Unit: School of Engineering and Applied Science
Department: Department of Engineering and Society
Office location and address
156 Engineer's WayCharlottesville, Virginia 22903
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.
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.
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.
Analyzes systems of linear equations; vector spaces; linear dependence; bases; dimension; linear mappings; matrices; determinants; eigenvalues; eigenvectors; coordinates; diagonalization; inner product spaces. Prerequisite: APMA 2120 or equivalent.
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.
Applies mathematical techniques to special problems of current interest. Topic for each semester are announced at the time of course enrollment.