Analysis I (MATH 501)

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
Learner centered,Discussion based learning,Task based learning
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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 *
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) *
Mathematics - With Bachelor's Degree *
Mathematics - With Master's Degree *
Mathematics - With Thesis *
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

Lebesgue measure and integration on the line. Convergence theorems. General measure and integration. Lp spaces. Decomposition of measures. Radon Nikodym theorem. Product measures and Fubini's theorem.

OBJECTIVE

To teach the Measure Theory and Lebesgue Integration, together with some basic aplications to and connections with other parts of Analysis.

LEARNING OUTCOMES

  • Use Caratheodery definition to construct Lebesgue-Stieltjes measure on the line and Lebesgue measure on any Euclidean space
  • Define and use convergence theorems
  • Define the Lebesgue Integral
  • Use Radon Nikodym theorem, product measures and Fubini's theorem to evaluate integrals.

ASSESSMENT METHODS and CRITERIA

  Percentage (%)
Midterm 30
Homework 60
Other 10

RECOMENDED or REQUIRED READINGS

Readings

Walter Rudin, Real and Complex Analysis, McGraw-Hill, London, New York.