TÜRKÇE
ENGLISH
Information
Course Goal / Objective
Computation of physical and geometric quantities using multiple integrals.
Course Content
Definition of double integral. Computation of double integrals in rectangular and polar coordinates. Change of coordinates. Computing area, mass and centrer of mass. Definition of triple integral. Computation of triple integrals in rectangular and cylindirical and spherica coordinates. Change of coordinates. Computing volume, mass and centrer of mass.
Course Precondition
None.
Resources
Thomas Calculus 1. ve 2. cilt, G. B. Thomas, M. D. Weir, J. R. Hass, F. R. Giordano, çeviren: Recep Korkmaz, Beta Yayınevi, 11. Baskı, 2010.
Notes
Calculus: A Complete Course, Richard A. Adams, Prentice Hall, 6th ed, 2006.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Computes double integrals in rectangular coordinates. |
| LO02 | Computes double integrals in polar coordinates. |
| LO03 | Computes the masses and coordinates of center of mass of plane regions |
| LO04 | Computes surface areas. |
| LO05 | Computes triple integrals in rectangular coordinates. |
| LO06 | Computes triple integrals in cylindirical coordinates. |
| LO07 | Computes triple integrals in spherical coordinates. |
| LO08 | Computes the masses and coordinates of center of mass of space regions |
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 | Definition of the double integral | Studying the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım |
| 2 | Porperties of double integral. First and second type plane regions | Studying the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım |
| 3 | Computation of double integrals over the plane regions of the first or second type | Studying the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım |
| 4 | Changing the order of integration. Examples | Studying the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım |
| 5 | Computation of areas, masses and center of masses of plane regions. | Studying the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım |
| 6 | Computation of surface areas. | Studying the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım |
| 7 | Change of coordinate formula for plane regions | Studying the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Review and problem solving | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Definition of triple integrals over space regions. | Studying the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım |
| 10 | Computation of triple integrals in rectangular coordinates. | Studying the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım |
| 11 | Computation of volume, mass and center of mass of space regions.Examples | Studying the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım |
| 12 | Cylindirical coordinates. Computaion of triple integrals in cylindirical coordinates. | Studying the relevant parts of the textbook | Öğretim Yöntemleri: Alıştırma ve Uygulama |
| 13 | Examples. Problem solving | Studying the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım |
| 14 | Spherical coordinates. Computaion of triple integrals in spherical coordinates. | Studying the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım |
| 15 | Examples, applications. | Studying the relevant parts of the textbook | Öğretim Yöntemleri: Alıştırma ve Uygulama |
| 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 | 2 | 28 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 2 | 28 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 6 | 6 |
| Final Exam | 1 | 16 | 16 |
| Total Workload (Hour) | 78 | ||
| Total Workload / 25 (h) | 3,12 | ||
| ECTS | 3 ECTS | ||