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Information
| Code | MT132 |
| Name | Calculus II |
| Term | 2024-2025 Academic Year |
| Semester | 2. Semester |
| Duration (T+A) | 4-2 (T-A) (17 Week) |
| ECTS | 8 ECTS |
| National Credit | 5 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ALİ ARSLAN ÖZKURT |
| Course Instructor |
1 2 |
Course Goal / Objective
Calculating mathematical and physical quantities using integral and series summation. Introduction to functions of several variables.
Course Content
Infinite Sequences and Series. Power series. Polar coordinates and parametrized curves. Indefinite and definite integral. Applications of the definite integral. Functions of several variables.
Course Precondition
Pre-requisites None
Resources
http://math.cu.edu.tr/Dersler/MT132/MT132.htm
Notes
Analize Giriş Vol. II ; Fikri Akdeniz, Yusuf Ünlü, Doğan Dönmez
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Computes limits of sequences |
| LO02 | Determines the convergence of an infinite series |
| LO03 | Expresses functions as power series |
| LO04 | Recognizes and sketch different curves. |
| LO05 | Computes indefinite integrals |
| LO06 | Computes definite integrals. |
| LO07 | Computes area, volume, arc length, surface area and center of mass using definite integral. |
| LO08 | Finds the limits of functions of several variables. |
| LO09 | Computes partial derivatives of functions of several variables. |
| LO10 | Finds maxima and minima of functions of several variables. |
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. | 2 |
| 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. | 3 |
| 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. | 4 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 4 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 3 |
| 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. | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Understands the programming techniques and shows the ability to do programming. | 2 |
| 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. | 3 |
| PLO18 | Bilgi - Kuramsal, Olgusal | Gains the ability to use information technologies effectively for contemporary mathematical applications. | 3 |
| 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. | 3 |
| PLO20 | Bilgi - Kuramsal, Olgusal | Gains the consciousness of prefesional ethics and responsibility. | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Sequences, Limit. Limit theorems. Infinite limits. Monotone convergence theorem. Subsequences | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 2 | Convergence of series. n-th term Test. Geometric series and p-series. Comparison and Limit Comparison, Ratio and Root Tests. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 3 | Power Series, radius of convergence. Term by term integratron of power series. Taylor and McLaurin series. Binomial Theroem. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 4 | Polar coordinates. Some special curves. Sketching graphs. Slope of the tangent. Parametrized curves. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 5 | Indefinite integral, definition and properties. Change of variable, integration by parts. Integration of some trigonometric functions. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 6 | Integration of some algebraic functions by substitution. Reduction formulas. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 7 | Integration of the rational functions. Trigonometric and some special integrals. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 8 | Mid-Term Exam | Review and Problem Solving | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Definiton and properties of definite inegral. The fundamental theorems of Calculus. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 10 | Change of variable formula, Improper integrals, convergence. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 11 | Integral Test. Finding area in rectangular and polar coordinates. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 12 | Calculating volume using disc and cylindirical shell methods. Arc length. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 13 | Area of surface of revolution. Center of mass. Pappus theorem. Functions of several variables. Limit and Continuity. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 14 | Maximum-Minimum Theorem. Partial derivative and differentiability. Chain Rule. Finding maxima and minima. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 15 | Differential Forms. Exact forms and closed forms. Gradient. Normals of level curves and level surfaces. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 16 | Term Exams | Review and Problem Solving | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review and Problem Solving | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 6 | 84 |
| 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 | 6 | 6 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 192 | ||
| Total Workload / 25 (h) | 7,68 | ||
| ECTS | 8 ECTS | ||