Lower Division
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. Semester offered: Fall
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. Semester offered: Spring
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. Note: GEEN 1350, a 1-credit lab, is available for students who would like more practice working calculus problems in a group learning environment. Prereqs., 2 years of high school algebra, 1 year geometry, and 1/2 year of trigonometry; or approval by faculty advisor. Students with credit in APPM 1350 may not receive credit for MATH 1080, 1081, 1090, 1100, 1300, 1310, APPM 1345, or ECON 1088. 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. Students may not receive credit for both APPM 1360 and MATH 2300. Prereq., APPM 1350 or MATH 1300, with a grade of C- or better.
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.
APPM 1720-3. Programming and Simulation Development
Students learn to plan, develop, and test applications (games, simulations, and animations) that embody mathematical formulations of problems in areas such as transportation, nutrition, and alternative energy. Prereq., APPM 1710 or knowledge of an object-oriented programming language.
APPM 2350-4. Calculus 3 for Engineers.
Covers multivariable calculus, vector analysis, and theorems of Gauss, Green, and Stokes. Students may not receive credit for APPM 2350 and MATH 2400. Prereq., APPM 1360 or MATH 2300, with a grade of C- or better.
APPM 2360-4. Introduction to Ordinary 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. No credit is awarded to students already having credit in both MATH 3130 and 4430, both APPM 3310 and MATH 4430, or APPM 2380. Prereq., APPM 1360 or MATH 2300, with a grade of C- or better.
APPM 2450-1. Calculus 3 Computer Lab.
Selected topics in analytic geometry and calculus with a focus on symbolic computation using Mathematica, or Matlab. Coreq., APPM 2350
APPM 2460-1. Differential Equations Computer Lab.
Selected topics include differential equations and linear algebra, with a focus on symbolic computation using Mathematica, or Matlab. Coreq., APPM 2360.
APPM 2750-4. Java: Training and Mathematical Algorithms.
Designed for students familiar with object-oriented concepts. Learn to create Java applets and applications, create graphics context, 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., some programming experience, Calc 1 and concurrent enrollment in Calc 2.
Upper Division
APPM 3010-3. An Introduction to Nonlinear Systems: Chaos.
Both majors and minors in the physical sciences are introduced to classes of tools that are useful in the analysis of nonlinear systems. Prereq. APPM 1360 and 2360. Semester offered: Fall.
APPM 3050-3. Scientific Computing 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, accuracy of algorithms. The problem sets are application-oriented with examples taken from orbital mechanics, physics, genetics and fluid dynamics. Prereq. APPM 1360 and 2360. Semester offered: Spring.
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. Prereq. or coreq., APPM 3310. Semester offered: Fall.
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. Semester offered: Fall and Spring.
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. Students may not receive credit for both APPM 3570 and either ECEN 3810 or MATH 4510. Semester offered: Spring.
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 4120/5120. Semester offered: Spring.
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, 2360, or 2380 with a minimum grade of C-. Coreq., APPM 3310. Same as APPM 5350. Semester offered: Fall.
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, Teimann-Hilbert boundary-value problems, conformal mapping to ideal flow and/or electrostatics. Prereqs., APPM 2350 and 2360 with a minimum grade of C-. Coreq., APPM 3310. Same as APPM 5360. Semester offered: Spring.
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 can include: GPS navigation, medical imaging, ocean waves, computerized facial recognition. Prereqs., APPM 2350 and 2360. Recommended prereqs., APPM 3310, 4350, and 4650. Same as APPM 5380. Semester offered: Fall.
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. Semester offered: Spring.
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, Reimann sums, and integration, Taylor and power series and sequences of functions. Prereq., APPM 2350 and 2360. Semester offered: Fall
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. Prereq. APPM 2350 and APPM 2360. Semester offered: Spring
APPM 4520-3. Introduction to Mathematics 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. Prereqs., MATH 4510 or APPM 3570. Same as APPM 5520, MATH 4520/5520. Semester offered: Fall and Spring.
APPM 4540-3. Introduction of 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. Semester offered: Spring.
APPM 4560-3. Markov Processes, Queues, and Monte Carlo Simulations.
Brief review of conditional probability and expectation followed by a study of Markov chains, both discrete and continuous time. Queuing theory, terminology, and single queue systems are studied with some introduction to networks of queues. Uses Monte Carlo simulation of random variables throughout the semester to gain insight into the processes under study. Prereq., APPM 3570 or equivalent. Same as APPM 5560. Semester offered: Fall.
APPM 4570-3. Statistical Methods.
Covers discrete and continuous probability laws, random variables; expectations; laws of large numbers and central limit theorem; estimation, testing hypothesis, analysis of variance, regression analysis, and nonparametric methods. Emphasizes applications with an introduction to packaged computer programs. Prereq., APPM 1360 or equivalent Calc 2 course. Same as APPM 5570. Semester offered: Fall and Spring.
APPM 4580-3. Statistical Applications: Software and Methods.
Combines statistical methods with practical applications and computer software. Develops commonly used statistical models such as analysis of variance as well as linear and logistic regression. The statistical models are implemented and interpreted in the context of actual data sets using available statistical software. Prereq., APPM 4570 or any course in statistics. Same as APPM 5580. Semester offered: Spring.
APPM 4650-3. Intermediate Numerical Analysis 1.
Focuses on numerical solution of nonlinear equations, interpolation, methods in numerical integration, numerical solution of linear systems, and matrix eigenvalue problems. Stresses significant computer applications and software. Prereqs., APPM 3310 or MATH 3130 and knowledge of a programming language. Same as MATH 4650. Semester offered: Fall, Spring and Summer.
APPM 4660-3. Intermediate Numerical Analysis 2.
Continuation of 4650. Examines numerical solution of initial-value problems, and two-point boundary-value problems for ordinary partial differential equations. Also looks at numerical methods for solving partial differential equations. Prereq., APPM 4650 and knowledge of a programming language. Same as MATH 4660. Semester offered: Spring.
APPM 4720 (1-3). Open Topics in Applied Mathematics.
Provides a vehicle for the development and presentation of new topics that may be incorporated into the core courses in applied mathematics. Prereqs., variable, depending on topic -- see instructor. Same as APPM 5720. Semester offered: Varies.
APPM 4840 (1-3). Reading and Research in Applied Mathematics.
Introduces undergraduate students to the research foci of the Department of Applied Mathematics. May be repeated up to 9 total credit hours. Prereq., APPM 3310 or MATH 3130. Recommended prereq., a course in ordinary or partial differential equations. Semester offered: Fall, Spring and Summer.
APPM 4950 (1-3) Seminar in Applied Mathematics.
Introduces undergraduate students to the research foci of the Department of Applied Mathematics. It is also designed to be a capstone experience for the program’s majors. Prereq., APPM 3310 or MATH 3130. Recommended prereq., course in ordinary or partial differential equations. Similar to APPM 4955. Semester offered: Fall and Spring.