MATH214 MATHEMATICAL ANALYSIS
| Course Code: | 2360214 |
| METU Credit (Theoretical-Laboratory hours/week): | 4 (3.00 - 2.00) |
| ECTS Credit: | 7.5 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | Assoc.Prof.Dr. SEMRA PAMUK |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
This course is designed to provide fundamental concepts of analysis, including classical theory of functions of a real variable, differentiation and integration of real functions, as well as some fundamental topics in topology of Euclidean space. Emphasis will be placed on the understanding of the proofs of the major theorems in calculus courses. The aim also is to provide the background in analysis necessary for the student to take other advanced courses in metric spaces and topology.
Course Content
Real Number System. Sequences in R. Definitions of Limit and Continuity, Differentiability theorems, Integrability theorems in R. Infinite series of real numbers and infinite series of functions. Euclidean Spaces, topology of R^n. Convergence, differentiability and integrability on R^n.
Course Learning Outcomes
At the end of the course students are expected to:
- The students will learn the basic results in the field and get experience in standard methods of real analysis.
- The students will get acquainted with the basic notions of the real number system (axioms, convergence, limit superior/inferior of real sequences, etc.).
- The student will learn the proofs of the theorems in Calculus courses.
- The student will be able to demonstrate competence with topology of Euclidean space, like determining a subset of Euclidean space open/closed or neither.
- The student will be able to demonstrate competence with doing proofs by using basic results in real anaysis.
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Can produce innovative thoughts and products. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Has a comprehension of mathematical symbols, concepts together with the interactions among them and can express his/her solutions similarly. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Is responsive to life-long learning, improving his/her skills and abilities | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution