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Week |
Subject |
Related Preparation |
1) |
Definition and properties of variation, variational problems and their applications |
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2) |
The basic conceps about functional analysis linear vector spaces,linear transformations and functionals, normed spaces, iner product spaces |
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3) |
Variational formulation of boundary value problems, some integral relations |
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4) |
Sobolev Spaces and consept or generalized solution |
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5) |
Weak(or Generalized) solutions |
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6) |
Concepts from Variational Calculus |
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7) |
Linear operator equations |
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8) |
Linear operator equations (continued) |
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9) |
Variational boundary value problems |
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10) |
Variational problem and the existence of weak solution |
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11) |
Rayleigh-Ritz method |
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12) |
Convergence and stability |
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13) |
The Weighted Residual method(Collocation, least square, Galerkin,Subdomain methods) |
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14) |
The Kantorovich and Trefftz Methods |
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Course Notes: |
1.Alemdar Hasanoğlu(Hasanov), “Varyasyonel problemler ve sonlu elemanlar yöntemi”,Literatür yayıncılık, 2001. |
References: |
1. J.N.Reddy, “An introduction to the finite element method”, McGraw –Hill Inc., 1993.
2. J.N.Reddy, Applied Functional Analysis and Varyasyonel Methods in engineering, McGraw-Hill Inc.,1986.
3. Rao.L. 1982. The finite element method in engineering: Pergamon Pres
4. I.M. Gelfand, S.V. Fomin and R.A. Silverman, Calculus of Variations, Dover Pub., 2000. |
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Program Outcomes |
Level of Contribution |
1) |
Ability to assimilate mathematic related concepts and associate these concepts with each other.
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2) |
Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization.
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3) |
Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. |
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4) |
Ability to make individual and team work on issues related to working and social life. |
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5) |
Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. |
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6) |
Ability to use mathematical knowledge in technology. |
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7) |
To apply mathematical principles to real world problems. |
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8) |
Ability to use the approaches and knowledge of other disciplines in Mathematics. |
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9) |
Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary. |
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10) |
To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data. |
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11) |
To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. |
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12) |
To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself. |
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