CANKIRI KARATEKIN UNIVERSITY
Bologna Information System


  • Course Information
  • Course Title Code Semester Laboratory+Practice (Hour) Pool Type ECTS
    ADVANCED ANALYSIS I MAT201 FALL 4+2 C 7
    Learning Outcomes
    1-To explain fundamental topological properties of r^n space.
    2-To describe multivariable functions and basic concepts related to these functions.
    3-To explain basic theorems and their proofs related to limit, continuity and derivatives of functions of multivariableatives.
    4-To calculate partial derivatives and directional derivatives of functions of multivariable.
    5-To find tangent plane and normal line of a surface.
    6-To determine series expansions of multivariable functions.
    7-To solve extremum value problems related to multivariable functions.
  • ECTS / WORKLOAD
  • ActivityPercentage

    (100)

    NumberTime (Hours)Total Workload (hours)
    Course Duration (Weeks x Course Hours)14684
    Classroom study (Pre-study, practice)14570
    Assignments102816
    Short-Term Exams (exam + preparation) 102816
    Midterm exams (exam + preparation)3011616
    Project0000
    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 Basic properties of the topology of R^n
    2 Multivariable functions and their properties
    3 Limits and continuity of multivariable functions
    4 Basic differentiation rules, chain rule, gradient, directional derivatives
    5 The geometric meaning of differentials, tangent planes and normal lines
    6 Higher order partial derivatives, mean value theorem for multivariable functions
    7 Differentials, Jacobian matrices of multivariable functions
    8 Mean-value theorem for transformations
    9 Inverse transformations and inverse transformation theorem
    10 Implicit functions and implicite function theorem
    11 Extremum values of multivariable functions
    12 Maximum and minimum problems
    13 Extremum values with constraints, Lagrange multipliers method
    14 Vector and scalar fields, gradient, divergence, rotation
    Prerequisites ANALYSIS I, ANALYSIS II
    Language of Instruction Turkish
    Course Coordinator Prof. Dr. Hüseyin IRMAK
    Instructors

    1-)Müfit Şan

    Assistants -
    Resources Teori ve Çözümlü Problemlerle Analiz III, Binali Musayev, Nizami Mustafayev, Kerim Koca, Seçkin Yayıncılık, 2007.
    Supplementary Book [1] Calculus, Robert A. Adams, Addison-Wesley. [2] Introduction to Real Analysis, Robert G. Bartle, Donald R. Sherbert, John Wiley & Sons.
    Document Lecture Notes
    Goals To analyze basic topological properties of R^n, to extend the limit, continuity and derivative concepts to multivariable functions.
    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 3
    8 To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge 3
    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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