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Course Criteria
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4.00 Credits
Vectors in three dimensions, curves and parametric equations in three dimensions, geometry of surfaces, differential calculus of functions of more than one variable with applications, multiple integrals and their applications, the differential and integral calculus of vector fields. Prerequisite: M 145.
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3.00 Credits
Solutions of first-order linear, separable equations and applications; higher-order linear equations and applications. Nonhomogeneous equations; Laplace transforms and initial value problems; matrices, eigenvalues, and linear systems of differential equations. Qualitative analysis of equilibria and bifurcations. Prerequisite: M 145.
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4.00 Credits
Matrix algebra; first- and second-order linear differential equations, including numerical methods; an introduction to partial differential equations, including numerical methods; an introduction to probability and statistics. (A student may not receive credit for both this course and either M 242 or M 344.) Prerequisite: M 240.
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4.00 Credits
An introduction to exploratory and confirmatory data analysis. Classical, portable, and robust statistical methods. Emphasis on model-building, analysis, interpretation, and refinement using statistical software (Minitab, SAS, BMDP, SPSSx). Prerequisite: M 145.
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3.00 Credits
A historical study of the principal mathematicians of the past 2,500 years and their contributions to the development and growth of the various fields of mathematics. Prerequisite: M 222W or permission of instructor.
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3.00 Credits
Investigation of the arithmetic properties of the integers. Unique factorization, congruences, quadratic reciprocity, and other topics will be treated. Prerequisite: M 222W.
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3.00 Credits
A rigorous treatment of differentiation and Riemann integration. Topology of the real line, real-valued sequences and their limits, continuity of realvalued sequences and their limits, continuity of real-valued functions, the Mean Value Theorem, a rigorous definition of the definite (Riemann) integral and proofs of its elementary properties, the Fundamental Theorem of Calculus. Other topics may include sequences of functions, series, or function spaces. Prerequisite: M 222W.
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3.00 Credits
Series solutions of ordinary differential equations and Bessel functions, Sturm-Liouville systems, and Fourier Series. Partial differential equations in Cartesian and cylindrical coordinates. Prerequisites: M 240 and M 242.
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3.00 Credits
Floating point arithmetic; algorithms and error analysis; roots of nonlinear equations; systems of linear equations; direct methods, factorization schemes, and iterative techniques; interpolation: difference schemes, splines; numerical differentiation and integration; solutions of ordinary differential equations; the matrix eigenvalue problem. Prerequisites: M 145, M 220, and CS 114.
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3.00 Credits
The process of developing and simulating mathematical models of real-world phenomena will be studied. The types of models considered will vary from year to year. They may include discrete and continuous dynamical models, stochastic models, neural networks, and optimization models. Applications may be to the natural sciences, management science, engineering, or industry. With departmental permission, the course may be repeated for credit. Prerequisite: M 240 or permission of instructor.
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