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.

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

Includes point estimation methods, confidence intervals, hypothesis testing for one population and two populations, categorical data tests, single and multi-factor analysis of variance (ANOVA) techniques, linear and non-linear regression and correlation analysis, and non-parametric tests. Students cannot receive credit for both this course and APMA 3110. Prerequisite: APMA 3100 or MATH 3100.

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 or MATH 1320.

Introduces basic concepts of probability such as random variables, single and joint probability distributions, and the central limit theorem. The course then emphasizes applied statistics, including descriptive statistics, statistical inference, confidence intervals, hypothesis testing, correlation, linear regression, and ANOVA. Students cannot receive credit for both this course and APMA 3120. Prerequisite: APMA 2120 or equivalent.

First order differential equations, second order and higher order linear differential equations, undetermined coefficients, variation of parameters, Laplace transforms, linear systems of first order differential equations and the associated matrix theory, numerical methods. Applications. Prerequisite: APMA 2120 or equivalent.

Analyze and apply systems of linear equations; vector spaces; linear transformations; matrices; determinants; eigenvalues; eigenvectors; coordinates; diagonalization; orthogonality; projections; inner product spaces; quadratic forms; The course is both computational and applicable. MATLAB is frequently used and prior experience in MATLAB (loops, functions, arrays, conditional statements) is helpful. 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 or MATH 2310 or MATH 2315) AND (APMA 2130 or MATH 3250 or APMA 2501 topic Diff Equations & Linear Algebra)

Special topics in applied mathematics