Introduction to Mathematical Analysis (MATH 571)

2022 Fall
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
10
Nihat Gökhan Göğüş nggogus@sabanciuniv.edu,
Click here to view.
English
Doctoral, Master
--
Formal lecture,Interactive lecture
Interactive,Learner centered,Communicative
Click here to view.
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

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.

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.

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.
QA300.M37.1993