# Courses

## APPM-1340 (3) Calculus 1 with Algebra, Part A

Studies selected topics in analytical geometry and calculus: rates of change of functions, limits, derivatives and their applications. APPM 1340-1345 together are equivalent to APPM 1350. The sequence APPM 1340-1345 is specifically designed for students whose manipulative skills in the techniques of high school algebra and precalculus may be inadequate for APPM 1350. Prereqs., 2 years high school algebra, 1 year geometry, 1 semester trigonometry. Credit not granted for this course and MATH 1150.

## APPM-1345 (3) Calculus 1 with Algebra, Part B

Continuation of APPM 1340. Studies selected topics in calculus: derivatives and their applications, integration, differentiation and integration of transcendental functions. Algebraic and trigonometric topics are studied throughout, as needed. Prereq., APPM 1340. Credit not granted for this course and APPM 1350 or MATH 1300.

## APPM-1350 (4) Calculus 1 for Engineers

Topics in analytical geometry and calculus including limits, rates of change of functions, derivatives and integrals of algebraic and transcendental functions, applications of differentiations and integration. Prereqs., 2 years high school algebra, 1 year geometry, and 1/2 year trigonometry; or approval by faculty advisor. Credit not granted for this course and MATH 1080, 1081, 1090, 1100, 1300, 1310, APPM 1345, or ECON 1088. Approved for GT-MA1. Approved for arts and sciences core curriculum: quantitative reasoning and mathematical skills.

## APPM-1360 (4) Calculus 2 for Engineers

Continuation of APPM 1350. Focuses on applications of the definite integral, methods of integration, improper integrals, Taylor's theorem, and infinite series. Prereqs., APPM 1350 or MATH 1300 (min. grade C-). Credit not granted for this course and MATH 2300.

## APPM-1710 (3) Tools and Methods for Engineering Computing

Designed for students with little or no programming background. Students learn procedural and object-oriented programming through development of games, simulations, and animations using Flash/ActionScript, VB/Excel, Java, MATLAB, and real-world applications. Activities are oriented toward smaller projects that address topics in beginning science, engineering, and mathematics courses. Students gain practical, applicable skills. Same as ATLS 1710.

## APPM-2350 (4) Calculus 3 for Engineers

Covers multivariable calculus, vector analysis, and theorems of Gauss, Green, and Stokes. Prereq., APPM 1360 or MATH 2300 (min. grade C-). Credit not granted for this course and MATH 2400.

## APPM-2360 (4) Introduction to Differential Equations with Linear Algebra

Introduces ordinary differential equations, systems of linear equations, matrices, determinants, vector spaces, linear transformations, and systems of linear differential equations. Prereq., APPM 1360 or MATH 2300 (min. grade C-). Credit not granted for this course and both MATH 3130 and 4430.

## APPM-2450 (1) Calculus 3 Computer Lab

Selected topics in analytic geometry and calculus with a focus on symbolic computation using Mathematica. Coreq., APPM 2350.

## APPM-2460 (1) Differential Equations Computer Lab

Selected topics in differential equations and linear algebra with a focus on symbolic computation using Mathematica. Coreq., APPM 2360.

## APPM-2750 (4) Java: Training, Mathematical Algorithms, and Mobile Apps

Preparatory course for Java programming. Provides necessary background for Java language: basic object-oriented concepts, analysis, and design. Learn to create Java applets, applications and mobile apps, create graphic context, and identify the key features of Java foundation classes as well as other Java-related technology. Material is taught in the context of mathematical algorithms from calculus. Prereqs., APPM 1350 and programming experience. Recommended prereq., APPM 1360.

## APPM-3010 (3) An Introduction to Nonlinear Systems: Chaos

Both majors and minors in the physical sciences are introduced to classes of tools useful in the analysis of nonlinear systems. Prereqs., APPM 1360 and 2360.

## APPM-3050 (3) Scientific Computing in Matlab

Topics covered include: approximations in computing, computer arithmetic, interpolation, matrix computations, nonlinear equations, optimization, and initial-value problems with emphasis on the computational cost, efficiency, and accuracy of algorithms. The problem sets are application-oriented with examples taken from orbital mechanics, physics, genetics, and fluid dynamics. Prereqs., APPM 1360 and 2360.

## APPM-3170 (3) Discrete Applied Mathematics

Emphasizes selected applications of graph theory to computer science, engineering, operations research, social sciences, and biology. Topics include the basic properties of graphs and diagraphs, and their matrix representations. Relates graph properties to applications such as scheduling, architecture of parallel processors, gray codes, traveling salesman problems, and assignment problems. Coreq., APPM 2350 or 2360 and some knowledge of matrix algebra.

## APPM-3310 (3) Matrix Methods and Applications

Introduces linear algebra and matrices, with an emphasis on applications, including methods to solve systems of linear algebraic and linear ordinary differential equations. Discusses vector space concepts, decomposition theorems, and eigenvalue problems. Credit not granted for this course and MATH 3130. Prereq., APPM 2350 or 2360.

## APPM-3350 (3) Advanced Engineering Calculus

Extends the treatment of engineering mathematics beyond the topics covered in Calculus 3 and differential equations. Topics include non-dimensionalization, elementary asymptotics and perturbation theory, Reynold's transport theorem and extensions of Leibnitz's rule, as applied to continuum conservation equations, Hamiltonian formulations, Legendre and Laplace transforms, special functions and their orthogonality properties. Prereq., APPM 2350 and 2360 or equivalent.

## APPM-3570 (3) Applied Probability

Studies axioms, counting formulas, conditional probability, independence, random variables, continuous and discrete distribution, expectation, moment generating functions, law of large numbers, central limit theorem, Poisson process, and multivariate Gaussian distribution. Prereq., APPM 2350 or MATH 2400. Credit not granted for this course and ECEN 3810 or MATH 4510.

## APPM-4120 (3) Introduction to Operations Research

Studies linear and nonlinear programming, the simplex method, duality, sensitivity, transportation and network flow problems, some constrained and unconstrained optimization theory, and the Kuhn-Tucker conditions, as time permits. Prereqs., APPM 3310 or MATH 3130. Same as APPM 5120 and MATH 4120.

## APPM-4350 (3) Methods in Applied Mathematics: Fourier Series and Boundary Value Problems

Reviews ordinary differential equations, including solutions by Fourier series. Physical derivation of the classical linear partial differential equations (heat, wave, and Laplace equations). Solution of these equations via separation of variables, with Fourier series, Fourier integrals, and more general eigenfunction expansions. Prereqs., APPM 2350 and 2360 (min. grade C-). Coreq., APPM 3310. Same as APPM 5350.

## APPM-4360 (3) Methods in Applied Mathematics: Complex Variables and Applications

Introduces methods of complex variables, contour integration, and theory of residues. Applications include solving partial differential equations by transform methods, Fourier and Laplace transforms, and Reimann-Hilbert boundary-value problems, conformal mapping to ideal fluid flow and/or electrostatics. Prereqs., APPM 2350 and 2360, or 3310 (min. grade C-) or instructor consent. Same as APPM 5360.

## APPM-4380 (3) Modeling in Applied Mathematics

An exposition of a variety of mathematical models arising in the physical and biological sciences. Students' modeling projects are presented in class. Topics may include: GPS navigation, medical imaging, ocean waves, and computerized facial recognition. Prereqs., APPM 2350 and 2360. Recommended prereqs., APPM 3310, 4350 and 4650. Same as APPM 5380.

## APPM-4390 (3) Modeling in Mathematical Biology

Investigates how complex systems in biology can be studied using applied mathematics. Examines several case studies which include topics from microbiology, enzyme reaction kinetics, neuroscience, ecology, epidemiology, physiology, and bioengineering. Coreq., APPM 4350 or instructor consent. Same as APPM 5390.

## APPM-4440 (3) Undergraduate Applied Analysis 1

Provides a rigorous treatment of topics covered in Calculus 1 and 2. Topics include convergent sequences; continuous functions; differentiable functions; Darboux sums, Riemann sums, and integration; Taylor and power series and sequences of functions. Prereq., APPM 2350 and 2360 or equivalent. Coreq., APPM 3310.

## APPM-4450 (3) Undergraduate Applied Analysis 2

Continuation of APPM 4440. Study of multidimensional analysis including n-dimensional Euclidean space, continuity and uniform continuity of functions of several variables, differentiation, linear and nonlinear approximation, inverse function and implicit function theorems, and a short introduction to metric spaces. Prereqs., APPM 2350, 2360, and 4440.

## APPM-4520 (3) Introduction to Mathematical Statistics

Examines point and confidence interval estimation. Principles of maximum likelihood, sufficiency, and completeness; tests of simple and composite hypotheses, linear models, and multiple regression analysis. Analyzes variance distribution-free methods. Prereq., MATH 4510 or APPM 3570. Same as APPM 5520 and MATH 4520.

## APPM-4540 (3) Introduction to Time Series

Single and multivariable regression, forecasting using regression models, time series models, and modeling with MA, AR, ARMA, and ARIMA models, forecasting with time series models, and spectral analysis. Prereqs., APPM 3570 or MATH 4510, and APPM 4520 or MATH 4520. Same as APPM 5540 and MATH 4540.