Contents |
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Course Code
IAM 781 (9700781)
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Credit
(3-0) 3
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Prerequisites
Properties of real numbers,limitsand convergence of sequences of numbers,exponential and logarith function,continuity and uniform continuity of functions,intermidiate value theorem,Hölder and Lipschitz continuity,differentiabilty,and differentiation rules
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Content/Aims
Basic analysis , Banach spaces in particular Lp spaces,Sobelev spaces. The students will be equipped with sufficient knowledge of analysis to pursue their own research.
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Learning Outcomes
The students will be equipped with sufficient knowledge of analysis to pursue their own research.
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Suggested Textbooks/Resources
- J.Jost.Postmodern analysis Springer Universitext,1998
- T.Terzioğlu: Fonksiyonel Analizin Yontemleri Matematik Vakfı
- T.Terzioğlu :Introduction to Real Analysis.Matematik Vakfı
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Outline
- Banach Spaces and Banach fixed point Theorem
- Integrals and ODEs
- Metric spaces
- Differential calculus in Rn
- Implicit Function Theorem and Applications
- System of ODEs
- Semi continous functions
- Lebesgue integrals of semi continuous functions
- Lebesgue integrable functions
- Fubini Therem
- Convergence Theorem of Lebesgue integrable functions
- Jensen’s inequality and Egorov Theorem
- Lp spaces
- Weak derivatives and Sobelev spaces