Bologna Information System

  • Course Information
  • Course Title Code Semester Laboratory+Practice (Hour) Pool Type ECTS
    Learning Outcomes
    1-To describe real valued sequences, cauchy sequences, functions sequences, series, power series, taylor series and maclaurin series.
    2-To prove the basic theorems relating to real valued sequences, cauchy sequences, functions sequences, series, power series, taylor series and maclaurin series.
    3-To apprehend properties or to do applications of sequences, functions sequences, series, power series, taylor series and maclaurin series.
  • ActivityPercentage


    NumberTime (Hours)Total Workload (hours)
    Course Duration (Weeks x Course Hours)14456
    Classroom study (Pre-study, practice)14456
    Short-Term Exams (exam + preparation) 102816
    Midterm exams (exam + preparation)3011212
    Laboratory 0000
    Final exam (exam + preparation) 5011818
    Other 0000
    Total Workload (hours)   174
    Total Workload (hours) / 30 (s)     5,8 ---- (6)
    ECTS Credit   6
  • Course Content
  • Week Topics Study Metarials
    1 Foreknowledge
    2 Certain topological properties of real numbers
    3 Rean number sequences, related definitions, theorems, certain applications, upper-lower limits, and their applications
    4 Real Cauchy sequence, its definiton, related definitions and theorems
    5 Introduction to real series
    6 Convergence and divergence of series
    7 Tests for convergence and divergence of series
    8 Real function sequences, related definitions, theorems amd certain applications
    9 Real valued function series, related definitions, theorems and certain applications
    10 Introduction to power series
    11 Convergence and divergence of power series
    12 Weirstrass M-test and its applications
    13 Maclaurin series and their applications
    14 Taylor series and and pplications
    Prerequisites Analiz I, Analiz II
    Language of Instruction Turkish
    Course Coordinator Prof. Dr. Hüseyin IRMAK
    Instructors -
    Assistants -
    Resources An introduction to real analysis, T. Terzioğlu, Matematik Vakfı yayınları, 2000.
    Supplementary Book [1] Analiz, M. Balcı, Balcı Yayınları, ISBN: 978-975-6683-03-3, 2009. [2] The Elements of Real Analysis, R. G. Bartle, John Wiley and Sons, 1967 [3] Real analysis with Real Applications, K. R. Davidson, A. P. Donsig, Prentice Hall, 2002 [4] Introduction to Real Analysis, Robert G. Bartle, Donald R. Sherbert, John Wiley & Sons [5] Analiz, M. Balcı, Balcı Yayınlar, ISBN:978-9756683-02-6, 2008.
    Document Ders Notları
    Goals Real sayı dizlerini, Caouchy dizilerini, fonksiyon dizilerini, serileri, kuvvet serilerini ve fonksiyon serilerini tanıtmak ve bunlarla ilgili teoremlerin ispatlarını ve uygulamalarını öğretmek.
    Content -
  • Program Learning Outcomes
  • Program Learning Outcomes Level of Contribution
    1 To have a grasp of theoretical and applied knowledge in main fields of mathematics 5
    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 5
    4 To be able to relate the gained mathematical acquisitions with different disciplines and apply in real life 2
    5 To have the qualification of studying independently in a problem or a project requiring mathematical knowledge 3
    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 4
    8 To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge 4
    9 To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time 2
    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 4
    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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