MECHATRONICS ENGINEERING
Bachelor TR-NQF-HE: Level 6 QF-EHEA: First Cycle EQF-LLL: Level 6

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT2069 Engineering Mathematics II Spring 2 2 3 6

Basic information

Language of instruction: English
Type of course: Must Course
Course Level: Bachelor’s Degree (First Cycle)
Mode of Delivery: Face to face
Course Coordinator : Dr. Öğr. Üyesi GÜLSEMAY YİĞİT
Course Lecturer(s): Prof. Dr. NAFİZ ARICA
Recommended Optional Program Components: None
Course Objectives: This course provides an introduction to the theory of functions of complex variable. It starts with fundamental arithmetic and complex numbers geometry. Then it continues with analytic functions, Cauchy-Riemann equations and Cauchy integral formula. The representation of functions with power series and Residue theorems are given. The course ends with Fourier series and Fourier transform.

Learning Outcomes

The students who have succeeded in this course;
1. Represent complex numbers and use basic elementary operations on them
2. Analyze limits and continuity, calculate derivatives of function of complex variable and use Cauchy-Riemann equations
3. Define analytic and harmonic functions
4. Analyze the properties of elementary complex-valued functions and evaluate contour integrals
5. Apply Cauchy’s integral formula for analytic functions
6. Use sequences, series and Laurent series and classify the singularities
7. Understand and apply Residue theorem
8. Understand Fourier transform

Course Content

Complex numbers, elementary functions of complex variables, derivative, analytic functions, Cauchy-Riemann equations, Cauchy's integral theorem, zeros of analytic functions, Laurent series, single classification of isolated points, Residue theorem, Fourier series, Fourier transform.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Complex Numbers. Point representation of complex numbers. Vector representation of complex numbers. Polar form.
2) Complex Exponential. Powers and roots of complex numbers.
3) Functions of a complex variable. Limits and continuity.
4) Derivative of complex-valued functions. Analytic functions. Cauchy-Riemann equations. Harmonic functions.
5) Derivative of complex-valued functions. Analytic functions. Cauchy-Riemann equations. Harmonic functions.
6) Some Elementary functions: Polynomials, Rational functions, Exponential function, Trigonometric functions, Logarithmic function, Complex Powers
7) Some Elementary functions: Polynomials, Rational functions, Exponential function, Trigonometric functions, Logarithmic function, Complex Powers
8) Complex Integration. Contour Integrals.
9) Complex Integration. Contour Integrals.
10) Cauchy's Integral theorem. Cauchy's Integral Formula.
11) Sequences and series. Taylor series. Power Series.
12) Laurent Series. Zeros and singularities.
13) Residue theorem and applications.
14) Fourier series, Fourier transform.

Sources

Course Notes / Textbooks: E. B. Saff and A. D. Snider, "Fundamentals of complex analysis with applications to Engineering and Science", 3rd edition, 2003
References: Any other book on Complex Numbers and their functions, and lecture notes.

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Quizzes 2 % 10
Midterms 1 % 40
Final 1 % 50
Total % 100
PERCENTAGE OF SEMESTER WORK % 50
PERCENTAGE OF FINAL WORK % 50
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 2 28
Application 14 2 28
Study Hours Out of Class 14 6 84
Quizzes 2 1 2
Midterms 1 2 2
Final 1 2 2
Total Workload 146

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) Build up a body of knowledge in mathematics, science and Mechatronics Engineering subjects; use theoretical and applied information in these areas to model and solve complex engineering problems.
2) Identify, formulate, and solve complex Mechatronics Engineering problems; select and apply proper modeling and analysis methods for this purpose.
3) Design complex Mechatronic systems, processes, devices or products under realistic constraints and conditions, in such a way as to meet the desired result; apply modern design methods for this purpose.
4) Devise, select, and use modern techniques and tools needed for solving complex problems in Mechatronics Engineering practice; employ information technologies effectively.
5) Design and conduct numerical or pysical experiments, collect data, analyze and interpret results for investigating the complex problems specific to Mechatronics Engineering.
6) Cooperate efficiently in intra-disciplinary and multi-disciplinary teams; and show self-reliance when working on Mechatronics-related problems.
7) Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing. Write and understand reports, prepare design and production reports, deliver effective presentations, give and receive clear and understandable instructions.
8) Recognize the need for life-long learning; show ability to access information, to follow developments in science and technology, and to continuously educate oneself.
9) Develop an awareness of professional and ethical responsibility, and behave accordingly. Be informed about the standards used in Mechatronics Engineering applications.
10) Learn about business life practices such as project management, risk management, and change management; develop an awareness of entrepreneurship, innovation, and sustainable development.
11) Acquire knowledge about the effects of practices of Mechatronics Engineering on health, environment, security in universal and social scope, and the contemporary problems of Mechatronics engineering; is aware of the legal consequences of Mechatronics engineering solutions.