MAT6010 Advanced Calculus IIBahçeşehir UniversityDegree Programs MATHEMATICS (TURKISH, PHD)General Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
MATHEMATICS (TURKISH, PHD)
PhD TR-NQF-HE: Level 8 QF-EHEA: Third Cycle EQF-LLL: Level 8

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT6010 Advanced Calculus II Fall 3 0 3 8
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: Turkish
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Assoc. Prof. ERSİN ÖZUĞURLU
Recommended Optional Program Components: None
Course Objectives: To teach fundamental concepts of real analysis, teaching fundamental proof methods, to gain ability of solving theoretical questions.

Learning Outcomes

The students who have succeeded in this course;
He/She knows measure spaces and measurable functions.
He/She knows convergence theorems.
He/She knows Bounded variation space.
He /She knows Lp spaces.
He/She knows outer measures.
He/She knows Lebesgue-Stieltjes integral.
He/She recodnise integral operators.
He/She knows Caratheodory outer measure.

Course Content

Measure Spaces, measurable sets, integration, general convergence theorems, bounded variation space, Lp spaces, outer measure and measurability, extension theorem, Lebesgue_Stieltjes integral, product measures, integral operators, extension with null sets, Caratheodory outer measure, Haussdorff measures.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Measure spaces.
2) Measurable functions, integration.
3) General convergence theorems.
4) Space of bounded variation.
5) Radon-Nikodym Theorem, Lp Spaces.
6) Radon-Nikodym Theorem, Lp Spaces (continued)
7) Outer measure and measurability.
8) Extension theorem.
9) Lebesgue-Stieltjes integral.
10) Product measures.
11) Integral operators
12) Integral operators (continued)
13) extension with null sets.
14) Caratheodory outer measure

Sources

Course Notes / Textbooks: Gerald B. Folland, Real Analysis: Modern Techniques and Their Applications, 1999, Wiley Publications.
References: H. L. Royden, Real Analysis, 1988, Prentice-Hall, Inc.
So Bon Chae, Lebesgue integration, 1998, Springer Verlag.
A. N. Kolmogorov, S. V. Fomin, Introductory Real Analysis 2000, Dover Publications.
Paul R. Halmos, Measure Theory, 1978, Springer Verlag.

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Project 1 % 20
Midterms 1 % 30
Final 1 % 50
Total % 100
PERCENTAGE OF SEMESTER WORK % 30
PERCENTAGE OF FINAL WORK % 70
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Study Hours Out of Class 14 3 42
Project 1 60 60
Midterms 1 26 26
Final 1 30 30
Total Workload 200

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution