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Information
| Code | EEE104 |
| Name | Calculus II |
| Term | 2024-2025 Academic Year |
| 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. HAYRULLAH AYIK |
| Course Instructor |
1 2 |
Course Goal / Objective
The purpose is 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
Integral applications, volumes and areas of surfaces of revolution, arc length. Parametric equations and curves, polar coordinates. Infinite sequences and series, convergence tests, power series, Taylor and Maclaurin series, approximation with Taylor polynomials. Functions of several variables, partial derivatives. Double and triple integrals, change of variables, integrals over polar coordinates. Surface area, line integrals, Greens theorem, surface integrals, divergence theorem, Stokes theorem.
Course Precondition
NONE
Resources
1. Thomas' Calculus 12th Edition, George B. Thomas,
Notes
2. Calculus 8th Edition, James Stewart 3. Calculus 4th Edition, JDennis G. Zill, Warren S. Wright
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Evaluates definite integrals using appropriate methods. |
| LO02 | Evaluates areas and valumes by using integrals. |
| LO03 | Finds the length of curves and surface areas. |
| LO04 | Analyzes infinite series in conjuction with convergence and divergence concepts |
| LO05 | Derives the Taylor-Maclaurin expansion of a given function. |
| LO06 | Calculates and comments on the partial derivatives of multivariable functions. |
| LO07 | Calculates multiple integrals, line and surface integrals |
| LO08 | Uses variable substitution methods in double and triple integrals. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in complex engineering problems. | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. | 2 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Ability to devise, select, and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ computer programming techniques, and information technologies effectively. | 1 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions. | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually. | 4 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, | |
| PLO08 | Bilgi - Kuramsal, Olgusal | Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself. | 3 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Consciousness to behave according to ethical principles and professional and ethical responsibility; knowledge on standards used in engineering practice. | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development. | 3 |
| PLO11 | Bilgi - Kuramsal, Olgusal | Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions. | 2 |
| PLO12 | Bilgi - Kuramsal, Olgusal | Ability to apply the knowledge of electrical-electronics engineering to profession-specific tools and devices. | |
| PLO13 | Bilgi - Kuramsal, Olgusal | Having consciousness about the scientific, social, historical, economical and political facts of the society, world and age lived in. | 3 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Integral applications, arc length, volume and surface area calculation | Preparation | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 2 | Parametric curves | Preparation | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 3 | Polar coordinates, polar curves | Preparation | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 4 | Infinite series, convergence tests | Preparation | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 5 | Convergence tests (continued) | Preparation | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 6 | Taylor and Maclaurin expansions, Taylor approximation | Preparation | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 7 | Introduction to multivariable functions, partial derivatives and the chain rule | Preparation | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme |
| 8 | Mid-Term Exam | Preparation for Exam Quations | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Double integrals over general regions | Preparation | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 10 | Triple integrals, change of variables in multiple integrals | Preparation | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 11 | Double and triple integrals in polar coordinates | Preparation | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 12 | Surface area calculation, line integrals | Preparation | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 13 | Surface integrals, Greens theorem | Preparation | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 14 | Stokes and Divergence theorems | Preparation | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 15 | Review | Preparation | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 16 | Term Exams | Preparation for Exam Quations | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Preparation for Exam Quations | 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 | ||