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Course Criteria
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4.00 Credits
An intermediate course serving to introduce both the qualitative properties of solutions of partial differential equations and methods of solution, including separation of variables. Topics include first-order equations, derivation of the classical equations of mathematical physics (wave, potential, and heat equations), method of characteristics, construction and behavior of solutions, maximum principles, energy integrals. Prerequisites/Corequisites: Prerequisite: MATH 4600 or permission of instructor. When Offered: Spring term annually. Credit Hours: 4
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4.00 Credits
Topics include differentials and derivatives of functions of several variables, Jacobians, Lagrange multipliers, line, surface and volume integrals, independence of path, curvilinear coordinates, vector calculus, calculus of variations, theorems of Green, Gauss, and Stokes. Prerequisites/Corequisites: Prerequisite: MATH 2010. When Offered: Fall and spring terms annually. Credit Hours: 4
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4.00 Credits
Mathematical formulation of models for various processes. Derivation of relevant differential equations from conservation laws and constitutive relations. Use of dimensional analysis, scaling, and elementary perturbation methods. Description of basic wave motion. Examples from areas including biology, elasticity, fluid dynamics, particle mechanics, chemistry, geophysics, and finance. Prerequisites/Corequisites: Prerequisite: MATH 2400 or equivalent. When Offered: Fall term annually. Credit Hours: 4
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4.00 Credits
An introduction to mathematics used in biology, biophysics, biomedical engineering, and medicine. The mathematical topics covered are selected from calculus, linear algebra, differential equations, numerical methods, and Fourier analysis. The biological applications covered are selected from human physiology (heart, lung, brain), population models (microorganisms, cells, animals), and the diagnosis and treatment of disease (heart, cancer). Prerequisites/Corequisites: Prerequisite: MATH 1020. When Offered: Fall term odd-numbered years. Credit Hours: 4
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4.00 Credits
This course is designed to introduce students to mathematical and computational finance. Topics include a mathematical approach to risk analysis, portfolio selection theory, futures, options and other derivative investment instruments. Finite difference and finite element methods for computing American option prices are discussed. A working knowledge of MAPLE or MATLAB is required to compute optimal portfolios. Prerequisites/Corequisites: Prerequisite: MATH 1020. When Offered: Fall term annually. Credit Hours: 4
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4.00 Credits
A survey of numerical methods for scientific and engineering problems. Topics include numerical solution of linear and nonlinear algebraic equations, interpolation and least squares approximations, numerical integration and differentiation, eigenvalue problems, and an introduction to the numerical solution of ordinary differential equations. Emphasis placed on efficient computational procedures including the use of library and student written procedures using high-level software such as MATLAB. Prerequisites/Corequisites: Prerequisites: CSCI 1100 and MATH 2010 or ENGR 1100. Corequisite: MATH 2400. When Offered: Fall and spring terms annually. Cross Listed: Cross-listed as CSCI 4800. Students cannot obtain credit for both this course and CSCI 4800. Credit Hours: 4
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4.00 Credits
Derivation, analysis, and use of computational procedures for solving differential equations. Topics covered include ordinary differential equations (both initial value and boundary value problems) and partial differential equations. Runge-Kutta and multistep methods for initial value problems. Finite difference methods for partial differential equations including techniques for heat conduction, wave propagation, and potential problems. Basic convergence and stability theory. Prerequisites/Corequisites: Prerequisite: MATH 4800 or CSCI 4800 When Offered: Spring term annually . Cross Listed: Cross-listed as CSCI 4820. Students cannot obtain credit for both this course and CSCI 4820. Credit Hours: 4
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1.00 - 4.00 Credits
Credit Hours: 1 to 4
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4.00 Credits
Undergraduate mathematics projects that utilize students' mathematical knowledge will result in formal reports and final presentations. Examples are research projects or critical in-depth mathematical literature reviews. Information about projects will be exchanged in weekly meetings. Students wishing to work on research should make arrangements with faculty in advance. Students already engaged in research may extend and present their results. This is a communication-intensive course. Prerequisites/Corequisites: Prerequisite: Open to mathematics seniors only. When Offered: Fall term annually. Graded: To be graded S/U. Credit Hours: 4
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1.00 - 4.00 Credits
Credit Hours: 1 to 4
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