Bologna Information System

  • Course Information
  • Course Title Code Semester Laboratory+Practice (Hour) Pool Type ECTS
    ANALYSIS I MAT101 FALL 4+2 C 7
    Learning Outcomes
    1-To apprehend basic theorems and their proofs related to limit, continuity and derivative of functions of one variable.
    2-To apprehend computation techniques related to limit, continuity and derivative of functions of one variable.
    3-To determine maximum, minimum and inflection points of functions of one variable.
    4-To sketch the graphs of functions of one variable.
    5-To solve maximum and minimum problems.
  • ActivityPercentage


    NumberTime (Hours)Total Workload (hours)
    Course Duration (Weeks x Course Hours)14684
    Classroom study (Pre-study, practice)14570
    Short-Term Exams (exam + preparation) 102816
    Midterm exams (exam + preparation)3011616
    Laboratory 0000
    Final exam (exam + preparation) 5011818
    Other 0000
    Total Workload (hours)   220
    Total Workload (hours) / 30 (s)     7,33 ---- (7)
    ECTS Credit   7
  • Course Content
  • Week Topics Study Metarials
    1 Real numbers, absolute value, equations and inequalities, basic definitions related to functions
    2 Polinomials, rational functions, piecewise defined functions, trigonometric functions, exponential and logarithmic functions
    3 Limit of functions, one sided limis, limit theorems
    4 Limits at infinity, infinite limits, undetermined condtitions, examples related to limits
    5 Limits of trigonometric, exponential, and logarithmic functions
    6 Continuous functions, basic properties of continuous functions
    7 Properties of continuous functions defined on a closed and bounded interval
    8 Uniform continuity and related results
    9 The notion of derivative, rules of taking derivatives, chain rule, higher order derivatives, derivatives of exponential and logarithmic functions
    10 Chain rule, higher order derivativesdecreasing functions
    11 Derivatives of exponential and logarithmic functions, implicit differentiation, derivatives of parametric functions
    12 Mean-value theorem, increasing and decreasing functions, maximum and minumum values, first derivative test.
    13 Maximum and minimum values, concavity and inflection points, second derivative test, asymptotes, sketcing graphs
    14 Maximum, Minimum problems, related rates, L`hospital rule
    Prerequisites -
    Language of Instruction Turkish
    Course Coordinator Prof. Dr. Hüseyin IRMAK
    Instructors -
    Assistants -
    Resources Teori ve Çözümlü Problemlerle Analiz I, Binali Musayev, Murat Alp, Nizami Mustafayev, İsmail Ekincioğlu, Seçkin Yayıncılık, 2007.
    Supplementary Book [1] Analiz, M. Balcı, Balcı Yayınlar, ISBN:978-9756683-02-6, 2008. [2] Calculus, Robert A. Adams, Addison-Wesley. [3] Yüksek Matematik 1, Hüseyin Halilov, Alemdar Hasanoğlu, Mehmet Can, Literatür Yayıncılık, 2009. [4] Introduction to Real Analysis, Robert G. Bartle, Donald R. Sherbert, John Wiley & Sons
    Document Lecture Notes
    Goals Teaching basic theorems and their proofs related to limit, continuity and derivative of functions in one variable and give their applications.
    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 4
    5 To have the qualification of studying independently in a problem or a project requiring mathematical knowledge 2
    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 2
    8 To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge 2
    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 3
    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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