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Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| MATHEMATICS PR. | |
| Code | MT332 |
| Name | Real Analysis |
| Term | 2018-2019 Academic Year |
| Semester | 6. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Label | C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. GONCA AYIK |
| Course Instructor |
Prof. Dr. GONCA AYIK
(Bahar)
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The aim of this course is to make students comprehend Riemann integrability criteria, integrable functions, fundamental theorem of calculus, Darbox theorem, inverse and implicit function theorem.
Course Content
In this course 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 are described.
Course Precondition
Resources
Principle of Mathematical Analysis,Walter Rudin,McGraw-Hill, 1976. <br> Analiz I,II, Erdal Coşkun, Alp Yayınevi, 2002. <br> Introduction To Real Analysis , Robert G. Bartle, Donald R. Bartle,Wiley, 1992.
Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Realises Riemann integrability criteria. |
| LO02 | Recognizes integrable functions. |
| LO03 | Realises fundamental theorem of calculus. |
| LO04 | Realises integral as a limit and improper integral. |
| LO05 | Realises uniform convergence and intercahange of limits. |
| LO06 | Realises the Taylor formula. |
| LO07 | Realises the Darbox theorem. |
| LO08 | Realises inverse and implicit function theorems. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | - | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | 5 |
| PLO02 | - | Understands importance of basic consepts of Algebra, Analaysis and Topology. | 5 |
| PLO03 | - | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 3 |
| PLO04 | - | Demonstrate the ability to express the basic theories of mathematics both correctly. | 4 |
| PLO05 | - | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 3 |
| PLO06 | - | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | 4 |
| PLO07 | - | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 5 |
| PLO08 | - | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 5 |
| PLO09 | - | Comprehends at least one of the computer programming languages. | 5 |
| PLO10 | - | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 0 |
| PLO11 | - | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | 0 |
| PLO12 | - | In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities. | 0 |
| PLO13 | - | Understands the programming techniques and shows the ability to do programming. | 0 |
| PLO14 | - | Demonstrates the ability to study mathematics both independently and as a group. | 0 |
| PLO15 | - | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | |
| PLO16 | - | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | |
| PLO17 | - | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | |
| PLO18 | - | Gains the ability to use information technologies effectively for contemporary mathematical applications. | |
| PLO19 | - | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | |
| PLO20 | - | Gains the consciousness of prefesional ethics and responsibility. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Reimann Integral | Review of the relevant pages from sources | |
| 2 | Reimann integrability | Review of the relevant pages from sources | |
| 3 | Integrable functions | Review of the relevant pages from sources | |
| 4 | Solving problem | Review of the relevant pages from sources | |
| 5 | Properties of Riemann integral | Review of the relevant pages from sources | |
| 6 | Integrability of continuous and monotone functions | Review of the relevant pages from sources | |
| 7 | Fundamental theorem of calculus | Review of the relevant pages from sources | |
| 8 | Mid-Term Exam | Review and problem solving | |
| 9 | Taylor formula | Review of the relevant pages from sources | |
| 10 | Darboux theorem | Review of the relevant pages from sources | |
| 11 | Improper Integral | Review of the relevant pages from sources | |
| 12 | Functions of several variables | Review of the relevant pages from sources | |
| 13 | Inverse function theorem | Review of the relevant pages from sources | |
| 14 | Implicit function theorem | Review of the relevant pages from sources | |
| 15 | Implicit function theorem | Review of the relevant pages from sources | |
| 16 | Term Exams | Review and problem solving | |
| 17 | Term Exams | Review and problem solving |
Assessment (Exam) Methods and Criteria
| Assessment Type | Midterm / Year Impact | End of Term / End of Year Impact |
|---|---|---|
| 1. Midterm Exam | 100 | 40 |
| General Assessment | ||
| Midterm / Year Total | 100 | 40 |
| 1. Final Exam | - | 60 |
| Grand Total | - | 100 |
Student Workload - ECTS
| Works | Number | Time (Hour) | 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 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 114 | ||
| Total Workload / 25 (h) | 4,56 | ||
| ECTS | 5 ECTS | ||