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| Course Description |
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| Course Name |
: |
Real Analysis |
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| Course Code |
: |
MT 332 |
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| Course Type |
: |
Compulsory |
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| Level of Course |
: |
First Cycle |
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| Year of Study |
: |
3 |
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| Course Semester |
: |
Spring (16 Weeks) |
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| ECTS |
: |
5 |
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| Name of Lecturer(s) |
: |
Prof.Dr. GONCA AYIK
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| Learning Outcomes of the Course |
: |
Uses Riemann integrability criteria.
Recognizes integrable functions.
Uses Fundamental theorem of calculus.
Is able to use the Taylor formula.
Is able to use the Darbox theorem.
Uses inverse and implicit function theorems.
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|
| Mode of Delivery |
: |
Face-to-Face |
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| Prerequisites and Co-Prerequisites |
: |
None |
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| Recommended Optional Programme Components |
: |
None |
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| Aim(s) of Course |
: |
Using Riemann integrability criteria, Recognize integrable functions,Using Fundamental theorem of calculus, using Darbox theorem, using inverse and implicit function theorem |
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| Course Contents |
: |
Riemann integral, Properties of Riemann integral, Fundamental theorem of calculus, Integral as a limit, improper integral, uniform convergence, intercahange of limits, Inverse and implicit function theorem. |
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| Language of Instruction |
: |
Turkish |
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| Work Place |
: |
Faculty of Arts and Sciences Annex Classrooms |
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Course Outline /Schedule (Weekly) Planned Learning Activities |
| Week | Subject | Student's Preliminary Work | Learning Activities and Teaching Methods |
|
1 |
Reimann Integral |
Review of the relevant pages from sources |
Lecture and discussion |
|
2 |
Reimann integrability |
Review of the relevant pages from sources |
Lecture and discussion |
|
3 |
Integrable functions |
Review of the relevant pages from sources |
Lecture and discussion |
|
4 |
Solving problem |
Review of the relevant pages from sources |
Lecture and discussion |
|
5 |
Properties of Riemann integral |
Review of the relevant pages from sources |
Lecture and discussion |
|
6 |
Integrability of continuous and monotone functions. |
Review of the relevant pages from sources |
Lecture and discussion |
|
7 |
Fundamental theorem of calculus |
Review of the relevant pages from sources |
Lecture and discussion |
|
8 |
Mid-term exam |
Review and problem solving |
Written exam |
|
9 |
Taylor´ s formula |
Review of the relevant pages from sources |
Lecture and discussion |
|
10 |
Darboux theorem |
Review of the relevant pages from sources |
Lecture and discussion |
|
11 |
Improper Integral |
Review of the relevant pages from sources |
Lecture and discussion |
|
12 |
Functions of several variables |
Review of the relevant pages from sources |
Lecture and discussion |
|
13 |
Inverse function theorem |
Review of the relevant pages from sources |
Lecture and discussion |
|
14 |
Implicit function theorem |
Review of the relevant pages from sources |
Lecture and discussion |
|
15 |
Implicit function theorem |
Review of the relevant pages from sources |
Lecture and discussion |
|
16/17 |
Final exam |
Review and problem solving |
written exam |
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|
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Required Course Resources |
| Resource Type | Resource Name |
| Recommended Course Material(s) |
 Principle of Mathematical Analysis,Walter Rudin,McGraw-Hill, 1976.
Analiz I,II, Erdal Coşkun, Alp Yayınevi, 2002.
Introduction To Real Analysis , Robert G. Bartle, Donald R. Bartle,Wiley, 1992.
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| |
| Required Course Material(s) | |
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Assessment Methods and Assessment Criteria |
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Semester/Year Assessments |
Number |
Contribution Percentage |
|
Mid-term Exams (Written, Oral, etc.) |
1 |
100 |
|
Homeworks/Projects/Others |
0 |
0 |
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Total |
100 |
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Rate of Semester/Year Assessments to Success |
40 |
| |
|
Final Assessments
|
100 |
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Rate of Final Assessments to Success
|
60 |
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Total |
100 |
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| Contribution of the Course to Key Learning Outcomes |
| # | Key Learning Outcome | Contribution* |
|
1 |
Is able to prove Mathematical facts encountered in secondary school. |
5 |
|
2 |
Recognizes the importance of basic notions in Algebra, Analysis and Topology |
5 |
|
3 |
Develops maturity of mathematical reasoning and writes and develops mathematical proofs. |
3 |
|
4 |
Is able to express basic theories of mathematics properly and correctly both written and verbally |
4 |
|
5 |
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. |
3 |
|
6 |
Expresses clearly the relationship between objects while constructing a model |
4 |
|
7 |
Draws mathematical models such as formulas, graphs and tables and explains them |
5 |
|
8 |
Is able to mathematically reorganize, analyze and model problems encountered. |
5 |
|
9 |
Knows at least one computer programming language |
5 |
|
10 |
Uses effective scientific methods and appropriate technologies to solve problems |
0 |
|
11 |
Knows programming techniques and is able to write a computer program |
0 |
|
12 |
Is able to do mathematics both individually and in a group. |
0 |
|
13 |
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians |
0 |
|
14 |
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields |
0 |
| * Contribution levels are between 0 (not) and 5 (maximum). |
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| Student Workload - ECTS |
| Works | Number | Time (Hour) | Total Workload (Hour) |
| Course Related Works |
|
Class Time (Exam weeks are excluded) |
14 |
3 |
42 |
|
Out of Class Study (Preliminary Work, Practice) |
14 |
3 |
42 |
| Assesment Related Works |
|
Homeworks, Projects, Others |
0 |
0 |
0 |
|
Mid-term Exams (Written, Oral, etc.) |
1 |
15 |
15 |
|
Final Exam |
1 |
20 |
20 |
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Total Workload: | 119 |
| Total Workload / 25 (h): | 4.76 |
| ECTS Credit: | 5 |
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