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MATH 4460: Partial Differential Equations
3.00 Credits
The University of Tennessee at Chattanooga
Classification and derivation of some elementary partial differential equations arising in applications. Separation of variables, Sturm-Liouville problems and orthogonality, Fourier Series. Diffusion, wave, and Laplace’s equations in various coordinate systems with various boundary and initial conditions. Laplace transform methods and D’Alembert’s solution. First order equations and weak solutions. On demand. Prerequisites: MATH 2450, MATH 2550 with minimum grades of C or department head approval.
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MATH 4460 - Partial Differential Equations
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MATH 450: Modern Analysis
3.00 Credits
The University of Tennessee at Chattanooga
Differentiation; inverse and implicit function theorems; functions of bounded variation. Integration and measure; integration on manifolds; Stokes' and Green'sTheorems; other selected topics. On demand. Prerequisite: Mathematics 350 with a minimum grade of C.
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MATH 450 - Modern Analysis
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MATH 4500: Modern Analysis
3.00 Credits
The University of Tennessee at Chattanooga
Differentiation; inverse and implicit function theorems; functions of bounded variation. Integration and measure; integration on manifolds; Stokes’ and Green’s Theorems; other selected topics. On demand.
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MATH 4500 - Modern Analysis
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MATH 4510: Introduction to Analysis II
3.00 Credits
The University of Tennessee at Chattanooga
Rigorous development of the derivative, the definite integral, sequences and series of functions, and improper integrals.
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MATH 4510 - Introduction to Analysis II
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MATH 452: Basic Concepts of Geometry
3.00 Credits
The University of Tennessee at Chattanooga
Deficiencies in Euclidean geometry, Euclid's parallel postulate, introduction to non-Euclidean geometry, consistency and validity of non-Euclidean geometry, incidence geometries, affine geometries, linear, planar, and spatial order properties. Prerequisite: Mathematics 300 with a minimum grade of C, or approval of the Mathematics Department Head.
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MATH 452 - Basic Concepts of Geometry
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MATH 454: Abstract Algebra
3.00 Credits
The University of Tennessee at Chattanooga
A study of special topics from advanced algebra, various algebraic structures, and the applications of algebra. On demand. Prerequisite: Mathematics 321 or 412 with a minimum grade of C, or approval of the Mathematics Department Head.
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MATH 454 - Abstract Algebra
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MATH 4550: Applied Analysis
3.00 Credits
The University of Tennessee at Chattanooga
Vector analysis through Stokes’ Theorem and the Divergence Theorem. Topics in advanced calculus including implicit functions, Jacobians, interchange of limit processes, and uniform convergence of series of functions; introduction to power series solutions of differential equations. Prerequisites: MATH 2450, MATH 2550 with minimum grades of C or department head approval.
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MATH 4550 - Applied Analysis
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MATH 4570: Complex Analysis
3.00 Credits
The University of Tennessee at Chattanooga
Complex numbers; differentiation and integration of functions of a complex variable; analytic functions; Cauchy’s Theorem; power series; residues and poles; conformal mapping; contour integration. Prerequisites: MATH 2450, MATH 2550 with minimum grades of C or department head approval.
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MATH 4570 - Complex Analysis
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MATH 460: Techniques of Applied Mathematics
3.00 Credits
The University of Tennessee at Chattanooga
Additional topics in vector calculus; series of orthogonal functions; integral transforms; treatment of some elementary partial differential equations arising in applications. Prerequisites: Mathematics 245, 255 with minimum grades of C.
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MATH 4600: Numerical Analysis I
3.00 Credits
The University of Tennessee at Chattanooga
Numerical solutions of equations in one variable; interpolation and polynomial approximation; numerical differentiation and integration; initial value problems for ordinary differential equations; direct methods for solving systems of linear equations. Prerequisites: MATH 2200 and MATH 2450 with minimum grades of C, and CPSC 1020 or CPSC 1100, or approval of the Mathematics Department Head.
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MATH 4600 - Numerical Analysis I
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