Course Code	Semester	Course Name	LE/RC/LA	Course Type	Language of Instruction	ECTS
MB0063		Advanced Analysis II	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, Analysis III, Analysis IV, Advanced 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.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	Euclidean Spaces, Algebraic Structure, Planes and Linear Transformations	Resitation and Oral Presentation
2. Week	Topology on R ^ n, Interior, Closure and BoundaryConcepts	Resitation and Oral Presentation
3. Week	Convergence on R ^ n, Limits of Sequences, Heine-Borel Theorem	Resitation and Oral Presentation
4. Week	Limits of Functions, Continuous Functions	Resitation and Oral Presentation
5. Week	Differentiability on R ^ n, Partial Derivatives and Integrals	Resitation and Oral Presentation
6. Week	Definition of Differentiability, Derivatives	Resitation and Oral Presentation
7. Week	Differentials and Tangent Planes	Resitation and Oral Presentation
8. Week	Chain Rule, Mean Value Theorem and Taylor Formula	Resitation and Oral Presentation
9. Week	Inverse Function Theory	Resitation and Oral Presentation
10. Week	Integral on R ^ n, Jordan Zones, Riemannian Integral on Jordan Zones	Resitation and Oral Presentation
11. Week	Sequential Integrals, Variable Transformation	Resitation and Oral Presentation
12. Week	Basics of Vector Calculus, Curves, Guided Curves	Resitation and Oral Presentation
13. Week	Surfaces, Guided Surfaces	Resitation and Oral Presentation
14. Week	Green and Gauss Theorems, Stokes Theorem	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 Understands the algebraic and topological structure of Euclidean spaces, analyzes their dependence on each other. LO-2 Understands the limit and continuity of functions defined on Euclidean spaces and analyzes them. LO-3 Understands and differentiates properties of defined functions on Euclidean spaces. LO-4 Understands the Mean Value Theorem and Taylor Formula and analyzes them. LO-5 Understands Riemann integral on Jordan regions and analyzes them. LO-6 Understands curves and directed curves and analyzes them. LO-7 Understands surfaces and guided surfaces and solves questions about them. LO-8 Understands Green, Gauss ve Stokes Teoremleri'ni and analyzes them.

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
LO 8