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Course Code: 
MATH 252
Semester: 
Spring
Course Type: 
Core
P: 
3
Lab: 
2
Laboratuvar Saati: 
0
Credits: 
4
ECTS: 
7
Course Language: 
English
Course Objectives: 
This course constitutes the pillar of many topics in mathematics such as complex analysis, differential equations, differential and integral calculus, and differential geometry. It is impossible to assimilate these areas of mathematics without having this basic knowledge of analysis. The aim of the course is to equip students with this basic knowledge.
Course Content: 

Elements of point set theory.Functions and the Real Number System. Open and closed sets in Rp. Accumulation points. Bolzano-Weierstrass theorem in Rp.  Compactness and connectedness.Heine Borel Theorem. Convergence of sequences in Rp. Sequences of Functions, Uniform Convergence Continuity and Uniform continuity.Sequences of Continuous Functions,Limits of Functions.

Course Methodology: 
1: Lecture, 2: Problem Solving
Course Evaluation Methods: 
A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes

Teaching Methods

Assessment Methods

1) Grasp the structure of the real numbers as a complete ordered field

1

A,B

2) Learn how to handle the convergence of sequences, series

1

A,B

3) Master the concept of the limit of functions and the concept of continuity;

1

A,B

4) Acquire the knowledge of differentiability of functions

1

A,B

5) Learn integration and classes of Riemann integrable functions

1

A,B

Course Flow

COURSE CONTENT

Week

Topics

Study Materials

1

Limits of Functions, Limit Theorems, Cauchy Convergence criterion

Textbook

2

Continuous Functions, Combinations of Continuous Functions, Continuous Functions on Intervals

Textbook

3

Uniform Continuity. Monotone functions. Inverse Function Theorem

Textbook

4

Continuous and Monotone Functions, Sequences of Functions, Pointwise and Uniform Convergence

Textbook

5

Cauchy Criterion for Uniform Convergence

Textbook

6

The Derivative, The Mean Value Theorem, L'Hospital Rules, Taylor's Theorem

Textbook

7

Partitions and Tagged Partitions, Riemann sum, Riemann integrability

Textbook

8

Some Properties of the Integral, Boundedness Theorem

Textbook

9

Riemann Integrable Functions, Cauchy Criterion,

Textbook

10

Squeeze Theorem, Classes of Riemann Integrable Functions

Textbook

11

Additivity Theorem, The Fundamental Theorem of Calculus,

Textbook

12

Substitution Theorem, Lebesgue’s lntegrability Criterion,

Textbook

13

Composition Theorem, The Product Theorem,

Textbook

14

Integration by Parts, Taylor’s Theorem with the Remainder

Textbook

Recommended Sources

RECOMMENDED SOURCES

Textbook

Robert G. Bartle, Donald R. Sherbert, Introduction to Real Anlaysis, Fourth Edition, John Wiley & Sons, Inc.(2011),ISBN-13: 978-0471433316ISBN-10: 9780471433316.

https://sciencemathematicseducation.files.wordpress.com/2014/01/0471433314realanalysis4.pdf

Additional Resources

Stephen Abbott, Understanding Analysis, Springer, 2. Edition (2015)

Material Sharing

Documents

 

Assignments

 

Exams

 

Assessment

IN-TERM STUDIES

NUMBER

PERCENTAGE

Mid-terms

2

70

Quizzes

 

-

Assignments

3

30

Total

 

100

CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE

 

40

CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE

 

60

Total

 

100

 

COURSE CATEGORY

Expertise/Field Courses

Course’s Contribution to Program

COURSE'S CONTRIBUTION TO PROGRAM

No

Program Learning Outcomes

Contribution

1

2

3

4

5

 

1

The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamental research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)

 

 

 

 

x

 

2

Acquiring fundamental knowledge on fundamental research fields in mathematics

 

 

 

 

x

 

3

Ability form and interpret the relations between research topics in mathematics

 

 

 

 

x

 

4

Ability to define, formulate and solve mathematical problems

 

 

 

 

x

 

5

Consciousness of professional ethics and responsibility

 

 

x

 

 

 

6

Ability to communicate actively

 

 

x

 

 

 

7

Ability of self-development in fields of interest

 

 

 

x

 

 

8

Ability to learn, choose and use necessary information technologies

 

 

x

 

 

 

9

Lifelong education

 

 

x

 

 

 

ECTS

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION

Activities

Quantity

Duration
(Hour)

Total
Workload
(Hour)

Course Duration (14x Total course hours)

14

5

70

Hours for off-the-classroom study (Pre-study, practice)

14

4

56

Mid-terms (Including self-study)

2

10

20

Quizzes

-

-

-

Assignments

3

5

15

Final examination (Including self-study)

1

15

15

Total Work Load

 

 

176

Total Work Load / 25 (h)

 

 

7

ECTS Credit of the Course

 

 

7

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