MT132 Calculus II

8 ECTS - 4-2 Duration (T+A)- 2. Semester- 5 National Credit

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
Prof. Dr. ALİ ARSLAN ÖZKURT (A Group) (Ins. in Charge)


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

Update Time: 25.06.2024 10:27