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Introduction to Engineering Mathematics

Does not count toward the degree requirements in engineering Includes algebra, trigonometry, and analytic geometry, with special emphasis on graphing and attaining proficiency in the manipulation of mathematical expressions, designed to promote the mathematical maturity necessary for success in calculus.

**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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