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,
Click here to view.
English
Undergraduate
--
Formal lecture
Interactive,Communicative,Discussion based learning
Click
here
to view.
Programs\Type | Required | Core Elective | Area Elective |
BA- Political Science | |||
BA-Cultural Studies | |||
BA-Cultural Studies | |||
BA-Economics | |||
BA-Economics | |||
BA-International Studies | |||
BA-International Studies | |||
BA-Management | |||
BA-Management | |||
BA-Political Sci.&Inter.Relat. | |||
BA-Political Sci.&Inter.Relat. | |||
BA-Social & Political Sciences | |||
BA-Visual Arts&Visual Com.Des. | |||
BA-Visual Arts&Visual Com.Des. | |||
BS-Biological Sci.&Bioeng. | * | ||
BS-Computer Science & Eng. | * | ||
BS-Computer Science & Eng. | * | ||
BS-Electronics Engineering | * | ||
BS-Electronics Engineering | * | ||
BS-Industrial Engineering | * | ||
BS-Manufacturing Systems Eng. | * | ||
BS-Materials Sci. & Nano Eng. | * | ||
BS-Materials Science & Eng. | * | ||
BS-Mechatronics | * | ||
BS-Mechatronics | * | ||
BS-Microelectronics | |||
BS-Molecular Bio.Gen.&Bioeng | * | ||
BS-Telecommunications | * | ||
Mathematics | * |
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. |