her research focused on studentsâ€™ transition from high school to college calculus. Prior to joining UVa, Dr. Ryalsworked for 14 years supervising and training undergraduate math and science tutors and teaching undergraduate mathematics, which motivates her current research interests in math resource centers.

##### Publications

##### Courses

Credits: 4

The concepts of differential and integral calculus are developed and applied to the elementary functions of a single variable. Limits, rates of change, derivatives, and integrals. Applications are made to problems in analytic geometry and elementary physics. For students with no exposure to high school calculus.

Credits: 4

Includes the concepts of differential and integral calculus and applications to problems in geometry and elementary physics, including inverse functions, indeterminate forms, techniques of integration, parametric equations, polar coordinates, infinite series, including Taylor and Maclaurin series. Applications. Prerequisite: APMA 1090 or equivalent.

Credits: 4

A second calculus course for natural-science majors, students planning additional work in mathematics, and students intending to pursue graduate work in the applied social sciences. Topics include applications of the integral, techniques of integration, differential equations, infinite series, parametric equations, and polar coordinates. Prerequisite: MATH 1310 or equivalent; at most one of MATH 1220 and MATH 1320 may be taken for credit.

Credits: 4

Topics include vectors in three-space and vector valued functions. The multivariate calculus, including partial differentiation, multiple integrals, line and surface integrals, and the vector calculus, including Green's theorem, the divergence theorem, and Stokes's theorem. Applications. Prerequisite: APMA 1110.

Credits: 4

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.

Credits: 3

A calculus-based introduction to probability theory and its applications in engineering and applied science. Includes counting techniques, conditional probability, independence, discrete and continuous random variables, probability distribution functions, expected value and variance, joint distributions, covariance, correlation, the Central Limit theorem, the Poisson process, an introduction to statistical inference. Prerequisite: APMA 2120 or equivalent.

Credits: 3

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.

Credits: 1–12

For master's students.

Credits: 1–12

For doctoral students.