TÜRKÇE
ENGLISH
Information
| Code | MT242 |
| Name | Advanced Calculus II |
| Term | 2024-2025 Academic Year |
| 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 Instructor |
1 2 |
Course Goal / Objective
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. | 4 |
| 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 | Demonstrates the ability to express the basic theories of mathematics accurately both in writing and orally. | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | |
| 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. | 4 |
| 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. | |
| 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. | 4 |
| 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, Soru-Cevap, Tartışma |
| 2 | Limit theorems | Reading the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 3 | Continuous functions and properties. | Reading the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 4 | Continuous functions on intervals. | Reading the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 5 | Uniform continuity | Reading the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 6 | Continuity of Monotone and inverse functions | Reading the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 7 | Derivative, differential. | Reading the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 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, Soru-Cevap, Tartışma |
| 10 | Taylor's theorem and its applications | Reading the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 11 | Sequences and series of functions | Reading the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 12 | Pointwise and uniform convergence, applications Weierstrass M-test | Reading the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 13 | Changing the order of limit in sequences of functions | Reading the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 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, Soru-Cevap, Tartışma |
| 15 | Power series | Reading the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 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 | ||