Understanding the structure of Euclidean spaces and limit, continuity and differentiability properties of functions of several variables on Euclidean spaces.
Prerequisite(s)
None
Corequisite(s)
None
Special Requisite(s)
Proficiency in English, enough to be able to follow undergraduate texts in Mathematics.
Instructor(s)
Professor Mert ÇAĞLAR
Course Assistant(s)
Schedule
Wednesday 11:00-13:00; Thursday 11:00-13:00.
Office Hour(s)
Thursday 13:00-14:00 via İKÜ-CATS.
Teaching Methods and Techniques
Lecture and recitation.
Principle Sources
-William R. Wade, An Introduction to Analysis, Prentice Hall, Englewood Cliffs, NJ, 1995
Other Sources
-R.C. Buck, Advanced Calculus, McGraw-Hill, New York, 1965
-W. Kaplan, Advanced Calculus, Addison-Wesley Publishing Company, Inc., Reading, MA, 1984
-T.W. Körner, A Companion to Analysis: A Second First and First Second Course in Analysis,
Graduate Studies in Mathematics, Vol. 62, American Mathematical Society, Providence, RI, 2003
-J.E. Marsden & M.J. Hoffman, Elementary Classical Analysis, 2nd ed., Tenth Printing, W.H.
Freeman and Company, New York, 2003
-A. Nesin, Analiz IV, Gözden geçirilmiş 2. baskı, Nesin Matematik Köyü Kitaplığı, Nesin Yayıncılık, İstanbul, 2012
- 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
-Karl R. Stromberg, An Introduction to Classical Real Analysis, Wadsworth, Inc., Belmont, CA,
1981
Course Schedules
Week
Contents
Learning Methods
1. Week
Algebraic structure of R^n
Lecture and recitation
2. Week
Open and closed sets in R^n
Lecture and recitation
3. Week
Sequences and compact sets in R^n
Lecture and recitation
4. Week
Heine-Borel's Theorem
Lecture and recitation
5. Week
Convex and connected sets in R^n
Lecture and recitation
6. Week
Limits of functions on R^n
Lecture and recitation
7. Week
Continuity of functions on R^n
Lecture and recitation
8. Week
Midterm Exam
9. Week
Partial derivatives and integrals
Lecture and recitation
10. Week
Differentiability
Lecture and recitation
11. Week
Mean Value Theorem and Taylor's Formula
Lecture and recitation
12. Week
Inverse Function Theorem
Lecture and recitation
13. Week
Extrema I
Lecture and recitation
14. Week
Extrema II
Lecture and recitation
15. Week
Final Exam Week
16. Week
Final Exam Week
17. Week
Final Exam Week
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
40
Final Exam
1
60
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 the algebraic structure of Euclidean spaces.
LO-2
Understanding the topological structure of Euclidean spaces.
LO-3
Analyzing the inter-dependence of the algebraic and topological structures of Euclidean spaces.
LO-4
Understanding and analyzing limits and continuity of functions defined on Euclidean spaces.
LO-5
Solving problems on limits and continuity of functions defined on Euclidean spaces.
LO-6
Understanding and analyzing differentiability properties of functions defined on Euclidean spaces, and solving problems involving these.
LO-7
Understanding and analyzing the Mean Value Theorem and the Taylor's Formula, and solving problems involving these.
LO-8
Understanding the Inverse Function Theorem and the Implicit Function Theorem, and solving problems involving these.
LO-9
Understanding the extrema of functions of several variables, and solving problems involving these.
