Applied Mathematics

Covers the fundamental concepts necessary for success in engineering courses and Applied Mathemtics courses.

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.

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

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.

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 1110 or equivalent and Engineering Undergraduate.

Special topics in applied mathematics

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.

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).

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.

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.

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 equivalent and APMA 2130 or equivalent and Engineering Undergraduate

This course uses a Case-Study approach to teach statistical techniques with R: confidence intervals, hypotheses tests, regression, and anova. Also, it covers major statistical learning techniques for both supervised and unsupervised learning. Supervised learning topics cover regression and classification, and unsupervised learning topics cover clustering & principal component analysis. Prior basic statistic skills are needed. Prerequisite: Engineering Undergraduate and APMA 3100 or APMA 3110.

Topics include analytic functions, Cauchy Theorems and formulas, power series, Taylor and Laurent series, complex integration, residue theorem, conformal mapping, and Laplace transforms. Prerequisite: APMA 2120 or MATH 2310 or APMA 2512 - Honors Engineering Mathematics II.

Applies mathematical techniques to special problems of current interest. Topic for each semester are announced at the time of course enrollment.

Reading and research under the direction of a faculty member. Prerequisite: Fourth-year standing.

Introduces techniques used in obtaining numerical solutions, emphasizing error estimation. Includes approximation and integration of functions, and solution of algebraic and differential equations. Prerequisite: Two years of college mathematics, including some linear algebra and differential equations, and the ability to write computer programs in any language.

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.

Further and deeper understanding of partial differential equations that govern physical phenomena in science and engineering. Solution of linear partial differential equations by eigenfunction expansion techniques. Green's functions for time-independent and time-dependent boundary value problems. Fourier transform methods, and Laplace transform methods. Solution of a variety of initial-value, boundary-value problems. Various physical applications. Study of complex variable theory. Functions of a complex variable, and complex integral calculus, Taylor series, Laurent series, and the residue theorem, and various applications. Serious work and efforts in the further development of analytical skills and expertise. Cross-listed as MAE 6420. Prerequisite: Graduate standing and APMA 6410 or equivalent.

Analyzes the role of statistics in science; hypothesis tests of significance; confidence intervals; design of experiments; regression; correlation analysis; analysis of variance; and introduction to statistical computing with statistical software libraries. Prerequisite: Admission to graduate studies.

Topics vary from year to year and are selected to fill special needs of graduate students.

For master's students.

For doctoral students.