Course Objectives
At the completion of this course, students will be able to
1) Calculate complex numbers.
2) Understand the polar form and complex plane of complex numbers.
3) Understand the meaning of regular functions and their properties, complex plane.
4) Understand complex functions can be differentiated and Cauchy Riemann's theorem.
5) Understand complex functions can be integrated and Cauchy's theorem.
6) Understand Taylor expansion and Laurent expansion of complex functions.
7) Understand the residue theorem can be understood and solve application problems of residues.
Each item of the rubric shown below becomes the target.
Rubric
| Ideal Level of Achievement | Standard Level of Achievement | Unacceptable Level of Achievement) |
Complex numbers calculation | Can calculate complex numbers. | Can understand complex numbers. | Can't calculate complex numbers. |
Complex polar forms and complex planes | Can explain complex polar forms and complex planes. | Can understand complex polar forms and complex planes. | Can't understand complex polar forms and complex planes. |
tThe meaning and nature of regular functions and complex function planes | Can explain the meaning and nature of regular functions and complex function planes. | Can understand the meaning and nature of regular functions and complex function planes. | Can't understand the meaning and nature of regular functions and complex function planes. |
Differentiation of complex functions and Cauchy Riemann's theorem | Can explain the differentiation of complex functions and Cauchy Riemann's theorem. | Can understand the differentiation of complex functions and Cauchy Riemann's theorem. | Can't understand differentiation of complex functions and Cauchy Riemann's theorem. |
The integration of complex functions and Cauchy's theorem | Can explain the integration of complex functions and Cauchy's theorem. | Can understand the integration of complex functions and Cauchy's theorem. | Can't understand the integration of complex functions and Cauchy's theorem. |
The development of complex functions such as the Taylor expansion and Laurent expansion | Can explain the development of complex functions such as the Taylor expansion and Laurent expansion. | Can understand the development of complex functions such as the Taylor expansion and Laurent expansion. | Can't understand the development of complex functions such as the Taylor expansion and Laurent expansion. |
Application of the residue theorem | Can solve application problems of the residue theorem. | Can solve problems of the residue theorem. | Can't solve problems of the residue theorem. |
Assigned Department Objectives
Learning and Educational Objectives of the “General Engineering” A-5
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JABEE 1(2)(c)
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Diploma policy 3
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Teaching Method
Outline:
Functions of complex variables are often used for stability determination in vibration phenomena and analysis of mechanical control, and knowledge of functions of complex variables is necessary to safely control a machine. Therefore, in this subject, the objective is to understand the calculation methods and rules of the complex variable functions to be used in control engineering, etc.
Style:
Lecture and exercise. First, the calculation of complex numbers , the pole form and complex plane of complex numbers will be revivewed and understood. Next, the regular functions, the complex function plane transformed by the function with various functions, will be understood. The differentiation and integration of the complex functions are solved and the residue theorem from the expansion of the complex functions are explained. Finally, application problems using the residence theorem are solved.
Notice:
The complex function theory is often used in fluid engineering, control engineering, etc. Please review your textbooks closely, and review the fundamentals of mathematics on your own. Also, since we will give a report after class, solve the problems, and please make sure you fully understand them before submitting them. Lesson plans may be changed according to the student's degree of understanding.Can take makeup exam in need aid up to maximum of 60 points.
Characteristics of Class / Division in Learning
Course Plan
|
|
|
Theme |
Goals |
1st Semester |
1st Quarter |
1st |
Complex numbers and arithmetic operations |
Conjugate complex numbers can be understood. Complex numbers can be calculated.
|
2nd |
Complex number plane (z plane) and vector, complex type polar form |
The complex number plane (z plane) can be understood. Absolute value calculation of vectors, complex numbers, argument and polar form of complex number can be calculated.
|
3rd |
Functions and complex function plane (w plane)(1) |
Exponential function, complex function plane, Euler's formula, de Moivre's theorem, power, n th root can be understood.
|
4th |
Functions and complex function plane (w plane)(2) |
Trigonometric functions, hyperbolic functions, logarithmic functions can be understood.
|
5th |
Differentiation of complex functions (1) |
Function limit, continuous function, differentiable, regular function, differentiation of power can be understood.
|
6th |
Differentiation of complex functions (2) |
Cauchy-Riemann's theorem, derivative of regular function, harmonic function, exponential function, trigonometric function, hyperbolic function, logarithmic function can be understood.
|
7th |
Integration of complex functions (1) |
The general definition of complex integral and integral path, integral of circular integral path, indefinite integral, complex integral can be understood.
|
8th |
Intermediate examination |
|
2nd Quarter |
9th |
Explanation of answer of intermediate examination |
|
10th |
Integration of complex functions (2) |
The closed curve integral path and area, Green's theorem, Cauchy's theorem can be understood.
|
11th |
Integration of complex functions (3) |
Cauchy's integrated display can be understood.
|
12th |
Expansion of complex functions |
Taylor expansion (McLoughlin development), Laurent expansion (function having singularities) can be understood.
|
13th |
Residue |
Poles and residues, residue calculation, residue theorem can be understood.
|
14th |
Application of residues |
The integration using the residue can be understood.
|
15th |
Term-end examination |
|
16th |
Explanation of answer of term-end examination and a questionnaire |
|
Evaluation Method and Weight (%)
| Examination | Report | Total |
Subtotal | 70 | 30 | 100 |
Understanding degree | 70 | 30 | 100 |