Bologna Information System

  • Course Information
  • Course Title Code Semester Laboratory+Practice (Hour) Pool Type ECTS
    Learning Outcomes
    1-To describe the concept of multiple integrals.
    2-To calculate double and triple integrals.
    3-To calculate line integrals.
    4-To use calculation techniques of surface integral.
  • 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 Basic definitions and theorems related to multiple integrals
    2 Reducing multiple integrals to consecutive integrals, changing variables in multiple integrals
    3 Improper multiple integrals and comparison test for convergence , changing variables in improper multiple integrals
    4 Double integrals, converting regions in double integrals, double integrals in polar coordinates
    5 Applications of double integrals: finding area and volume, center of mass, moment of inertia
    6 Triple integrals, spherical and cylindirical coordinates, triple improper integrals
    7 Application of triple integrals: volume, center of mass, moment of inertia
    8 Curves in n-dimensional space, parametrization of curves, basic definitions related to line integrals, line integrals of scalar and vector fields
    9 Line integrals in 3 dimensional space, path of independence, exact differentials, line integrals in plane
    10 Green`s theorem, multiple connected regions
    11 Surfaces in nth-dimensional space, parametrization of surfaces, smooth surfaces, directions in surfaces
    12 Surface integrals of scalar and vector fields
    13 Divergence and Stoke`s Theorem
    14 Applications of line and surface integrals
    Language of Instruction Turkish
    Course Coordinator Prof. Dr. Hüseyin IRMAK
    Instructors -
    Assistants -
    Resources Calculus, Robert A. Adams, Addison-Wesley, 2002.
    Supplementary Book Teori ve Çözümlü Problemlerle Analiz IV, Binali Musayev, Nizami Mustafayev, Kerim Koca, Seçkin Yayıncılık, 2007
    Document Lecture Notes
    Goals Teaching the basic properties of multiple integrals, double and triple integrals, applications of line integrals and surface integrals.
    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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