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. Students must have completed (APMA 2120 or MATH 2310 or MATH 2315) AND (CS 1110 or CS 1111 or CS 1112 or CS 1113 or successfully completed the CS 1110 place out test).

Advanced techniques of integration are introduced, and integration is used in physics applications like fluid force, work, and center of mass. Improper integrals and approximate integration using Simpson's Rule are also studied. Infinite series including Taylor series are studied and numerical methods involving Taylor polynomials are studied. Parametric equations and polar coordinates are introduced and applied. Complex numbers are introduced. Pre-requisite: APMA 1090 or MATH 1310

Review of ordinary differential equations, initial/boundary value problems. Linear algebra including systems of linear equations, matrices, eigenvalues, eigenvectors, diagonalization. Solution of partial differential equations that govern physical phenomena in science and engineering by separation by variables, superposition, Fourier series, variation of parameter, d'Alembert's solution. Cross-listed as APMA 6410. Prerequisite: Graduate standing.