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Analysis II
| Course Code | Semester |
Course Name |
LE/RC/LA |
Course Type |
Language of Instruction |
ECTS |
| MB0005 |
2 |
Analysis II |
2/2/0 |
CC |
Turkish |
6 |
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| Course Goals |
Understanding the theory of integration and its fundamental theorems and the concept of series. |
| Prerequisite(s) |
None |
| Corequisite(s) |
None |
| Special Requisite(s) |
None |
| Instructor(s) |
Dr. Öğretim Üyesi Uğur Gönüllü |
| Course Assistant(s) |
Araş.Gör. Deniz ÜÇÜNCÜ |
| Schedule |
Monday: 15:00-16:30, Z-A-1
Thursday: 13:00-14:30, B1-1 |
| Office Hour(s) |
Wednesday: 11:00-12:30, |
| Teaching Methods and Techniques |
-Lecture |
| 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. |
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| Course Schedules |
| Week |
Contents |
Learning Methods |
| 1. Week |
Derivatives of Inverse Trigonometric Functions |
Lecture and recitation |
| 2. Week |
The Mean Value Theorem |
Lecture and recitation |
| 3. Week |
Indeterminate forms and l’Hôpital’s Rule, Sketching the graph of a function |
Lecture and recitation |
| 4. Week |
Inverse Function Theorems |
Lecture and recitation |
| 5. Week |
Riemann Integral |
Lecture and recitation |
| 6. Week |
Riemann Sums |
Lecture and recitation |
| 7. Week |
The Fundamental Theorem of Calculus |
Lecture and recitation |
| 8. Week |
Improper Integrals |
Lecture and recitation |
| 9. Week |
Series with nonnegative terms |
Lecture and recitation |
| 10. Week |
Absolute Convergence |
Lecture and recitation |
| 11. Week |
Alternating Series |
Lecture and recitation |
| 12. Week |
Uniform Convergence of Sequences |
Lecture and recitation |
| 13. Week |
Power Series |
Lecture and recitation |
| 14. Week |
Analitic Functions |
Lecture and recitation |
| 15. Week |
Final week |
Exam |
| 16. Week |
Final week |
Exam |
| 17. Week |
Final week |
Exam |
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| 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 Riemann and generalized Riemann integrals, and solving problems involving these. | | LO-2 | Evaluating definite and indefinite integrals. | | LO-3 | Understanding the concept of the series and the convergence of the series. | | LO-4 | Convergence tests for the series. | | LO-5 | Evaluating the radius of convergence of a power series. | |
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| Course Assessment Matrix: |
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| | 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 | | | | | | | | | | | |
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