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Dersin Bilgileri

Dersin Adı
Türkçe Kısmı Differensiyel Denklemlere Giriş_2018
İngilizce Int.to Partial Diff.Eq. in Eng_2016
Dersin Kodu
UZB 218E Kredi Ders
(saat/hafta)
Uygulama
(saat/hafta)
Labratuvar
(saat/hafta)
Dönem -
3 - - -
Dersin Dili İngilizce
Dersin Koordinatörü Mehmet Şahin
Dersin Amaçları Students are introduced with linear partial differential equations through simple models, namely, the heat and wave equations, which describe a broad range of scientific phenomenon. Equations are formulated carefully from physical principles, motivating the mathematical solution techniques. Only exact solution methods are discussed.
Dersin Tanımı Review of ordinary differential equations. Boundary value problems. Heat Equation. Method of separation of variables: One dimensional heat equation. Laplace's equation in Cartesian and polar coordinates. Fourier series, Fourier sine and cosine series. Complex form of Fourier series. Vibrating strings and membranes. Sturm-Liouville eigenvalue problems. Rayleigh quotient. Vibrating circular membrane. Bessel functions. Laplace’s equation in a circular cylinder. Non-homogeneous problems. Eigenfunction expansions. Poisson's equation. A brief introduction to Laplace transforms
Dersin Çıktıları On completing this course students should :
1. Know how to solve an ordinary differential equation (a3 ,e2,h1,g1,k1)*
2. Understand what it is needed to solve a differential equation (a3 ,e1,h1,g1,k1)*
3. Be able to solve Laplace’s equation for simple geometries (a3 ,e1,h1,g1,k1)*
4. Be able to use Fourier series (a3 ,b1,e1,h1,g1,k1)*
5. Be able to solve vibrating string and membrane problems (a3 ,e1,h1,g1,k1)*
6. Be able to use Bessel function for the solution of Laplace’s equation (a3 ,e1,h1,g1,k1)*
7. Be able to use Laplace transform for the solution of differential equations (a3 ,e1,h1,g1,k1)*
8. Be able to use eigenvalue expansion for solving elliptic boundary value problems (a3 ,e1 ,g1,k1)*
9. Be able to appreciate the need and importance of analytical methods in the solution engineering problems (a3 ,b1,e1,h1,i1,j1,k1)*
Önkoşullar
Gereken Olanaklar
Diğer
Ders Kitabı 1. O'Neil, P.V. Beginning Partial Differential Equations, Wiley-Interscience, 2008.
2. Boyce, W.E. and DiPrima, R.C. Elementary Differential Equations and Boundary Value Problems, John Wiley and Sons Inc., 1997.
3. Zill, D.G. A First Course in Differential Equations. Thomson Brooks/Cole, 2005.
4. Powers, D.L. Boundary Value Problems. 4th Ed., Elsevier, 1999.
5. Bronson, R. Schaum’s Outline of Modern Introductory Differential Equations. McGraw-Hill Book Company, 1973.
Diğer Referanslar
 
 
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