Mathematical Analysis I
Mathematics
Institute of Natural and Applied Sciences
Second Cycle (Master's Degree)
| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Mathematical Analysis I | MAT522 | Compulsory | Master's degree | 1 | Fall | 8 |
Name of Lecturer(s)
Prof. Dr. Halis AYGÜN
Prof. Dr. Serap BULUT
Prof. Dr. Serdal PAMUK
Associate Prof. Dr. Arzu AKGÜL
Associate Prof. Dr. Vildan ÇETKİN
Associate Prof. Dr. Banu PAZAR VAROL
Learning Outcomes of the Course Unit
1) Expound the topological structure of IR and IRn.
2) Investigate the notion of convergence in IRn.
3) Explain the compact and connected sets and also learn the notions of continuity functions, uniform continuity of functions and uniform convergence in IRn.
4) Calculate the multi-valued differentials, the concept of curve in IRn and directional derivatve.
5) State the important definitions and theorems such as chain rule, multi-valued mean value theorem, Taylor theorem, Inverse function theorem, Closed function theorem, maximum and minimum problems, related to both of analysis and topology in IRn.
Program Competencies-Learning Outcomes Relation
| Program Competencies | ||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
| Learning Outcomes | ||||||||
| 1 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 2 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 3 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 4 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 5 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
Mode of Delivery
Face to Face
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
Not Required
Course Contents
This course provides candidates with profound knowledge on completeness of IR, topological structure of IRn, convergence sequence in IRn, compact and connected sets, continuous functions and uniform continuity, Stone-Weierstrass theorem, differential of multivariable functions, curves in IRn, directional derivatives and differential, definition of derivative and notation of matrix, differentiable mappings, chain rule, multivariable mean-value theorem, Taylor theorem, maximum-minimum problems, inverse function theorem, closed function theorem and Lagrange multipliers.
Recommended or Required Reading
Planned Learning Activities and Teaching Methods
Assessment Methods and Criteria
Language of Instruction
Other
Work Placement(s)
Not Required