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# TEL 529 - Advanced Engineering Mathematics

## Course Objectives

The course aims to give a solid background for theory of complex variables - di?erential & integral equations.

## Course Description

1. Giri¸s, Kompleks Sayılar ve Kompleks Du¨zlem, Kompleks Du¨zlemde Fonksiyon Kavramı (Complex Numbers, Complex Plane and Functions in Complex Plane) 2. Kompleks Du¨zlemde Fonksiyon Kavramı, Temel Fonksiyonlar ile 'Izdu¨¸su¨mler (Functions in Complex Plane and Basic Mappings) 3. Cauhcy Riemann Denklemleri, Analitik Fonksiyonlar (Cauchy Riemann Equations, Analytic Functions) 4. Cauchy Teoremi, Cauchy integral formu¨lu¨ (Cauchy Theorem, Cauchy Integral Formulae) 5. Cauchy Teoremi, Cauchy integral formu¨lu¨ (Cauchy Theorem, Cauchy Integral Formulae) 6. Rezidu¨ Formu¨lu¨ ve c¸e¸sitli integrallerin hesabı, Tekillikler (Residue Formula, Evaluation of Various Integrals, Singularities) 7. Taylor ve Laurent serileri (Taylor and Laurent Series) 8. Kısmi tu¨revli diferansiyel denklemler, Denklemlerin sını?andırılması, De^gi¸skenlerine Ayırma Y¨ontemi (Partial Di?erential Equations (PDE), Classi?cation of PDEs, Seperation of Variables) 9. Diferansiyel denklemlerin Tekil Noktaları, Seri C¸¨ozu¨mler (Singular points of Di?erential Equations (DE), Series Solutions to DEs) 10. 'Inhomogen denklemler, Green Fonksiyonları (Inhomogeneous DEs, Green’s Function Technique for Solution of DEs) 11. Strum Liouville Problemi, ¨ozfonksiyon a¸cınımları (Strum Liouville Problem, Eigenfunction Solutions for DEs) 12. 'Integral denklemler, sını?andırma ve genel c¸¨ozu¨m teknikleri (Integral Equations (IE), Classi?cation of IEs and General Solution Techniques for IEs) 13. Neumann serileri, ayrılabilir c¸ekirdekler, Hilbert-Schmidt yakla¸sımı (Neumann Series, Seperable Kernels, Hilbert-Schmidt Approach) 14. Varyasyonel hesap, Euler denklemine uygulama, (Variationel Calculus and its application to Euler’s Equation) 15. Varyasyonel hesabın c¸e¸sitli mu¨hendislik uygulamaları (Various Applications of Variational Calculus in Engineering) 16. C¸ok de^gi¸skenli fonksiyonlarda varyasyonel hesap, Lagrange ¸carpanları (Variational Calculus for Multi-variable Functions, Lagrange Multipliers) 17. Rayleigh-Ritz varyasyonel tekni^gi (Rayleigh-Ritz Variational Technique)

 Course Coordinator Mehmet Nuri Akıncı Course Language Turkish