CANKIRI KARATEKIN UNIVERSITY Bologna Information System


  • Course Information
  • Course Title Code Semester Laboratory+Practice (Hour) Pool Type ECTS
    Complex Analysis II MATH302 SPRING 4+0 C 7
    Learning Outcomes
    1-Comments derivative of complex functions and related theorems.
    2-Analyzes Cauchy Riemann equations and their applications.
    3-Solves complex integrals.
    4-Solves rezidues and improper integrals.
  • ECTS / WORKLOAD
  • ActivityPercentage

    (100)

    NumberTime (Hours)Total Workload (hours)
    Course Duration (Weeks x Course Hours)14456
    Classroom study (Pre-study, practice)14570
    Assignments1012020
    Short-Term Exams (exam + preparation) 1012020
    Midterm exams (exam + preparation)3011616
    Project0000
    Laboratory 0000
    Final exam (exam + preparation) 5011818
    Other 0000
    Total Workload (hours)   200
    Total Workload (hours) / 30 (s)     6,67 ---- (7)
    ECTS Credit   7
  • Course Content
  • Week Topics Study Metarials
    1 Certain basic foreknowledge, introduction to elementer complex functions R1) Lecture Notes
    2 Derivatives of elementer complex functions and related theorems R1) Lecture Notes
    3 Analytic functions and their derivatives R1) Lecture Notes
    4 Cauchy-Riemann equations and their applications R1) Lecture Notes
    5 Harmonic functions, w(t) curves in complex plane, countours, domains. R1) Lecture Notes
    6 Concept of complex integral, basic definitions, related theorems R1) Lecture Notes
    7 Cauchy Goursat theorem, related theorem, certain applications R1) Lecture Notes
    8 Midterm exams
    9 Cauchy Integral formulas, related theorems and applications R1) Lecture Notes
    10 Morera theorem R1) Lecture Notes
    11 Maksimum modulus theorem, Liouville theorem and fundemental theorem of algebra Goursat theorem and related results R1) Lecture Notes
    12 Taylor and Laurent Series R1) Lecture Notes
    13 Zeros and poles of analytic functions, rezidue and related theorems R1) Lecture Notes
    14 Rezidues and related theorems, concepts of improper integrals R1) Lecture Notes
    15 Some applications of improper integrals R1) Lecture Notes
    Prerequisites -
    Language of Instruction English
    Coordinator Assoc. Prof. Dr. Faruk POLAT
    Instructors -
    Assistants -
    Resources R1: Lecture notes R2: Brown, J. W., Complex variables and applications - 6th ed., McGraw-Hill., 2005. R3: Spiegel, M., Theory and problems of complex analysis, Schaum`s Outlines Series, Metric Editions. R4: Silverman, R. A., Calculus with Analytic Geometry, Prentice Hall., 1985.
    Supplementary Book [1]: Rudin, W., Real and Complex Analysis, McGraw-Hill., 1991. [2]: Complex variable with applicatins, Ponnusamy, S. and Silverman, H., Birkhauser, Berlin, 2006.
    Goals To introduce elementer functions, their derivatives, integrals and to apply them to complex functions and to know important theorems.
    Content 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.
  • Program Learning Outcomes
  • Program Learning Outcomes Level of Contribution
    1 To have a grasp of theoretical and applied knowledge in main fields of mathematics 3
    2 To have the ability of abstract thinking 4
    3 To be able to use the gained mathematical knowledge in the process of identifying the problem, analyzing and determining the solution steps 3
    4 To be able to relate the gained mathematical acquisitions with different disciplines and apply in real life -
    5 To have the qualification of studying independently in a problem or a project requiring mathematical knowledge -
    6 To be able to work compatibly and effectively in national and international groups and take responsibility -
    7 To be able to consider the knowledge gained from different fields of mathematics with a critical approach and have the ability to improve the knowledge -
    8 To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge -
    9 To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time -
    10 To be able to transfer thoughts on issues related to mathematics, proposals for solutions to the problems to the expert and non-expert shareholders written and verbally -
    11 To be able to produce projects and arrange activities with awareness of social responsibility -
    12 To be able to follow publications in mathematics and exchange information with colleagues by mastering a foreign language at least European Language Portfolio B1 General Level -
    13 To be able to make use of the necessary computer softwares (at least European Computer Driving Licence Advanced Level), information and communication technologies for mathematical problem solving, transfer of thoughts and results -
    14 To have the awareness of acting compatible with social, scientific, cultural and ethical values -
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