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 571)
2021 Fall
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
10.00
Turgay Bayraktar tbayraktar@sabanciuniv.edu,
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English
Doctoral, Master
--
Formal lecture,Interactive lecture
Interactive,Learner centered,Communicative
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| Programs\Type | Required | Core Elective | Area Elective |
| MA-Economics | * | ||
| MA-Economics-Non Thesis | |||
| MA-European Studies | |||
| MA-European Studies-Non Thesis | |||
| MA-Political Science | |||
| MA-Political Science-Non Thes | |||
| MA-Visual Arts&Vis. Com Des-NT | |||
| MA-Visual Arts&Visual Com Des | |||
| MS-Bio. Sci. & Bioeng. LFI | |||
| MS-Bio. Sci. & Bioeng. LFI-ENG | |||
| MS-Biological Sci&Bioeng. | * | ||
| MS-Computer Sci.&Eng. LFI | |||
| MS-Computer Sci.&Eng. LFI-ENG | |||
| MS-Computer Science and Eng. | * | ||
| MS-Cyber Security(with thesis) | * | ||
| MS-Data Science | |||
| MS-Elec. Eng&Comp Sc.LFI-ENG | |||
| MS-Electronics Eng&Comp Sc.LFI | |||
| MS-Electronics Eng&Computer Sc | * | ||
| MS-Electronics Eng. | * | ||
| MS-Electronics Eng. LFI | |||
| MS-Electronics Eng. LFI-ENG | |||
| MS-Energy Techno.&Man. | * | ||
| MS-Industrial Eng. LFI-ENG | |||
| MS-Industrial Engineering | * | ||
| MS-Industrial Engineering LFI | |||
| MS-Manufacturing Eng-Non Thes | * | ||
| MS-Manufacturing Engineering | * | ||
| MS-Materials Sci & Engineering | * | ||
| MS-Materials Sci. & Eng. LFI | |||
| MS-Materials Sci.&Eng. LFI-ENG | |||
| MS-Mechatronics | * | ||
| MS-Mechatronics LFI | |||
| MS-Mechatronics LFI-ENG | |||
| MS-Physics | |||
| MS-Physics-Non Thesis | * | ||
| MS-Psychology | |||
| MS-Psychology-Non Thesis | |||
| PHD-Biological Sci&Bioeng. | * | ||
| PHD-Comp. Sci and Eng.after UG | * | ||
| PHD-Computer Science and Eng. | * | ||
| PHD-Cyber Security | * | ||
| PHD-Electronics Eng&ComputerSc | * | ||
| PHD-Electronics Eng. | * | ||
| PHD-Electronics Eng. after UG | * | ||
| PHD-Experimental Psychology | |||
| PHD-Industrial Engineering | * | ||
| PHD-Management | |||
| PHD-Manufacturing Eng after UG | * | ||
| PHD-Manufacturing Engineering | * | ||
| PHD-Materials Sci.&Engineering | * | ||
| PHD-Mechatronics | * | ||
| PHD-Mechatronics after UG | * | ||
| PHD-Physics | |||
| PHD-Physics after UG | |||
| PHD-Social Psychology | |||
| PHDBIO after UG | * | ||
| PHDCYSEC after UG | * | ||
| PHDECON after UG | |||
| PHDEECS after UG | * | ||
| PHDEPSY after UG | |||
| PHDIE after UG | * | ||
| PHDMAN after UG | |||
| PHDMAN after UG-Finance | |||
| PHDMAN after UG-Man. and Org. | |||
| PHDMAN after UG-Op.&Sup. Cha. | |||
| PHDMAN-Finance Area | |||
| PHDMAN-Man. and Org. Area | |||
| PHDMAN-Op. & Supp. Chain Area | |||
| PHDMAT after UG | * | ||
| PHDSPSY after UG |
CONTENT
OBJECTIVE
Learning the basics of mathematical analysis; i.e. basic theorems and basic techniques in analysis.
LEARNING OUTCOME
Comprehend the language of analysis
Read definitions, theorems, proofs.
Produce "own" proofs in simpler cases.
Comprehend the structure of real numbers and the Euclidean space.
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.
Update Date:
ASSESSMENT METHODS and CRITERIA
| Percentage (%) | |
| Final | 30 |
| Midterm | 30 |
| Exam | 30 |
| Other | 10 |
RECOMENDED or REQUIRED READINGS
| Textbook |
Elementary Classical Analysis; Marsden & Hoffman, Freeman 1974. |