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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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Some basic information, complex numbers, complex sequences, complex series.
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R1. Section 1.1
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2
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Certain complex functions and transformations.
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R1. Section 2.1
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3
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Complex functions sequences, complex powers, and certain special complex series.
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R1. Section 3.1
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4
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Convergence and uniform convergence in the complex plane.
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R1. Section 4.1
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5
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Analytic functions
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R1. Section 5.1
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6
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Complex integrations
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R1. Section 6.1
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7
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Harmonic functions
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R1. Section 7.1
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8
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Singularity
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R1. Section 8.1
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9
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Residues and their applications
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R1. Section 9.1
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10
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Cauchy theorem and its applications
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R1. Section 10.1
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11
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Argument principal
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R1. Section 11.1
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12
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Maximum modulus theorem
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R1. Section 12.1
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13
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Schwarz Lemma
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R1. Section 13.1
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14
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Analytic continuous and some of its applications.
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R1. Section 14.1
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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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Prof. Dr. Hüseyin IRMAK
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Instructors
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1-)10143 10143 10143
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Assistants
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Resources
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R1. Lecture notes
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Supplementary Book
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SR1. Ponnusamy, S., Silverman, H. (2006). Complex variable with applications, Birkhauser, Berlin.
SR2. Rudin, W. (1991). Real and Complex Analysis, McGraw-Hill. The USA.
SR3. Spiegel, M. (1998). Theory and problems of complex analysis. Schaum`s Outlines Series, Metric Editions.
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Goals
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To comprehend complex sequences, complex functions, complex transformations, and analytic functions, complex series, complex integrals, argument, and maximum modulus principals, Schwarz lemma, analytic continuous, their fundamental theorems and certain applications.
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Content
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Complex sequences, complex functions, complex transformations and analytic functions, complex series, complex integrals, argument and maximum modulus principals, Schwarz lemma, analytic continous, , their fundamental theorems and certain applications.
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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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3
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4
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Analyze mathematical problems by using the gained research methods
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-
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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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