TÜRKÇE
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Information
| Code | CEN106 |
| Name | Mathematics 2 |
| Semester | 2. Semester |
| Duration (T+A) | 4-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 4 National Credit |
| Teaching Language | İngilizce |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ŞEHMUS FINDIK |
Course Goal
To teach the student the topics of infinite series, functions of several variables, multiple integrals and integral theorems, which are the main topics of engineering mathematics, in a functional integrity.
Course Content
Sequence and series of numbers, power series, Taylor series. Quadratic curves, polar coordinates. Analytic geometry in R , vector functions. Functions of several variables, partial derivatives, minimum and maximum problems. Multiple integrals and applications. Line integral, Green's theorem. Surface integral, divergence theorem, Stokes' theorem.
Course Precondition
None.
Resources
Calculus, J. Stewart
Notes
None.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Analyzes infinite series in conjuction with convergence and divergence concepts |
| LO02 | Derives the Taylor-Maclaurin expansion of a given function. |
| LO03 | Calculates and comments on the partial derivatives of multivariable functions. |
| LO04 | Calculates multiple integrals, |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Has capability in the fields of mathematics, science and computer that form the foundations of engineering | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Identifies, formulates, and solves engineering problems, selects and applies appropriate analytical methods and modeling techniques, | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Analyzes a system, its component, or process and designs under realistic constraints to meet the desired requirements,gains the ability to apply the methods of modern design accordingly. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Ability to use modern techniques and tools necessary for engineering practice and information technologies effectively. | 3 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Ability to design and to conduct experiments, to collect data, to analyze and to interpret results | 5 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Has ability to work effectively as an individual and in multi-disciplinary teams, take sresponsibility and builds self-confidence | |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Can access information,gains the ability to do resource research and uses information resources | 5 |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Awareness of the requirement of lifelong learning, to follow developments in science and technology and continuous self-renewal ability | 5 |
| PLO09 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Ability to communicate effectively orally and in writing, and to read and understand technical publications in at least one foreign language | |
| PLO10 | Yetkinlikler - Öğrenme Yetkinliği | Professional and ethical responsibility, | 3 |
| PLO11 | Yetkinlikler - Öğrenme Yetkinliği | Awareness about project management, workplace practices, employee health, environmental and occupational safety, and the legal implications of engineering applications, | |
| PLO12 | Yetkinlikler - Öğrenme Yetkinliği | Becomes aware of universal and social effects of engineering solutions and applications, entrepreneurship and innovation, and knowledge of contemporary issues | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Integral applications, arc length, volume and surface area calculation | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 2 | Parametric curves | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 3 | Polar coordinates, polar curves | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 4 | Infinite series, convergence tests | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 5 | Convergence tests (continued) | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 6 | Taylor and Maclaurin expansions, Taylor approximation | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 7 | Introduction to multivariable functions, partial derivatives and the chain rule | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Reading the lecture notes | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Double integrals over general regions | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 10 | Triple integrals, change of variables in multiple integrals | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 11 | Double and triple integrals in polar coordinates | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 12 | Surface area calculation, line integrals | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 13 | Surface integrals, Green's theorem | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 14 | Stokes and Divergence theorems | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 15 | FINAL | Reading the lecture notes | Ölçme Yöntemleri: Yazılı Sınav |
| 16 | Term Exams | Reading the lecture notes | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Reading the lecture notes | 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 | 3 | 42 |
| 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) | 122 | ||
| Total Workload / 25 (h) | 4,88 | ||
| ECTS | 5 ECTS | ||