• Course Information
  • Course Title Code Semester Laboratory+Practice (Hour) Pool Type ECTS
    Advanced Analysis II MATH202 SPRING 4+2 C 7
    Learning Outcomes
    1-Defines the concept of multiple integrals.
    2-Calculates double and triple integrals.
    3-Calculates line integrals.
    4-Uses calculation techniques of surface integral.
  • ActivityPercentage


    NumberTime (Hours)Total Workload (hours)
    Course Duration (Weeks x Course Hours)14684
    Classroom study (Pre-study, practice)14684
    Short-Term Exams (exam + preparation) 10166
    Midterm exams (exam + preparation)4011010
    Laboratory 0000
    Final exam (exam + preparation) 5011212
    Other 0000
    Total Workload (hours)   196
    Total Workload (hours) / 30 (s)     6,53 ---- (7)
    ECTS Credit   7
  • Course Content
  • Week Topics Study Metarials
    1 Basic definitions and theorems related to multiple integrals R1) Lecture Notes
    2 Reducing multiple integrals to consecutive integrals, changing variables in multiple integrals R1) Lecture Notes
    3 Improper multiple integrals and comparison test for convergence , changing variables in improper multiple integrals R1) Lecture Notes
    4 Double integrals, converting regions in double integrals, double integrals in polar coordinates R1) Lecture Notes
    5 Applications of double integrals: finding area and volume, center of mass, moment of inertia R1) Lecture Notes
    6 Triple integrals, spherical and cylindirical coordinates, triple improper integrals R1) Lecture Notes
    7 Application of triple integrals: volume, center of mass, moment of inertia R1) Lecture Notes
    8 Midterm exams
    9 Curves in n-dimensional space, parametrization of curves, basic definitions related to line integrals, line integrals of scalar and vector fields R1) Lecture Notes
    10 Line integrals in 3 dimensional space, path of independence, exact differentials, line integrals in plane R1) Lecture Notes
    11 Green`s theorem, multiple connected regions R1) Lecture Notes
    12 Surfaces in nth-dimensional space, parametrization of surfaces, smooth surfaces, directions in surfaces R1) Lecture Notes
    13 Surface integrals of scalar and vector fields R1) Lecture Notes
    14 Divergence and Stoke`s Theorem R1) Lecture Notes
    15 Applications of line and surface integrals R1) Lecture Notes
    Prerequisites -
    Language of Instruction English
    Coordinator Prof. Dr. Hüseyin Irmak
    Instructors -
    Assistants -
    Resources R1) Robert, A. A., Essex, C. (2007). Calculus: A Complete Course (7th Ed.). Pearson Education, Canada. R2) Stewart, J. (2015). Calculus (8th Ed.). Cengage Learning, Boston. R3) Hass, J.R., Heil, C.E., Weir, M.D. (2017). Thomas` Calculus (14 Ed.). Pearson, London.
    Supplementary Book -
    Goals To teach the basic properties of multiple integrals, double and triple integrals, applications of line integrals and surface integrals.
    Content Double integrals, triple integrals, line integrals, surface integrals, Green`s and Stokes` Theorems.
  • Program Learning Outcomes
  • Program Learning Outcomes Level of Contribution
    1 To have a grasp of theoretical and applied knowledge in main fields of mathematics 4
    2 To have the ability of abstract thinking 2
    3 To be able to use the gained mathematical knowledge in the process of identifying the problem, analyzing and determining the solution steps 4
    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 -
    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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