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Syllabus ( MATH 111 )


   Basic information
Course title: Analysis I
Course code: MATH 111
Lecturer: Prof. Dr. Serkan Sütlü
ECTS credits: 7
GTU credits: 5 (4+2+0)
Year, Semester: 1, Fall
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 knowledge of numerical sequences, series and differential calculus of functions of a single real variable.
   Learning outcomes Up

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

  1. Gain the basic knowledge of numerical sequences and 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. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
    3. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Written exam
  2. Explain the basic knowledge of differential calculus of functions of a single 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.

    Method of assessment

    1. Written exam
  3. Explain the basic concepts of mathematical analysis.

    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
   Contents Up
Week 1: Sets, Logic Symbols, Functions.
Week 2: Real Numbers.
Week 3: Sequence of numbers, Limit of a sequence, convergence.
Week 4: Monotone sequences. Cauchy sequences.
Week 5: Series of numbers, tests for series of positive terms.
Week 6: Series of mixed terms, alternating series, Riemanns theorem.
Week 7: Functions of a single real variable, Limit of a function.
Week 8: Continuity, properties of continuous functions on a closed interval, uniform continuity. Midterm exam 1.
Week 9: Derivative, differential and their geometric interpretations.
Week 10: Rolles theorem, mean value theorem of differential calculus and its applications.
Week 11: Higher-order derivatives, Leibnitz formula.
Week 12: Taylors formula with Lagrange remainder.
Week 13: Extremum values, concavity. LHospitals rule.
Week 14: Curve sketching. Midterm exam 2.
Week 15*: -
Week 16*: Final exam
Textbooks and materials:
Recommended readings: G.M..FIKHTENGOL’TS “The fundamentals of Mathematical Analysis”, W.R.Parzynski “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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