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)
2022 Fall
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
10
Nihat Gökhan Göğüş nggogus@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 |
Computer Science and Engineering - With Bachelor's Degree | * | ||
Computer Science and Engineering - With Master's Degree | * | ||
Computer Science and Engineering - With Thesis | * | ||
Cyber Security - With Bachelor's Degree | * | ||
Cyber Security - With Master's Degree | * | ||
Cyber Security - With Thesis | * | ||
Data Science - With Thesis | * | ||
Economics - Non Thesis | * | ||
Economics - With Bachelor's Degree | * | ||
Economics - With Thesis | * | ||
Electronics Engineering and Computer Science - With Bachelor's Degree | * | ||
Electronics Engineering and Computer Science - With Master's Degree | * | ||
Electronics Engineering and Computer Science - With Thesis | * | ||
Electronics Engineering - With Bachelor's Degree | * | ||
Electronics Engineering - With Master's Degree | * | ||
Electronics Engineering - With Thesis | * | ||
Energy Technologies and Management-With Thesis | * | ||
Industrial Engineering - With Bachelor's Degree | * | ||
Industrial Engineering - With Master's Degree | * | ||
Industrial Engineering - With Thesis | * | ||
Leaders for Industry Biological Sciences and Bioengineering - Non Thesis | * | ||
Leaders for Industry Computer Science and Engineering - Non Thesis | * | ||
Leaders for Industry Electronics Engineering and Computer Science - Non Thesis | * | ||
Leaders for Industry Electronics Engineering - Non Thesis | * | ||
Leaders for Industry Industrial Engineering - Non Thesis | * | ||
Leaders for Industry Materials Science and Engineering - Non Thesis | * | ||
Leaders for Industry Mechatronics Engineering - Non Thesis | * | ||
Manufacturing Engineering - Non Thesis | * | ||
Manufacturing Engineering - With Bachelor's Degree | * | ||
Manufacturing Engineering - With Master's Degree | * | ||
Manufacturing Engineering - With Thesis | * | ||
Materials Science and Nano Engineering-(Pre:Materials Science and Engineering) | * | ||
Materials Science and Nano Engineering-(Pre:Materials Science and Engineering) | * | ||
Materials Science and Nano Engineering - With Thesis (Pre.Name: Materials Science and Engineering) | * | ||
Mechatronics Engineering - With Bachelor's Degree | * | ||
Mechatronics Engineering - With Master's Degree | * | ||
Mechatronics Engineering - With Thesis | * | ||
Molecular Biology, Genetics and Bioengineering (Prev. Name: Biological Sciences and Bioengineering) | * | ||
Molecular Biology, Genetics and Bioengineering-(Prev. Name: Biological Sciences and Bioengineering) | * | ||
Molecular Biology,Genetics and Bioengineering-With Thesis (Pre.Name:Biological Sciences and Bioeng.) | * | ||
Physics - Non Thesis | * | ||
Physics - With Bachelor's Degree | * | ||
Physics - With Master's Degree | * | ||
Physics - With Thesis | * |
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 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 |
Quiz | 30 |
Other | 10 |
RECOMENDED or REQUIRED READINGS
Textbook |
Elementary Classical Analysis; Marsden & Hoffman, Freeman 1974. |