TÜRKÇE
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Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| MATHEMATICS PR. | |
| Code | MTS225 |
| Name | Integration |
| Term | 2021-2022 Academic Year |
| Semester | 3. Semester |
| Duration (T+A) | 2-0 (T-A) (17 Week) |
| ECTS | 3 ECTS |
| National Credit | 2 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Label | E Elective |
| Mode of study | Uzaktan Öğretim |
| Catalog Information Coordinator | Dr. Öğr. Üyesi Doğa Can SERTBAŞ |
| Course Instructor |
Dr. Öğr. Üyesi Doğa Can SERTBAŞ
(Güz)
(A Group)
(Ins. in Charge)
|
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
Resources
Notes
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 | - | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | 1 |
| PLO02 | - | Understands importance of basic consepts of Algebra, Analaysis and Topology. | 2 |
| PLO03 | - | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 1 |
| PLO04 | - | Demonstrate the ability to express the basic theories of mathematics both correctly. | 1 |
| PLO05 | - | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 5 |
| PLO06 | - | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | 4 |
| PLO07 | - | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 4 |
| PLO08 | - | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 1 |
| PLO09 | - | Comprehends at least one of the computer programming languages. | 0 |
| PLO10 | - | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 2 |
| PLO11 | - | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | 0 |
| PLO12 | - | 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. | 0 |
| PLO13 | - | Understands the programming techniques and shows the ability to do programming. | 0 |
| PLO14 | - | Demonstrates the ability to study mathematics both independently and as a group. | 0 |
| PLO15 | - | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | 0 |
| PLO16 | - | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | 0 |
| PLO17 | - | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | 0 |
| PLO18 | - | Gains the ability to use information technologies effectively for contemporary mathematical applications. | 0 |
| PLO19 | - | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | 0 |
| PLO20 | - | Gains the consciousness of prefesional ethics and responsibility. | 0 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Definition of the double integral | Studying the relevant parts of the textbook | |
| 2 | Porperties of double integral. First and second type plane regions | Studying the relevant parts of the textbook | |
| 3 | Computation of double integrals over the plane regions of the first or second type | Studying the relevant parts of the textbook | |
| 4 | Changing the order of integration. Examples | Studying the relevant parts of the textbook | |
| 5 | Computation of areas, masses and center of masses of plane regions. | Studying the relevant parts of the textbook | |
| 6 | Computation of surface areas. | Studying the relevant parts of the textbook | |
| 7 | Change of coordinate formula for plane regions | Studying the relevant parts of the textbook | |
| 8 | Mid-Term Exam | Review and problem solving | |
| 9 | Definition of triple integrals over space regions. | Studying the relevant parts of the textbook | |
| 10 | Computation of triple integrals in rectangular coordinates. | Studying the relevant parts of the textbook | |
| 11 | Computation of volume, mass and center of mass of space regions.Examples | Studying the relevant parts of the textbook | |
| 12 | Cylindirical coordinates. Computaion of triple integrals in cylindirical coordinates. | Studying the relevant parts of the textbook | |
| 13 | Examples. Problem solving | Studying the relevant parts of the textbook | |
| 14 | Spherical coordinates. Computaion of triple integrals in spherical coordinates. | Studying the relevant parts of the textbook | |
| 15 | Examples, applications. | Studying the relevant parts of the textbook | |
| 16 | Term Exams | Review and problem solving | |
| 17 | Term Exams | Review and problem solving |
Assessment (Exam) Methods and Criteria
| Assessment Type | Midterm / Year Impact | End of Term / End of Year Impact |
|---|---|---|
| 1. Midterm Exam | 100 | 40 |
| General Assessment | ||
| Midterm / Year Total | 100 | 40 |
| 1. Final Exam | - | 60 |
| Grand Total | - | 100 |
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 | ||