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Syllabus ( MATH 112 )


   Basic information
Course title: Analysis II
Course code: MATH 112
Lecturer: Prof. Dr. Serkan Sütlü
ECTS credits: 7
GTU credits: 5 (4+2+0)
Year, Semester: 1, Spring
Level of course: First Cycle (Undergraduate)
Type of course: Compulsory
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: None
Professional practice: No
Purpose of the course: To teach the basic principles of Integral Calculus and its applications for functions of a real variable.
   Learning outcomes Up

Upon successful completion of this course, students will be able to:

  1. Explain the basic principles of Integral Calculus and its applications for functions of a real variable.

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

    Method of assessment

    1. Written exam
    2. Laboratory exercise/exam
  2. Recognize improper integrals.

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.

    Method of assessment

    1. Written exam
  3. Gain basic knowledge about sequences of functions, series of functions and Fourier series.

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Written exam
   Contents Up
Week 1: Indefinite Integrals: Primitive, basic properties of indefinite integrals.
Week 2: Substitution method, integration by parts,
Week 3: Integrals of rational functions.
Week 4: Integrals of some irrational and transandental functions.
Week 5: Definite Integrals: Riemann integral and its properties, some classes of integrable functions.
Week 6: Mean Value Theorem of integral calculus, the fundamental therem of integral calculus.
Week 7: Substitution in definite integral and integration by parts, functions of bounded variation.
Week 8: Improper integrals, convergence of improper integrals, convergence tests.
Midterm exam I
Week 9: Applications of definite integrals: Area, arc length, volume, surface area.
Week 10: Uniform convergence of sequences of functions, continuity of limit function. Uniform Cauchy sequence. Uniform convergence of series, term-by-term integration and differentiation.
Week 11: Power series, radius of convergence, interval of convergence. Taylor series.
Week 12: Weierstrass approximation theorem. Fourier series: Systems of orthogonal functions.
Week 13: Pointwise Convergence of Fourier series, uniform convergence criteria, Bessel’s inequality, convergence in the mean, Parseval’s equality.
Week 14: Fourier integrals and Fourier transformations.
Midterm exam II
Week 15*: -
Week 16*: Final exam
Textbooks and materials:
Recommended readings: G.M..FIKHTENGOL’TS “The fundamentals of Mathematical Analysis”, W.R.Parzgnski “Introduction to Mathematical Analysis”, Murray R.Spiegel “Advanced Calculus”
  * Between 15th and 16th weeks is there a free week for students to prepare for final exam.
Assessment Up
Method of assessment Week number Weight (%)
Mid-terms: 8, 14 40
Other in-term studies: 0
Project: 0
Homework: 0
Quiz: 0
Final exam: 16 60
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 4 14
Own studies outside class: 5 14
Practice, Recitation: 2 14
Homework: 0 0
Term project: 0 0
Term project presentation: 0 0
Quiz: 0 0
Own study for mid-term exam: 4 2
Mid-term: 4 2
Personal studies for final exam: 6 1
Final exam: 2 1
    Total workload:
    Total ECTS credits:
*
  * ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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