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Week
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Topics
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Study Metarials
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1
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Mathematical models, vibrating string and membrane, waves in an elastic medium Conduction of heat in solids, the gravitational potential
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R1) Lecture notes
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2
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Sturm-Liouville systems, eigenvalues and eigenfunctions
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R1) Lecture notes
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3
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Eigenfunction expansions, convergence in the mean, completeness and Parseval`s equality
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R1) Lecture notes
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4
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Bessel`s equation and Bessel`s function
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R1) Lecture notes
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5
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Adjoint forms and Lagrange identity; singular
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R1) Lecture notes
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6
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Sturm-Liouville systems
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R1) Lecture notes
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7
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Legendre`s equation and Legendre`s function
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R1) Lecture notes
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8
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Boundary value problems involving ordinary differential equations and Green?s functions
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R1) Lecture notes
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9
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Laplace equation, Dirichlet problem for a cube, cylinder and sphere
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R1) Lecture notes
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10
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Two dimensional wave and heat equations, vibration of a rectangular and circular membrane, heat flow in a rectangular plate
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R1) Lecture notes
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11
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Three dimensional wave and heat equations, wave propagation in a rectangular volume
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R1) Lecture notes
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12
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Spherical and cylindrical wave equation
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R1) Lecture notes
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13
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Method of eigenfunction
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R1) Lecture notes
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14
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Applications
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R1) Lecture notes
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Prerequisites
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-
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Language of Instruction
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English
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Responsible
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Prof. Dr. Ahmet Yaşar ÖZBAN
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Instructors
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-
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Assistants
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[1] Assist. Prof. Dr. Şerifenur CEBESOY ERDAL [2] Teach. Assist. Dr. Harun BALDEMİR [3] Teach. Assist. Dr. Emel BOLAT YEŞİLOVA
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Resources
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[1] Lecture notes [2] Kısmi Diferansiyel Denklemler, İbrahim Ethem Anar, Palme Yayınevi, 2005 [3] Linear Partial Differential Equations for Scientists and Engineers, 4th Ed., Tyn Myint-U, Lokenath Debnath, 2007
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Supplementary Book
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[1] Kısmi Türevli Denklemler, Alemdar Hasanoğlu (Hasanov), Literatür Yayıncılık, 2010 [2] Kısmi Diferensiyel Denklemler, Mehmet Çağlıyan, Okay Çelebi, Dora Basım Yayın, 2010 [3] Kısmi Türevli Denklemler ve Çözümlü Problemler, A. Neşe Dernek, Nobel Yayın Dağıtım, 2009 [4]. Kısmi Diferensiyel Denklemler, David W. Zachmann, Paul DuChateau, Çeviri: H. Hilmi Hacısalihoğlu, Nobel Yayın Dağıtım
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Goals
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To describe fundamental equations and problems of applied mathematics and to teach solution techniques of the related problems.
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Content
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Eigenvalue problems, Sturm-Liouville systems, eigenfunctions and orthogonal function spaces, eigenfunctions expansions, convergence in the mean, completeness, Parseval`s identity, adjoint forms and Lagrange identity, singular Sturm-Liouville Systems, oscillating solutions on a half axis, Sturm`s separation and Sturm`s comparison theorems, Bessel differenstial equation and Bessel functions, the orthogonality property of Bessel functions, norm of Bessel functions and Bessel series, Neumann functions, Hankel functions, modified Bessel functions, generating functions,generating functions for Bessel functions of exact order, Legendre differential equation and Legendre polynomials, Rodrigues formula, generating function, orthogonality property and norm of Legendre polynomials, some important orthogonal polynomials and Legendre series, Gauss differential equation and hypergeometric functions.
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Program Learning Outcomes |
Level of Contribution |
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1
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To have a grasp of theoretical and applied knowledge in main fields of mathematics
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4
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2
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To have the ability of abstract thinking
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-
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3
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To be able to use the gained mathematical knowledge in the process of identifying the problem, analyzing and determining the solution steps
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-
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4
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To be able to relate the gained mathematical acquisitions with different disciplines and apply in real life
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-
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5
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To have the qualification of studying independently in a problem or a project requiring mathematical knowledge
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-
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6
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To be able to work compatibly and effectively in national and international groups and take responsibility
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4
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7
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To be able to consider the knowledge gained from different fields of mathematics with a critical approach and have the ability to improve the knowledge
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-
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8
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To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge
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3
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9
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To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time
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-
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10
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To be able to transfer thoughts on issues related to mathematics, proposals for solutions to the problems to the expert and non-expert shareholders written and verbally
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-
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11
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To be able to produce projects and arrange activities with awareness of social responsibility
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-
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12
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To be able to follow publications in mathematics and exchange information with colleagues by mastering a foreign language at least European Language Portfolio B1 General Level
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-
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13
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To be able to make use of the necessary computer softwares (at least European Computer Driving Licence Advanced Level), information and communication technologies for mathematical problem solving, transfer of thoughts and results
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14
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To have the awareness of acting compatible with social, scientific, cultural and ethical values
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