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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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Certain basic foreknowledge, introduction to elementry complex functions
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R1- Chapter 3
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2
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Derivatives of elementer complex functions and related theorems
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R1- Chapter 3
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3
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Analytic functions and their derivatives
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R1- Chapter 2
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4
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Cauchy-Riemann equations and their applications
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R1- Chapter 2
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5
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Harmonic functions, w(t) curves in complex plane, countours, domains
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R1- Chapter 2
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6
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Concept of complex integral, basic definitions, related theorems
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R1- Chapter 4
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7
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Cauchy Goursat theorem, related theorem, certain applications
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R1- Chapter 4
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8
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Cauchy Integral formulas, related theorems and applications
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R1- Chapter 4
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9
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Morera theorem
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R1- Chapter 4
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10
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Maksimum modulus theorem, Liouville theorem and fundemental theorem of algebra Goursat theorem and related results
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R1- Chapter 4
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11
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Taylor and Laurent Series
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R1- Chapter 5
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12
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Zeros and poles of analytic functions, residue and related theorems
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R1- Chapter 6
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13
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Residues and related theorems, concepts of improper integrals
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R1- Chapter 6
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14
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Some applications of improper integrals
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R1- Chapter 7
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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. Faruk POLAT
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Instructors
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Assistants
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-
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Resources
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R1. Brown, J. W. and Churchill R. V. (2003). Complex variables and applications (7th ed.). McGraw-Hill Company, New York.
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Supplementary Book
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SR1- Rudin, W. (1991). Real and Complex Analysis. McGraw-Hill, New York.
SR2- Bak, J. and Newman, D.J. (1997). Complex Analysis (3rd ed.) Springer, New York.
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Goals
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To introduce elementer functions, their derivatives, integrals and to apply them to complex functions and to know important theorems.
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Content
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Elementary functions, their derivatives, Cauchy-Riemann equations, harmonic functions, w(t) curves in complex plane, their perimeters, their domains, complex integral notion , Cauchy Goursat theorem, Cauchy integral formula, Liouville theorem and fundamental theorem of algebra, Taylor and Laurent series, zeros, polar points and residue of analytic 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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3
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2
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Ability of abstract thinking
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3
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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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-
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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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-
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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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-
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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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-
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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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-
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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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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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-
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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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-
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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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4
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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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-
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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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