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1 - 10 of 45 results for: CME

CME 100: Vector Calculus for Engineers (ENGR 154)

Computation and visualization using MATLAB. Differential vector calculus: analytic geometry in space, functions of several variables, partial derivatives, gradient, unconstrained maxima and minima, Lagrange multipliers. Integral vector calculus: multiple integrals in Cartesian, cylindrical, and spherical coordinates, line integrals, scalar potential, surface integrals, Green's, divergence, and Stokes' theorems. Examples and applications drawn from various engineering fields. Prerequisites: MATH 41 and 42, or 10 units AP credit.
Terms: Aut | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR

CME 102: Ordinary Differential Equations for Engineers (ENGR 155A)

Analytical and numerical methods for solving ordinary differential equations arising in engineering applications: Solution of initial and boundary value problems, series solutions, Laplace transforms, and non-linear equations; numerical methods for solving ordinary differential equations, accuracy of numerical methods, linear stability theory, finite differences. Introduction to MATLAB programming as a basic tool kit for computations. Problems from various engineering fields. Prerequisite: CME 100/ ENGR 154 or MATH 51.
Terms: Win, Sum | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR

CME 104: Linear Algebra and Partial Differential Equations for Engineers (ENGR 155B)

Linear algebra: matrix operations, systems of algebraic equations, Gaussian elimination, undertermined and overdetermined systems, coupled systems of ordinary differential equations, eigensystem analysis, normal modes. Fourier series with applications, partial differential equations arising in science and engineering, analytical solutions of partial differential equations. Numerical methods for solution of partial differential equations: iterative techniques, stability and convergence, time advancement, implicit methods, von Neumann stability analysis. Examples and applications from various engineering fields. Prerequisite: CME 102/ ENGR 155A.
Terms: Spr | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR
Instructors: Khayms, V. (PI)

CME 106: Introduction to Probability and Statistics for Engineers (ENGR 155C)

Probability: random variables, independence, and conditional probability; discrete and continuous distributions, moments, distributions of several random variables. Topics in mathematical statistics: random sampling, point estimation, confidence intervals, hypothesis testing, non-parametric tests, regression and correlation analyses; applications in engineering, industrial manufacturing, medicine, biology, and other fields. Prerequisite: CME 100/ENGR154 or MATH 51.
Terms: Win, Sum | Units: 3-4 | UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR
Instructors: Khayms, V. (PI)

CME 108: Introduction to Scientific Computing

Numerical computation for mathematical, computational, and physical sciences and engineering: numerical solution of systems of algebraic equations, least squares, quadrature, minimization of a function, banded matrices, nonlinear equations, numerical solution of ordinary and partial differential equations; truncation error, numerical stability for time dependent problems, stiffness, boundary value problems. Prerequisites: CS106A or familiarity with MATLAB; MATH 51, 52, 53; inappropriate for students who have taken CME 102,104/ ENGR 155A,B.
Terms: Win | Units: 3-4 | UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-FR
Instructors: Lambers, J. (PI)

CME 191: Special Studies or Projects

Independent work under faculty direction. Individual or team activities involving lab work or directed reading. May be repeated for credit.
Terms: Aut, Win, Spr | Units: 1 | Repeatable for credit
Instructors: Murray, W. (PI)

CME 200: Linear Algebra with Application to Enginering Computations (ME 300A)

Solving matrix-vector systems. Direct and iterative solvers for non-singular linear systems of equations; their accuracy, convergence properties, and computational efficiency. Under- and over-determined systems, and nonlinear systems of equations. Eigenvalues, eigenvectors, and singular values; their application to engineering problems. Concepts such as basis, linear independence, column space, null space, rank, norms and condition numbers, projections, and matrix properties. Recommended: familiarity with computer programming; mathematics background equivalent to MATH 103, 130.
Terms: Aut | Units: 3

CME 204: Partial Differential Equations in Engineering (ME 300B)

Geometric interpretation of partial differential equation (PDE) characteristics; solution of first order PDEs and classification of second-order PDEs; self-similarity; separation of variables as applied to parabolic, hyperbolic, and elliptic PDEs; special functions; eigenfunction expansions; the method of characteristics. If time permits, Fourier integrals and transforms, Laplace transforms. Prerequisite: CME 200/ ME 300A, equivalent, or consent of instructor.
Terms: Win | Units: 3
Instructors: Shaqfeh, E. (PI)

CME 206: Introduction to Numerical Methods for Engineering (ME 300C)

Numerical methods from a user's point of view. Lagrange interpolation, splines. Integration: trapezoid, Romberg, Gauss, adaptive quadrature; numerical solution of ordinary differential equations: explicit and implicit methods, multistep methods, Runge-Kutta and predictor-corrector methods, boundary value problems, eigenvalue problems; systems of differential equations, stiffness. Emphasis is on analysis of numerical methods for accuracy, stability, and convergence. Introduction to numerical solutions of partial differential equations; Von Neumann stability analysis; alternating direction implicit methods and nonlinear equations. Prerequisites: CME 200/ ME 300A, CME 204/ ME 300B.
Terms: Spr | Units: 3
Instructors: Moin, P. (PI)

CME 211: Computer Programming in C++ for Earth Scientists and Engineers (ENERGY 211)

Computer programming methodology emphasizing modern software engineering principles: object-oriented design, decomposition, encapsulation, abstraction, and modularity. Fundamental data structures. Time and space complexity analysis. The basic facilities of the programming language C++. Numerical problems from various science and engineering applications.
Terms: Aut | Units: 3
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