The least upper bound property in R, equivalents and consequences. Metric spaces. Completeness, compactness, connectedness. Functions,continuity. Sequences and series of functions. Contraction mapping theorem and applications to calculus: Inverse and implicit function theorems.
Introduction to Mathematical Analysis (MATH 301)
| Programs\Type | Required | Core Elective | Area Elective |
| Computer Science and Engineering | * | ||
| Computer Science and Engineering | * | ||
| Electronics Engineering | * | ||
| Electronics Engineering | * | ||
| Industrial Engineering | * | ||
| Industrial Engineering (Previous Name: Manufacturing Systems Engineering) | * | ||
| Materials Science and Nano Engineering | * | ||
| Materials Science and Nano Engineering (Previous Name: Materials Science and Engineering) | * | ||
| Mathematics Minor | * | ||
| Mechatronics Engineering | * | ||
| Mechatronics Engineering | * | ||
| Microelectronics | * | ||
| Molecular Biology, Genetics and Bioengineering | * | ||
| Molecular Biology, Genetics and Bioengineering (Pre. Name: Biological Sciences and Bioengineering) | * | ||
| Telecommunications | * |
CONTENT
OBJECTIVE
Learning the basics of mathematical analysis; i.e. basic theorems and basic techniques in analysis.
LEARNING OUTCOMES
- Comprehend the language of analysis
- Read and understand definitions, theorems, proofs.
- Produce their "own" proofs in some cases.
- Comprehend the structure of real numbers and the Euclidean space. Comprehend the basic theorems of Calculus.
- Comprehend the topology of the Euclidean space.
- Comprehend the notion and use the facts of continuity.
- Comprehend the notion and use the facts of differentiability.
- Comprehend the notion and use the inverse and implicit function theorems.
- Comprehend the notion and use the facts of Riemann integrals.
PROGRAMME OUTCOMES
1. Understand the world, their country, their society, as well as themselves and have awareness of ethical problems, social rights, values and responsibility to the self and to others. 1
2. Understand different disciplines from natural and social sciences to mathematics and art, and develop interdisciplinary approaches in thinking and practice. 4
3. Think critically, follow innovations and developments in science and technology, demonstrate personal and organizational entrepreneurship and engage in life-long learning in various subjects; have the ability to continue to educate him/herself. 2
4. Communicate effectively in Turkish and English by oral, written, graphical and technological means. 1
5. Take individual and team responsibility, function effectively and respectively as an individual and a member or a leader of a team; and have the skills to work effectively in multi-disciplinary teams. 3
1. Possess sufficient knowledge of mathematics, science, fundamental engineering, computational methods and program-specific engineering topics; use theoretical and applied knowledge of these areas in complex engineering problems. 4
2. Identify, define, formulate and solve complex engineering problems while considering the UN Sustainable Development Goals; choose and apply suitable analysis, design, estimation/prediction and modeling methods for this purpose. 3
3. Develop, choose and use modern techniques and tools that are needed for analysis and solution of complex problems faced in engineering applications; use information technologies effectively. 2
4. Have the ability to design a complex system, process, instrument or a product under realistic constraints and conditions, with the goal of fulfilling creative current and future requirements. 2
5. Use research methods, including conducting literature reviews, designing experiments, performing experiments, collecting data, analyzing results, and interpreting results, to investigate complex engineering problems or discipline-specific research topics. 3
6. Possess knowledge of business practices such as project management, risk management, change management, and economic feasibility analysis; awareness on entrepreneurship and innovation. 3
7. Possess knowledge of impact of engineering solutions on society, health and safety, the economy, sustainability, and the environment within the framework of the UN Sustainable Development Goals; awareness on legal outcomes of engineering solutions; awareness of acting impartially and inclusively without any form of discrimination; act in accordance with ethical principles, possessing knowledge of professional and ethical responsibilities. 2
8. Communicate effectively, both orally and in writing, on technical subjects, considering the diverse characteristics of the target audience (such as education, language, and profession). 2
Update Date:
ASSESSMENT METHODS and CRITERIA
| Percentage (%) | |
| Final | 40 |
| Midterm | 30 |
| Homework | 30 |
RECOMENDED or REQUIRED READINGS
| Textbook |
Michael C. Reed, Fundamental Ideas of Analysis, John Wiley \& Sons, Inc., 1998. We will cover the first 6 chapters, we will skip some sections. |