MT242 Advanced Calculus II

7 ECTS - 4-0 Duration (T+A)- 4. Semester- 4 National Credit

Information

Code MT242
Name Advanced Calculus II
Semester 4. Semester
Duration (T+A) 4-0 (T-A) (17 Week)
ECTS 7 ECTS
National Credit 4 National Credit
Teaching Language Türkçe
Level Lisans Dersi
Type Normal
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator Dr. Öğr. Üyesi Doğa Can SERTBAŞ


Course Goal

To comprehend fully the structure of and prove the properties of the real numbers analytically which were used in MT131 and MT 132 . Thus, equipped with the basic infrastructure of real-analysis, the student is able to comprehend advamced abstract concepts of analysis.

Course Content

Limit, continuity, derivatives in functions. Sequences and series of functions.

Course Precondition

None.

Resources

Introduction to Real Analysis, Robert G. Bartle, Donald R. Sherbert http://matematik.cu.edu.tr/Dersler/MT241/MT241.htm

Notes

Principles of Mathematical Analysis, Walter Rudin


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Knows limit theorems for functions, continuity, and proper continuity
LO02 Uses monotone and inverse functions to solve the problems faced by using fundamental theorems.
LO03 Knows derivatives and differential calculus.
LO04 Knows the Mean value theorem and its applications.
LO05 Knows Taylor series expansion of the functions and how it is used for numerical computations.
LO06 Knows to use sequences and series of functions to define new functions.
LO07 Knows the Weirstrass M-test and the advantages of uniform convergence.
LO08 Knows the analytical definitions of geometrically defined functions, using power series.


Relation with Program Learning Outcome

Order Type Program Learning Outcomes Level
PLO01 Bilgi - Kuramsal, Olgusal Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. 5
PLO02 Bilgi - Kuramsal, Olgusal Understands importance of basic consepts of Algebra, Analaysis and Topology. 3
PLO03 Yetkinlikler - Öğrenme Yetkinliği Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. 4
PLO04 Bilgi - Kuramsal, Olgusal Demonstrate the ability to express the basic theories of mathematics both correctly. 5
PLO05 Bilgi - Kuramsal, Olgusal Understands the relationship between the different fields of mathematics and its relation to other disciplines. 4
PLO06 Bilgi - Kuramsal, Olgusal Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem.
PLO07 Bilgi - Kuramsal, Olgusal Comprehend and explain mathematical models such as formulas, graphs, tables and schema. 2
PLO08 Bilgi - Kuramsal, Olgusal Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. 5
PLO09 Bilgi - Kuramsal, Olgusal Comprehends at least one of the computer programming languages.
PLO10 Bilgi - Kuramsal, Olgusal Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. 4
PLO11 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
PLO12 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities. 2
PLO13 Yetkinlikler - Öğrenme Yetkinliği Understands the programming techniques and shows the ability to do programming.
PLO14 Yetkinlikler - Öğrenme Yetkinliği Demonstrates the ability to study mathematics both independently and as a group. 5
PLO15 Bilgi - Kuramsal, Olgusal Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. 4
PLO16 Bilgi - Kuramsal, Olgusal Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. 3
PLO17 Bilgi - Kuramsal, Olgusal It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability.
PLO18 Bilgi - Kuramsal, Olgusal Gains the ability to use information technologies effectively for contemporary mathematical applications.
PLO19 Bilgi - Kuramsal, Olgusal Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. 4
PLO20 Bilgi - Kuramsal, Olgusal Gains the consciousness of prefesional ethics and responsibility. 4


Week Plan

Week Topic Preparation Methods
1 Limits of functions and properties. Reading the relevant pages from sources Öğretim Yöntemleri:
Anlatım
2 Limit theorems Reading the relevant pages from sources Öğretim Yöntemleri:
Anlatım
3 Continuous functions and properties. Reading the relevant pages from sources Öğretim Yöntemleri:
Anlatım
4 Continuous functions on intervals. Reading the relevant pages from sources Öğretim Yöntemleri:
Anlatım
5 Uniform continuity Reading the relevant pages from sources Öğretim Yöntemleri:
Anlatım
6 Continuity of Monotone and inverse functions Reading the relevant pages from sources Öğretim Yöntemleri:
Anlatım
7 Derivative, differential. Reading the relevant pages from sources Öğretim Yöntemleri:
Anlatım
8 Mid-Term Exam Review topics discussed in the lecture notes and sources Ölçme Yöntemleri:
Yazılı Sınav
9 The mean value theorem and its applications Reading the relevant pages from sources Öğretim Yöntemleri:
Anlatım
10 Taylor's theorem and its applications Reading the relevant pages from sources Öğretim Yöntemleri:
Anlatım
11 Sequences and series of functions Reading the relevant pages from sources Öğretim Yöntemleri:
Anlatım
12 Pointwise and uniform convergence, applications Weierstrass M-test Reading the relevant pages from sources Öğretim Yöntemleri:
Anlatım
13 Changing the order of limit in sequences of functions Reading the relevant pages from sources Öğretim Yöntemleri:
Anlatım
14 Relationship between the derivative of the limit and the limit of the derivatives in sequences of functions Reading the relevant pages from sources Öğretim Yöntemleri:
Anlatım
15 Power series Reading the relevant pages from sources Öğretim Yöntemleri:
Anlatım
16 Term Exams Review topics discussed in the lecture notes and sources Ölçme Yöntemleri:
Yazılı Sınav
17 Term Exams Review topics discussed in the lecture notes and sources Ölçme Yöntemleri:
Yazılı Sınav


Student Workload - ECTS

Works Number Time (Hour) Workload (Hour)
Course Related Works
Class Time (Exam weeks are excluded) 14 4 56
Out of Class Study (Preliminary Work, Practice) 14 6 84
Assesment Related Works
Homeworks, Projects, Others 0 0 0
Mid-term Exams (Written, Oral, etc.) 1 8 8
Final Exam 1 16 16
Total Workload (Hour) 164
Total Workload / 25 (h) 6,56
ECTS 7 ECTS