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)
2021 Fall
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
6.00 / 6.00 ECTS (for students admitted in the 2013-14 Academic Year or following years)
Turgay Bayraktar tbayraktar@sabanciuniv.edu,
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English
Undergraduate
--
Formal lecture
Interactive,Communicative,Discussion based learning
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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 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.
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. |