Code ENS 525
Term 201801
Title Mathematical Methods for Scientists and Engineers I
Faculty Faculty of Engineering and Natural Sciences
Subject Engineering Sciences(ENS)
SU Credit 3
ECTS Credit 10.00
Instructor(s) Cihan Kemal Sacl?o?lu -saclioglu@sabanciuniv.edu,
Language of Instruction English
Level of Course Doctoral
Master
Prerequisites
(only for SU students)
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Mode of Delivery Formal lecture
Planned Learning Activities Communicative,Discussion based learning
Content

Analytic functions of a complex variable: Cauchy-Riemann equations, conformal mappings, integration, Cauchy theorem, Taylor and Laurent series, residues, contour evaluation of definite integrals. Linear vector spaces: Inner products, linear operators, eigenvalue problems, functions of operators and matrices, Fourier transforms, Hilbert spaces, Sturm-Liouville theory, classical orthogonal polynomials, Fourier series, Bessel functions.

Objective

The student will acquire mathematical tools for graduate level research in physics and engineering.

Learning Outcome

Upon successful completion of ENS 525 Mathematical Methods for Scientists and Engineers I, students are expected to:

Perform calculations with the real elementary functions (power, exponential, trigonometric and hyperbolic functions and their inverses) and evaluate their derivatives and integrals,
Acquire proficiency in calculating line integrals and area integrals in the real plane,
Absorb the algebraic properties of complex numbers and their geometric interpretation in the complex plane,
Derive power series expansions of the elementary complex functions
Connect the convergence of the power series to the singularities of the functions in the complex plane,
Calculate integrals in the complex plane over closed contours using the residues of the singularities enclosed by the contour,
Calculate the Fourier and Laplace transforms of simple functions as well as recover the starting functions by performing the inverse transforms,
Solve the eigenvalue problem of real and complex matrices,
Develop the notion that vector and matrix algebra are one possible realization of abstract linear vector spaces
View square integrable functions as another example of a linear vector space in which the role of matrices is played by differential and integral operators.

Programme Outcomes