Syllabus Application
Mathematical Methods for Scientists and Engineers I
ENS 525
Faculty:
Faculty of Engineering and Natural Sciences
Semester:
Fall 2025-2026
Course:
Mathematical Methods for Scientists and Engineers I - ENS 525
Classroom:
FENS-2019,FENS-L029
Level of course:
Masters
Course Credits:
SU Credit:3.000, ECTS:10
Prerequisites:
-
Corequisites:
Course Type:
Lecture
Instructor(s) Information
Göktuğ Karpat
Course Information
Catalog Course Description
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.
Course Learning Outcomes:
| 1. | 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, |
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| 2. | Acquire proficiency in calculating line integrals and area integrals in the real plane, |
| 3. | Absorb the algebraic properties of complex numbers and their geometric interpretation in the complex plane, |
| 4. | Derive power series expansions of the elementary complex functions |
| 5. | Connect the convergence of the power series to the singularities of the functions in the complex plane, |
| 6. | Calculate integrals in the complex plane over closed contours using the residues of the singularities enclosed by the contour, |
| 7. | Calculate the Fourier and Laplace transforms of simple functions as well as recover the starting functions by performing the inverse transforms, |
| 8. | Solve the eigenvalue problem of real and complex matrices, |
| 9. | Develop the notion that vector and matrix algebra are one possible realization of abstract linear vector spaces |
| 10. | 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. |
Course Objective
The student will acquire mathematical tools for graduate level research in physics and engineering.