Course Code	Semester	Course Name	LE/RC/LA	Course Type	Language of Instruction	ECTS
MB0062		Advanced Analysis I	2/2/0	DE	Turkish	5

Course Goals	Introduce students to theoretical concepts of analysis and bring them into use.
Prerequisite(s)	Analysis I, Analysis II
Corequisite(s)	None
Special Requisite(s)	The minimum qualifications that are expected from the students who want to attend the course.(Examples: Foreign language level, attendance, known theoretical pre-qualifications, etc.)
Instructor(s)	Assoc. Prof. Emel Yavuz
Course Assistant(s)
Schedule	Day, hours, XXX Campus, classroom number.
Office Hour(s)	Instructor name, day, hours, XXX Campus, office number.
Teaching Methods and Techniques	-Resitation and Oral Presentation
Principle Sources	-William R. Wade, An Introdution to Analysis, Fourth Edition, Prentice Hall, Englewood Cliffs, NJ, 2010.
Other Sources	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 ·         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 ·         Karl R. Stromberg, An Introduction to Classical Real Analysis, Wadsworth, Inc., Belmont, CA, 1981.

Course Schedules
Week	Contents	Learning Methods
1. Week	Real Number Series, Limits of Series, Limit Theorems	Resitation and Oral Presentation
2. Week	Bolzano-Weierstrass Theorem, Cauchy Series	Resitation and Oral Presentation
3. Week	Limit Supremum and Limit Infimum Concepts	Resitation and Oral Presentation
4. Week	Real Valuable Functions, Bi-Directional Limits	Resitation and Oral Presentation
5. Week	One-Way Limits and Infinity Limits, Continuity	Resitation and Oral Presentation
6. Week	Uniform Continuity	Resitation and Oral Presentation
7. Week	Concept of differentiation, differentiation theorems	Resitation and Oral Presentation
8. Week	Mean Value Theory, Taylor Theorem, l'Hôpital Rule	Resitation and Oral Presentation
9. Week	Inverse Function Theorems	Resitation and Oral Presentation
10. Week	Riemann Integrals, Riemann Totals	Resitation and Oral Presentation
11. Week	The Theory of Calculation, Generalized Riemann Integral	Resitation and Oral Presentation
12. Week	Infinite Series of Real Numbers, Non-Negative Series	Resitation and Oral Presentation
13. Week	Absolute Convergence, Alternate Series, Uniform Consistency of Series	Resitation and Oral Presentation
14. Week	Power Series, Analytic Functions	Resitation and Oral Presentation
15. Week
16. Week
17. 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 Investigate limit and continuity of sequences and functions and comments them. LO-2 Analyzes Derivative concept, mean value theory and comments their results. LO-3 Analyzes Monoton Functions, Inverse Function Theorem and comments their results. LO-4 Understands Riemannian Integral and Generalized Riemannian Integral concepts. LO-5 Will be able to calculate definite and indefinite integrals. LO-6 Understands the concept of series and convergence of series, checks convergence of series. LO-7 Calculates the radius of power series convergence.

Course Assessment Matrix:

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7	PO 8	PO 9	PO 10	PO 11
LO 1
LO 2
LO 3
LO 4
LO 5
LO 6
LO 7