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 Course Name Turkish Mühendislik Matematiği 2017 English Engineering Mathematics Course Code UUM 535E Credit Lecture (hour/week) Recitation (hour/week) Laboratory (hour/week) Semester 1 3 - - - Course Language English Course Coordinator Mehmet Şahin Course Objectives Introduce graduate student to the applications of linear systems and complex analysis methods in engineering problems. Course Description Vectors and vectors spaces; Matris representation and system of linear equations; Eigenvalue problems; Spectral decomposition; Characteristic and minimal polynomials; Inner product spaces and orthogonality; Orthogonal and Hermitian matrices; Hilbert spaces; Fourier series and transform; Laplace transform; Limit, continuity and differentiability of functions of a complex variable; Cauchy-Riemann equations; Complex integration and Cauchy’s theorem; Taylor and Laurent series; Residue theorem; Complex mapping and its application to boundary value problems; Vector differential and integral calculus; Numerical mathematics. Course Outcomes M.Sc./Ph.D. students who successfully pass this course gain knowledge, skill and competency in the following subjects; 1. Able use basic vector and matrix operations 2. Able to reduce a matrix into a row-reduced echelon form 3. Able to compute eigenvalues and eigenvectors of a matrix 4. Able to apply Fourier transform to a periodic function and use Fourier transform 5. Able to use Laplace transform 6. Able to compute complex line integrals 7. Able to use complex mapping for some boundary value problems 8. Able to use Gauss divergence theorem, Stokes’ theorem, Green theorem 9. Able to apply numerical methods for engineering problems Pre-requisite(s) Required Facilities Other Textbook • A. Jeffrey, Advanced Engineering Mathematics. Harcourt/Academic Press, 2002. • R. W. Brockett, Finite Dimensional Linear Systems. Wiley, 1970. • R. A. Silverman, Introductory Complex Analysis. Dover, 1972. Other References 