Understanding the structure of real number system and limit, continuity and differentiability properties of functions.
Prerequisite(s)
None
Corequisite(s)
None
Special Requisite(s)
None
Instructor(s)
Assist. Prof. Dr. Uğur GÖNÜLLÜ
Course Assistant(s)
Res. Assist. Deniz ÜÇÜNCÜ
Schedule
Monday 11:00-13:00, Thursday 15:00-17:00.
Office Hour(s)
Thursday 10:00-11:00, 3-A-15
Teaching Methods and Techniques
Lectures, recitations.
Principle Sources
William R. Wade, An Introduction to Analysis, Prentice Hall, Englewood Cliffs, NJ, 2004.
Other Sources
E. Bayar & Y. Gündüzalp, Analiz, I, Karadeniz Teknik Üniversitesi Basımevi, Trabzon, 1988.
R. Berker, Analiz Dersleri, İstanbul Üniversitesi Fen Fakültesi Döner Sermaye İsletmesi, Prof. Dr. Nâzım Terzioglu Basım Atölyesi, İstanbul, 1993.
Witold A.J. Kosmala, A Friendly Introduction to Analysis, 2nd Edition, Prentice Hall, Inc., Upper Saddle River, NJ, 2004
J.E. Marsden & M.J. Hoffman, Elementary Classical Analysis, 2nd ed., Tenth Printing, W.H. Freeman and Company, New York, 2003
William R. Parzynski & Philip W. Zipse, Introduction to Mathematical Analysis, McGraw-Hill Book Co., Singapore, 1987
W. Rudin, Principles of Mathematical Analysis, 3rd Edition, McGraw-Hill Book Co., New York, 1987
G. Saban, Analiz Dersleri, I, İstanbul Üniversitesi Yayınları, No: 1680, Fen Fakültesi Basımevi, İstanbul, 1971.
G. Saban, Analiz Dersleri, II, İkinci baskı, İstanbul Üniversitesi Yayınları, No: 2795, Fen Fakültesi Basımevi, İstanbul, 1981.
G. Saban, Analize Giriş, İstanbul Üniversitesi Yayınları, No: 3549, Fen Fakültesi Basımevi, İstanbul, 1989.
Karl R. Stromberg, An Introduction to Classical Real Analysis, Wadsworth, Inc., Belmont, CA, 1981.
Course Schedules
Week
Contents
Learning Methods
1. Week
The Real Number System: Introduction, Ordered Field Axioms
Lecture and recitation
2. Week
Completeness Axiom, Inverse Functions and Images
Lecture and recitation
3. Week
Sequences in R: Limits of Sequences, Limit Theorems, Bolzano–Weierstrass Theorem
Lecture and recitation
4. Week
Cauchy Sequences, Limits Supremum and Infimum
Lecture and recitation
5. Week
Functions on R: Two-Sided Limits, One-Sided Limits and Limits at Infinity
Lecture and recitation
6. Week
Continuity
Lecture and recitation
7. Week
Uniform Continuity
Lecture and recitation
8. Week
Differentiability on R: The Derivative, Differentiability Theorems
Lecture and recitation
9. Week
Derivatives of some functions I
Lecture and recitation
10. Week
Derivatives of some functions II
Lecture and recitation
11. Week
The Mean Value Theorem
Lecture and recitation
12. Week
Taylor’s Theorem and l’Hôpital’s Rule
Lecture and recitation
13. Week
Sketching the graph of a function
Lecture and recitation
14. Week
Inverse Function Theorems
Lecture and recitation
15. Week
Final week
16. Week
Final week
17. Week
Final week
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
2
60
Final Exam
1
40
Program Outcomes
PO-1
Interpreting advanced theoretical and applied knowledge in Mathematics and Computer Science.
PO-2
Critiquing and evaluating data by implementing the acquired knowledge and skills in Mathematics and Computer Science.
PO-3
Recognizing, describing, and analyzing problems in Mathematics and Computer Science; producing solution proposals based on research and evidence.
PO-4
Understanding the operating logic of computer and recognizing computational-based thinking using mathematics as a discipline.
PO-5
Collaborating as a team-member, as well as individually, to produce solutions to problems in Mathematics and Computer Science.
PO-6
Communicating in a foreign language, and interpreting oral and written communicational abilities in Turkish.
PO-7
Using time effectively in inventing solutions by implementing analytical thinking.
PO-8
Understanding professional ethics and responsibilities.
PO-9
Having the ability to behave independently, to take initiative, and to be creative.
PO-10
Understanding the importance of lifelong learning and developing professional skills continuously.
PO-11
Using professional knowledge for the benefit of the society.
Learning Outcomes
LO-1
Understanding and analyzing real number system, the concept of metric spaces, and in connection with this axiom of completeness, sequences and functions.
LO-2
Understanding the limit and continuity of functions and sequences, and solving problems involving these.
LO-3
Understanding and analyzing the concept of derivative, the Mean Value Theorem and its consequences, and solving problems involving these.
LO-4
Understanding the Inverse Function Theorem and its consequences, and monotone functions, and solving problems involving these.
LO-5
Analyzing and calculating the extrema of functions and sketching the graph of a function.
