CATALOG March 27, 1992 DATA:
Continuation of AE/ME 561. Partial differential equations, characteristics, separation of variables, similarity and transform solutions, complex variable theory, singular integral equations, integral transforms.

TEXTBOOKS:
F.B. Hildebrand, Advanced Calculus for Applications, Prentice-Hall, Englewood Cliffs, N.J., 1976.

GOALS:
To continue the introduction to the mathematics commonly used in engineering applications.

Topics:

• Partial differential equations: Definitions and examples, quasi-linear equations of first order-characteristics, linear and quasi-linear equations of second order, Cauchy's problem, classification of hyperbolic, parabolic and elliptic equations, method of characteristics.
• Self-similar solutions: Existence, dimensional analysis.
• Separation of variables: Introduction and examples, Sturm-Liouville theory, orthogonal function expansions, Fourier series, special functions.
• Elliptic equations: Laplace and Poisson equations, existence and uniqueness-Dirichlet and Neumann conditions, Green's function, integral transform, solution to inhomogeneous equations.
• Functions of a complex variable: Introduction-examples, analytic functions, Cauchy's integral formula, series expansions, singularities-branch points, evaluation of integrals-residues, Cauchy principal value, applications-conformal mapping-2D flows.
• Integral transforms: Introduction, Fourier transform, Laplace transform.
• Singular integral equations: Cauchy's principal value, sectionally analytic functions, Plemelj formula, Poisson formula, Riemann's problem, Hilbert's problem, inversion of integral equations, applications.
• Hyperbolic equations: Wave equation, method of characteristics, systems of quasi-linear equations of first order, applications-compressible flows.
• Parabolic equations: Diffusion equation.
• Asymptotic methods: Asymptotic expansions, solutions of transcendental equations, integrals-method of stationary phase, differential equations, WKB approximation.
• Nonlinear problems: Algebraic and differential, approximate methods and solutions, perturbation methods.

ABET category content as estimated by faculty member who prepared the course description:
Engineering Science: 3 credits or 100%
Engineering Design: 0 credits

Prepared by: Professor Hafiz M. Atassi
Last Update:

 

Direct comments, questions, and corrections to amedept@nd.edu