Understanding the theory of integration on Euclidean spaces and its fundamental theorems.
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 via İKÜ-CATS.
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
-C. Buck, Advanced Calculus, McGraw-Hill, New York, 1965
-W. Fleming, Functions of Several Variables, 2nd ed., Springer-Verlag, New York, 2004
-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
-S. Lang, Calculus of Several Variables, 3rd ed., Springer-Verlag, New York, 1987
-W. Rudin, Principles of Mathematical Analysis, 3rd Edition, McGraw-Hill Book Co., New York,
1987
-M. Spivak, Calculus on Manifolds, HarperCollins Publishers, 1965
-Karl R. Stromberg, An Introduction to Classical Real Analysis, Wadsworth, Inc., Belmont, CA,
1981
-V.A. Zorich, Mathematical Analysis, Vol. I & Vol. II, Springer-Verlag, Berlin-Heidelberg, 2004
Course Schedules
Week
Contents
Learning Methods
1. Week
Jordan regions
Lecture and recitation
2. Week
Riemann integrability on Jordan regions I
Lecture and recitation
3. Week
Riemann integrability on Jordan regions II
Lecture and recitation
4. Week
Iterated integrals
Lecture and recitation
5. Week
Change-of-variables
Lecture and recitation
6. Week
Partitions of unity
Lecture and recitation
7. Week
Gamma function and volume
Lecture and recitation
8. Week
Midterm Exam
9. Week
Curves
Lecture and recitation
10. Week
Oriented curves
Lecture and recitation
11. Week
Surfaces
Lecture and recitation
12. Week
Oriented surfaces
Lecture and recitation
13. Week
Theorems of Green and Gauss
Lecture and recitation
14. Week
Stokes's Theorem
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 and analyzing Riemann integral on Jordan regions, and solving problems involving it.
LO-2
Understanding iterated integrals and solving problems involving them.
LO-3
Understanding change-of-variables and solving problems involving it.
LO-4
Understanding partitions of unity and solving problems involving them.
LO-5
Understanding the relation between the gamma function and volume.
LO-6
Understanding and analyzing curves and oriented curves, and solving problems involving these.
LO-7
Understanding and analyzing surfaces and oriented surfaces, and solving problems involving these.
LO-8
Understanding and analyzing the theorems of Green and Gauss, and solving problems involving them.
LO-9
Understanding and analyzing Stokes's Theorem, and solving problems involving it.
