Deterministic and probablistic models are considered for both discrete and continuous problems. Applications to a variety of fields. Students cannot receive credit for MATH 433 if they have already received credit for MATH 435 . Students cannot receive credit for MATH 434 if they have already received credit for MATH 436 or 438 . This sequence is an integrated course in advanced engineering mathematics, including vector and tensor analysis, analytic functions of a complex variable, infinite series in the complex plane, the theory of residues, conformal mappings, Laplace and Fourier transforms, Fourier series and integrals, boundary value problems, separation of variables, Laplace equation, diffusion equation, wave equation, calculus of variations.
Emphasis is towards applications.
Students cannot receive credit for MATH 433 if they have already received credit for MATH 435 . Students cannot receive credit for MATH 434 if they have already received credit for MATH 436 or 438 . Algebra of complex numbers, analytic functions and Cauchy-Riemann equations, complex integration and Cauchy's theorem, integral formulae, power series, residues and contour integration, analytic continuation, Riemann surfaces. Students cannot receive credit for MATH 434 if they have already received credit for MATH 436 or 438 . Topics selected from linear ordinary differential equations in the complex plane, special functions, conformal mapping, Laplace transform, Fourier and Hilbert transforms.