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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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Metric spaces and metric topology, the Cauchy-Schwarz and Minkowski inequality
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R1 - Chapter 1.1
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2
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Some basic definitions of complete metric spaces, theorems and examples
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R1 - Chapter 1.2
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3
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Introduction to fixed point theory
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R1 - Chapter 2.1
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4
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Contraction mapping principle and examples
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R1 - Chapter 2.2
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5
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Banach fixed point theorem and properties of its
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R1 - Chapter 2.3
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6
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Edelstein Fixed point theorems and properties of its
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R1 - Chapter 2.4
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7
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Some applications of Banach fixed point theorem
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R1 - Chapter 3
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8
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Picard`s theorem and examples of its
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R1 - Chapter 4
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9
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Linear Fredholm integral equation
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R1 - Chapter 5.1
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10
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Linear Volterra integral equation
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R1 - Chapter 5.2
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11
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Examples of integral equations
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R1 - Chapter 5.3
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12
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Cantor and some special is fixed point theorems
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R1 - Chapter 6
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13
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Non-linear contractions
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R1 - Chapter 7
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14
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Fixed-point theorem made with non-linear contraction
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R1 - Chapter 7.1
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Prerequisites
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-
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Language of Instruction
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Turkish
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Responsible
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Assoc. Prof. Dr. Gonca DURMAZ GÜNGÖR
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Instructors
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-
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Assistants
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-
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Resources
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R1 - Lecturer Notes
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Supplementary Book
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SR1 - Granas, A. and Dudundji, J. (2003). Fixed Point Theory. Springer.
SR2 - Agarwal, P. R., Mechan, M. and O`Regan. (2004). Fixed Point Theory Cambridge Universty Press.
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Goals
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Iıntroduce the fixed-point theorems, put forward their importance and the solutions.
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Content
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Metric space, some basic definitions of complete metric spaces, theorems and examples, the contraction mapping principle and example, Banach fixed-point theorem, properties and applications of linear integral equations and samples, fixed-point theorem made with non-linear contraction
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Program Learning Outcomes |
Level of Contribution |
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1
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Improve and deepen the gained knowledge in Mathematics in the speciality level
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3
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2
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Use gained speciality level theoretical and applied knowledge in mathematics
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4
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3
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Perform interdisciplinary studies by relating the gained knowledge in Mathematics with other fields.
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-
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4
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Analyze mathematical problems by using the gained research methods
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3
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5
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Conduct independently a study requiring speciliaty in Mathematics
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-
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6
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Develop different approaches and produce solutions by taking responsibility to problems encountered in applications
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-
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7
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Evaluate the gained speciality level knowledge and skills with a critical approach and guide the process of learning
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-
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8
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Transfer recent and own research related to mathematics to the expert and non-expert shareholders written, verbally and visually
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-
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9
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Uses computer software and information technologies related to the field of mathematics at an advanced level.
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-
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10
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Have the awareness of acting compatible with social, scientific, cultural and ethical values during the process of collecting, interpreting, applying and informing data related to Mathematics
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-
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