SOLVING PARTIAL DIFFERENTIAL EQUATIONS BY FACTORING

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## Course Catalog | ## 13.04.32 Mathematics - Course DescriptionsMTH 0313 Fundamentals of Mathematics 3,0 Review of arithmetic and elementary algebra with special emphasis on problem solving. This course does not satisfy the core mathematics requirement. This course will not count toward the total number of hours required for a degree. Credit for MTH 0313 may not be earned by students who have previously received credit for MTH 0320 or a higher Math course with a grade of "C" or better. Graded on a Credit/No Credit basis. MTH 0320 Intermediate Algebra 3,0 Course content is that of a second year high school algebra course. Designed to provide preparation for core mathematics courses. This course does not satisfy the core mathematics requirements. This course will not count toward the total number of hours required for a degree. Credit for MTH 0320 may not be earned by students who have previously received credit for a higher Math course with a grade of "C" or better. Graded on a Credit/No Credit basis. Prerequisite: MTH 0313 or appropriate placement test scores in math. MTH 1323 Quantitative Literacy 3,0 Fundamental concepts of logic and mathematics are explored to develop students ability to think logically, quantitatively, and mathematically and to help them develop their problem solving abilities. Topics include logic, mathematics of finance, probability and statistics. MTH 1325 Mathematics for Liberal Arts 3,0 A survey of topics designed to broaden the mathematical knowledge of students not intending to take pre-calculus or above. Topics include problem solving, algebra, consumer mathematics, probability, statistics and matrices. ADP use only. MTH 1330 Applied Finite Math Applied Finite Mathematics is a course designed to help students develop the ability to apply arithmetic and algebra to business. Time is spent discovering and learning how to apply arithmetic and algebraic techniques to solve supply and demand, break-even, maxima-minima, etc. problems. Also the Gauss Jordan elimination method and the inverse matrix method for solving systems of linear equations are learned. A geometric method for solving linear programming problems is discovered. Also several topics of mathematics of finance, including compound interest and annuities, are discussed. Students are introduced to some of the basic concepts of probability, including the multiplication principle, permutations, combinations, sample spaces, events, empirical and theoretical probabilities, and expected value. ADP use only . MTH 1331 Finite Mathematics 3,0 Applications of algebra to business, matrices, linear programming, simplex method, and derivatives. Prerequisite: MTH 0320 or appropriate test scores on math placement exams. MTH 1332 Applied Calculus 3,0 Differential and integral calculus with emphasis on business, economics, life sciences and social sciences applications. Prerequisite: MTH 1321 or MTH 1331. MTH 1341 Probability 3,0 Topics include permutations, combinations, equally likely outcomes, conditional probability, independence and dependence, mathematical expectations, and binomial distributions. Prerequisite: Two years of high school algebra or satisfactory test scores on the math placement exams. MTH 1351 Pre-calculus I 3,0 Treatment of the concept of functions and their graphs, with emphasis on polynomial, rational, exponential and logarithmic functions. The Fundamental Theory of Algebra with application to zeros of polynomials and solutions to equations and factoring. Analytic geometry with emphasis on conic sections. Systems of equations and inequalities using matrix arithmetic. Partial fraction decomposition. Credit for MTH 1351 may not be earned by students who have previously received credit for MTH 1332 or MTH 2401 with a grade of "C" or better. Prerequisite: MTH 0320 or satisfactory scores on the mathematics placement exam. MTH 1352 Pre-calculus II 3,0 Introduction and treatment of the six trigonometric functions and their extensions to the real line. Applications to the solution of triangles and graphing of trigonometric functions. Proofs of trigonometric identities. Introduction to complex numbers, hyperbolic trig functions, and polar coordinates and curves. Sequences and series, especially arithmetic and geometrics an introduction to induction proofs and the Binomial Theorem. Prerequisite: MTH 1351. MTH 2301 Introduction to Statistics 3,0 Provides students with the methods and logic necessary to perform elementary statistical analysis. Topics may include descriptive measures, probability, sampling, theory random variables, binomial and normal distributions, estimation and hypothesis testing, analysis of variance, regression and correlation, and nonparametric methods. Prerequisite: MTH 1321 or MTH 1325, or satisfactory scores on the mathematics placement tests. MTH 2305 Discrete Structures 3,0 Discrete mathematical structures will be studied emphasizing: Semi-groups, groups, sets, trees, graphs, logic, and combinatorics, all which have computer science applications in data structure, algorithm design and algorithmic analysis and testing. Cross-listed as CSC 2305.Prerequisite: CSC 1302 or MTH 2402 or permission of the instructor. MTH 2401 Calculus I 4,0 Review of elementary analysis; concepts of limits, continuity, derivatives and integrals. Prerequisite: MTH 1351 or consent of instructor. MTH 2402 Calculus II 4,0 Extension of concepts of limits, continuity, derivatives and integrals to transcendental functions and to multivariate calculus. Prerequisite: MTH 2401. MTH 3101 Problem Solving: Algebra, Geometry and Trig 1,0 General problem solving techniques and specific problem solving strategies will be used in solving algebra, geometry, and trigonometry problems. MTH 3102 Problem Solving: Number Theory 1,0 General problem solving techniques and specific problem solving strategies will be used in solving number theory problems. MTH 3103 Problem Solving: Combinatorics 1,0 General problem solving techniques and specific problem solving strategies will be used in solving combinatorics problems. MTH 3104 Problem Solving: Miscellaneous Problems 1,0 General problem solving techniques and specific problem solving strategies will be used in miscellaneous problems including recreational problems. MTH 3301 Mathematics for Elementary Teachers I 2,2 Logic, sets, relations, functions, operations, numeration systems, and elementary number theory. Field experience required. Prerequisites: Admission to Professional Education Program or consent of instructor: MTH 1321 or equivalent. MTH 3302 Mathematics for Elementary Teachers II 2,2 Rational numbers, real numbers, informal geometry, measurement, computers, probability, and statistics. Field experience required. Prerequisite: MTH 3301. MTH 3303 Mathematics for Secondary Teachers I 2,2 Concepts from 7th and 8th grade mathematics, mathematics of finance, algebra, and geometry are examined using manipulatives. Use of mathematics in modeling our world and techniques for teaching mathematics are emphasized. MTH 3304 Mathematics for Secondary Teachers II 2,2 Concepts from geometry, probability, statistics, trigonometry, analytical geometry, discrete mathematics, and calculus. Use of mathematics in modeling our world and techniques for teaching mathematics are emphasized. MTH 3309 Numerical Analysis 3,0 Algorithms of numerical analysis are covered. Topics include floating point arithmetic, approximation, numerical integration and differentiation, solution of nonlinear equations, and solution of ordinary differential equations. Programming assignments will give experience in applying selected algorithms. Prerequisites: CSC 1302, MTH 2402. Cross-listed with CSC 3309. MTH 3311 Linear Algebra 3,0 Systems of linear equations, vector spaces, linear transformations, representation of linear transformations by matrices, matrix algebra, and determinates. Prerequisite: MTH 2401. MTH 3313 Number Theory 3,0 Divisibility, primes, congruencies, quadric reciprocity, Diophantine equations and simple continued fractions. Prerequisite: Six semester hours of mathematics at or above the level of MTH 1341, excluding MTH 2301. MTH 3315 Abstract Algebra 3,0 The basic concepts of groups, rings, integral domains, fields, isomorphism's, and group homomorphism. Prerequisite: Three semester hours of upper level mathematics. MTH 3316 Geometry 3,0 The extension of geometry concepts including the study of tessellations, transformations, isometrics, topology, and non-Euclidean geometries. Prerequisite: Six semester hours of mathematics at or above the level of MTH 1341, excluding MTH 2301. MTH 3317 Differential Equations 3,0 Methods of solution to ordinary differential equations, including exponential, complex exponential, Laurent series solutions and Laplace transforms. Applications to simple harmonic motion, mixing problems and logistic problems. Phase portrait analysis and application to predator-prey and soft-spring problems. Prerequisite: MTH 3410 Calculus III. MTH 3318 Topics in Secondary School Mathematics 3,0 Topics discussed include applications of mathematics to business statistics (basic concepts), history of mathematics, problem solving using a graphic calculator and a computer, and discrete mathematics (introduction). Prerequisite: MTH 2402 Calculus II. MTH 3325 Real Analysis 3,0 Construction of the real numbers and rigorous study of their properties, including topological considerations, limits of sequences, continuity and differentiation of functions, the Riemann and Lebesgue integrals, and the topologies of function spaces. Prerequisite: MTH 3410 Calculus III and one other 3000-level mathematics course. MTH 3330 Introduction to Modeling 3,0 Design and application of modeling techniques using system dynamics and computer software. Prerequisites: MTH 1321 or higher, completion of computer literacy requirements (CIS 2304 recommended), and 6-8 semester hours of natural science and/or math beyond the core requirements. This course may not be used to satisfy natural science or math core requirements. Cross listed as SCI 3330. MTH 3410 Calculus III 4,0 Convergence properties of infinite series and power series, the calculus and geometry of vector-valued functions, the calculus and geometry of multi-variable functions, Divergence Theorem, Green's Theorem and Stokes' Theorem. Prerequisite MTH 2402 Calculus II. MTH 3412 Advanced Calculus for Applications 4,0 Infinite series, ordinary differential equations, practical differential equations, partial differential equations, and Fourier series. Prerequisite: MTH 2402. MTH 4310 Cryptology 3,0 Applications to abstract algebraic and number theoretic concepts to the science of secure cryptography. Topics include historical ciphers, public-key cryptography, signed messages, secure protocols, and cryptanalysis, especially as these deal with electronic communications. Prerequisite: MTH 3313 Number Theory or MTH 3315 Abstract Algebra and the ability to code algorithms in a computer language.
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