printer friendly pageCME 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
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
ENERGY 281: Applied Mathematics in Reservoir Engineering
The philosophy of the solution of engineering problems. Methods of solution of partial differential equations: Laplace transforms, Fourier transforms, wavelet transforms, Green's functions, and boundary element methods. Prerequisites:
CME 204 or
MATH 131, and consent of instructor.
Terms: Spr
| Units: 3
Instructors:
Tartakovsky, D. (PI)
;
Bakarji, J. (TA)
ME 300C: Introduction to Numerical Methods for Engineering (CME 206)
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
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