Applied Mathematics

APMA 101 - (4) (S)
Calculus I
The concepts of differential and integral calculus are developed and applied to the elementary functions of a single variable. Applications are made to problems in analytic geometry and elementary physics.

APMA 102 - (4) (S)
Calculus II
Prerequisite: APMA 101 or equivalent
A continuation of APMA 101. Topics include vectors in the plane and in three-space; techniques of integration; indeterminate forms; polar coordinates; infinite series; and solid analytic geometry.

APMA 103 - (4) (Y)
Calculus II
Prerequisite: Advanced standing, advanced placement, or permission of instructor
Course material is equivalent to APMA 102.

APMA 202 - (3) (Y)
Discrete Mathematics I
Prerequisites: APMA 102 and CS 101, or equivalent
Introduction to discrete mathematics and proof techniques involving first order predicate logic and induction. Application areas include sets (finite and infinite, such as, sets of strings over a finite alphabet), elementary combinatorial problems, and finite state automata. Development of tools and mechanisms for reasoning about discrete problems. Cross-listed as CS 202.

APMA 205 - (4) (S)
Calculus III
Prerequisite: APMA 102 or equivalent
Multivariable calculus including partial differentiation, multiple integrals, line integrals, the divergence theorem, and Stokes theorem. Introduction to linear algebra.

APMA 206 - (4) (S)
Differential Equations I
Prerequisites: APMA 102, APMA 205
Introduction to ordinary differential equations, systems of ordinary differential equations, Laplace transforms, and applications.

APMA 302 - (3) (Y)
Discrete Mathematics II
Prerequisites: APMA/CS 202 or equivalent
Analysis of the continuation of APMA 202 consisting of topics in combinatorics, including recurrence relations and generating functions. An introduction to graph theory, including connectivity properties; and Eulerian and Hamiltonian graphs, spanning trees and shortest path problems. Cross-listed as CS 302.

APMA 308 - (3) (Y)
Linear Algebra
Prerequisites: APMA 205 and APMA 206, or equivalent
Analysis of the systems of linear equations; vector spaces; linear dependence; bases; dimension; linear mappings; matrices; determinants; quadratic forms; eigenvalues; orthogonal reduction to diagonal form; and geometric applications.

APMA 310 - (3) (S)
Probability
Prerequisites: APMA 205 or equivalent
A calculus-based introduction to probability theory and its applications in engineering and applied science. Topics include: counting techniques, conditional probability, independence, discrete and continuous random variables, expected value and variance, joint distributions, covariance, correlation, Central Limit theorem, an introduction to stochastic processes.

APMA 312 - (3) (Y)
Statistics
Prerequisites: APMA 310 or equivalent
Topics include confidence interval and point estimation methods, hypothesis testing for single samples, inference procedures for single-sample and two-sample studies, single and multifactor analysis of variance techniques, linear and non-linear regression and correlation, and the use of computer software Minitab for large data sets.

APMA 315 - (3) (Y)
Vector Calculus and Complex Variables
Prerequisite: Two years of undergraduate mathematics
Analysis of plane and three-dimensional curves; directional derivative; gradient; line integrals; conservative force fields; surface and volume integrals; divergence and Stokes' theorems; the geometry and algebra of complex numbers; the exponential, logarithm; and other elementary functions; analytic functions; the Cauchy-Riemann equations; Laplace's equation; fluid flow; contour integrals; Cauchy's theorem and integral formula; the residue theorem; Laurent's expansion; and the evaluation of real-valued, definite integrals.

APMA 341 - (3) (S)
Differential Equations II
Prerequisites: APMA 205, APMA 206 or equivalents
Analysis of the derivation of equations governing physical phenomena; solution of partial differential equations by separation of variables; superposition; Fourier series; variation of parameters; and d'Alembert's solution.

APMA 484 - (3) (Y)
Mathematical Models
Prerequisite: APMA 206; corequisite: APMA 310
The mathematical formulation of problems arising in science, engineering, and social sciences; solutions of simplified formulations and their relation to the exact solution. The specific problems utilized will depend on the interest of the instructor and the students. The course introduces and uses MATHEMATICA.

APMA 495, 496 - (3) (Y)
Independent Reading and Research
Prerequisite: Fourth-year standing
Reading and research under the direction of a faculty member.

APMA 507 - (3) (Y)
Numerical Methods
Prerequisite: Two years of college mathematics, including some linear
algebra and differential equations, and the ability to write computer programs in any language Introduction to techniques used in obtaining numerical solutions, with emphasis on error estimation. Areas of application studied include approximation and integration of functions, solution of algebraic and differential equations.

APMA 513 - (3) (Y)
Vector Calculus and Complex Variables
Prerequisite: Two years of undergraduate mathematics
Analysis of plane and three-dimensional curves; directional derivative; gradient; line integrals; conservative force fields; surface and volume integrals; divergence and Stokes' theorems; the geometry and algebra of complex numbers; the exponential, logarithm, and other elementary functions; analytic functions; the Cauchy-Riemann equations; Laplace's equation; fluid flow; contour integrals; Cauchy's theorem and integral formula; the residue theorem; Laurent's expansion; and the evaluation of real-valued, definite integrals.

APMA 541 - (3) (Y-SS)
Engineering Mathematics
Prerequisite: Four semesters of calculus including ordinary differential equations
Solution of the heat, potential, and wave equations in rectangular and polar coordinates. Separation of variables and eigenfunction expansion techniques for nonhomogeneous boundary-value problems.

Note  Courses at the 600 level and above are listed in the Graduate Record.

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