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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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Systems of Linear differential Equatiions
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R2- Section 7.1
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2
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Differential operators and operator method
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R2- Section 7.1
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3
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Sturm-Liouville systems, eigenvalues and eigenfunctions
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R1- Section 8.1, Section 8.2
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4
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Eigenfunction expansions, convergence in the mean, completeness and Parseval`s equality
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R1- Section 8.3, Section 8.4, Section 8.5
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5
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Eigenfunction expansions, convergence in the mean, completeness and Parseval`s equality
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R1- Section 8.3, Section 8.4, Section 8.5
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6
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Adjoint forms and Lagrange identity; singular Sturm-Liouville systems
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R1- Section 8.7, Section 8.8
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7
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Legendre`s equation and Legendre`s function
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R1-Section 8.9
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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- Section 8.10, Section 8.11
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9
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Laplace equation, Dirichlet problem for a cube, cylinder and sphere
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R1- Section 10.1, Section 10.2, Section 10.3, Section 10.4
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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- Section 10.5, Section 10.6, Section 10.7
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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- Section 10.8, Section10.9
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12
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Spherical and cylindrical wave equation
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R1- Section10.8
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13
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Method of eigenfunction
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R1- Section11.8
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14
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Applications
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R1-Section 11.9
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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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Assistants
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Resources
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R1- Myint-U, T., Debnath, L. (2007). Linear Partial Differential Equations for Scientists and Engineers, 4th Ed.. R2- Ross, Shepley L. (1989). Differential Equations. John Wiley and Sons, New York.
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Supplementary Book
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SR1- Anar, İ. E., (2005). Kısmi Diferansiyel Denklemler, Palme Yayınevi.
SR2- Hasanoğlu (Hasanov), A. (2010). Kısmi Türevli Denklemler, Literatür Yayıncılık.
SR3- Çağlıyan, M., Çelebi, O. (2010). Kısmi Diferensiyel Denklemler, Dora Basım Yayın.
SR4- Dernek, A. N. (2009). Kısmi Türevli Denklemler ve Çözümlü Problemler. Nobel Yayın Dağıtım.
SR5- Zachmann, D. W., DuChateau, P. (2010). Kısmi Diferensiyel Denklemler. ( H. H. Hacısalihoğlu, Çev), 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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Systems of Linear Differential Equations, 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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Having advanced theoretical and applied knowledge in the basic areas of mathematics
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4
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2
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Ability of abstract thinking
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-
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3
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To be able to use the acquired mathematical knowledge in the process of defining, analyzing and separating the problem encountered into solution stages.
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-
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4
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Associating mathematical achievements with different disciplines and applying them in real life
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5
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Ability to work independently in a problem or project that requires knowledge of mathematics
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6
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Ability to work harmoniously and effectively in national or international teams and take responsibility
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4
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7
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Having the skills to critically evaluate and advance the knowledge gained from different areas of mathematics
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8
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To be able to determine what kind of knowledge learning the problem faced and to direct this knowledge learning process.
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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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10
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Ability to verbally and in writing convey thoughts on mathematical issues, and solution proposals to problems, to experts or non-experts.
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11
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Being able to produce projects and organize events with social responsibility awareness
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12
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Being able to follow publications in the field of mathematics and exchange information with colleagues by using a foreign language at least at the European Language Portfolio B1 General Level
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13
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Ability to use computer software (at least at the Advanced Level of European Computer Use License), information and communication technologies for solving mathematical problems, transferring ideas and results
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14
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Being conscious of acting in accordance with social, scientific, cultural and ethical values
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