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Course Criteria
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3.00 Credits
Matrices and systems of linear equations, vector spaces, change of base matrices, linear transformations, determinants, eigenvalues and eigenvectors, canonical forms. Prerequisite: MATH 180.
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3.00 Credits
Solving first order ordinary differential equations: exact, separable, and linear. Application to rates and mechanics. Theory of higher order linear differential equations. Method of undetermined coefficients and variation of parameters. Application to vibrating mass and electric circuits. Power series solutions: ordinary and singular points, the method of Frobenius. Partial differential equations: the method of separation of variables. Prerequisite: MATH 260.
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3.00 Credits
Topics include: Vector functions of several variables, the Jacobian matrix, the generalized chain rule, inverse function theorem, curvilinear coordinates, the Laplacian in cylindrical and spherical coordinates, Lagrange multipliers, line integrals, vector differential and integral calculus including Green's, Stokes's and Gauss's theorem. The change of variablin multiple integrals, Leibnitz's rule, sequences and uniform convergence of series. Prerequisite: MATH 260.
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3.00 Credits
The general theory of functions of a complex variable, analytic functions, the Cauchy-Riemann equations, the Cauchy integral theorem and formula, Taylor series, Laurent series, singularities and residues, conformal mappings with applications to problems in applied science. Prerequisite: MATH 260.
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3.00 Credits
Generalities on linear partial differential equations and their applications to physics. Solution of initial boundary value problems for the heat equation in one dimension, eigenfunction expansions. Definition and use of Fourier series and Fourier transform. Inhomogeneous problems. The wave equation in one dimension. Problems in two dimensions: vibrating rectangular membranes, Dirichlet and Neumann problems. Prerequisite: MATH 320.
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3.00 Credits
The following topics are covered: solution of algebraic and transcendental equations by Newton-Raphson, Muller, and other iterative methods including discussion of convergence considerations, finite and divided differences, numerical integration by Newton-Cotes and Gaussian methods, solution of ordinary differential equations by predictor-corrector and Runge-Kutta methods, Gaussian elimination and band matrices. Additional topics are selected from: Operator methods, interpolation, numerical differentiation, Romberg extrapolation, stability, boundary value problems, polynomial and spline approximation. Prerequisite: MATH 320.
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3.00 Credits
Advanced topics of current interest in mathematics. Prerequisite: permission of the instructor.
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2.00 Credits
An introduction to current graphic representations. Problems chosen to develop recognition and development skills in such areas as orthographics, pictorials, auxiliaries, sections, intersections and developments. Practical applications in screws and fasteners, welds, gears, cams, pipes, and electrical conventions. AUTOCAD applications.
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3.00 Credits
Introduction to fundamentals of computer tool use and machine tool use: Pro/Engineer, a 3D parametric, feature based, solid modeling package with fully detailed representation of design concepts, and Autocad with lab applications; bandsaw, milling machine, and lathe. Prerequisite: MENG 105.
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3.00 Credits
Statics of particles; force in plane and space; equivalent systems of forces; equilibrium of rigid bodies in two and three dimensions; analysis of structures, friction; distributed forces; centroids, centers of gravity and moment of inertia; method of virtual work. Prerequisites: PHYS 170, MATH 180.
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