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MATH 697P

MATHMATICAL METHODS FOR SCIENCE & ENGINEERING I

Instructor: Donald F. St. Mary

The first of a two-course sequence describing mathematical methods which are useful in science and engineering. The course discusses topics in complex variables, Fourier series, Laplace transforms, Fourier transforms, distributions and differential equations. The underlying theme of the course is transform methods with applications to partial differential equations.

Topics Include:

Functions of a complex variable - multi-valued functions and Riemann surfaces, Cauchy theorem and integral formula, Laurent series, and the residue theorem and applications. Linear differential equations of second order - the Wronskian, Green's function, power series solutions, and the Frobenius method. Fourier series - separation of variables in a partial differential equation, sine and cosine series, complex form of the Fourier series, general orthogonal functions, mean square approximation, and Sturm-Liouville problems. Laplace transforms - basic properties and examples, inversion, convolution, and the Mellin inversion formula. Distributions - delta sequences, Dirac delta function, delta calculus, and applications. Fourier transforms - basic properties and examples, Fourier inversion formula, applications to partial differential equations.

Text:

Mathematical Physics, E. Butkov; Addison-Wesley, 1968.

Course Notes:

Some materials will be sent via PDF format, to students with email access, at no charge. Students without email will need to contact the VIP to order these materials in printed form and will be charged.

Requirements:

Weekly homework assignments (20%) and two exams (40% each).

Computer Requirements:

None for course assignments. To receive notes via PDF format, students will need access to email.

On-Campus Computer Account:

Not required.

Prerequisites:

Calculus and a course in ordinary differential equations.

NTU National Technical University

NTU #MA 780-A

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