1、Course Information
| Course Code： | MAT23200T |
| Course Name(in Chinese)： | 复变函数和积分变换 |
| Course Name(in English)： | Complex Function and Integral Transform |
| Course Category： | The direction and characteristics of compulsory subject |
| Target Studendts： | Mechanical Engineering and Automation |
| TermAvaiable： | Autumn |
| Total Credit Hours： | 40hrs |
| Total Credits： | 2.5 |
| Prerequisites（Course Code）： | Higher Mathematics |
| Parallels（Course Code）： | No |
| Course Descriptions： | 《Complex Function and Integral Transform》includes complex function and integral transform, it`s a important basic maths course. It`s content includes the basic knowledge of Plural, Complex functions and Analytics functions; integral of complex function; series of complex; power complex; residue; Fourier transform; Laplace transform. The theory and methods in mathematics, natural sciences, Engineering and Technology has a wide range of applications, it is a powerful tool to resolve such as fluid mechanics, electromagneti**, thermal, elastic theory and industrial control problem.. In the learning process, make students correctly understand and grasp the basic concepts and methods, and gradually make the use of these concepts and methods to solve practical problems |
| Textbooks Recommended： | [1] Department of Higher Mathematics, Xi'an Jiaotong University. Complex function (fourth edition). Beijing: Higher Education Press, 1996 |
| Supplementary Materials: | [1] Zhong Yuquan. Complex function. Beijing: Higher Education Press, 1984 [2] Liu Jingyan. Engineering Practical integral transformation. Wuhan: Huazhong University Press, 1996 [3] Nanjing Institute of Technology, Teaching and Research Group. Integral transformation (third edition). Beijing: Higher Education Press, 1989 |
2、Learning Goals and Objectives
By teaching to let students
1. Correctly understand and grasp the basic concepts and methods of complex function. Master several complex representation methods, and to carry out each conversion; understand the differences and similarities of the Complex Functions and Real Variable, deepen the understanding of the complex function by comparison.
3. Understand the concept of complex function integration; master fundamental theorem of Cauchy -Gu Saji and its extension - Composite closed theorem, familiar with the Cauchy integral formula, and can apply the Theorem in the proper use.
4. Understand the basic concept and nature of series of complex and the complex function, focusing on how to change the ****ytic function expansion into power series and Laurent series.
5. Understand the concept of residue; master the basic methods in which how to calculated integral of the closure of surface according to the residue theorem.
6. Understand the concept of conformal mapping.
7. Gradually develop and establish the ability of solving basic problems by complex function.
8. Master the concepts of Fourier transform and Laplace transform and methods of its common use in engineering practice.
1. Complex variable (28 credit hours)
(1) complex and the complex function (5 credit hours)
Complex and it`s algebraic operations; complex geometric representation; complex power and the square root of religion; region; * The definition of complex function; * limit and continuous of complex function
(2) ****ytic functions (4 credit hours)
* The concept of ****ytic functions; △ necessary and sufficient conditions for ****ytic functions; several elementary functions
(3) the integral of the complex function (7 credit hours)
concept of Complex integration; * Cauchy - Gu Saji basic theorem; composite closed-loop theorem; the original function and indefinite integral; * Cauchy integral formula; △ higher derivative of ****ytic functions; the relationship between ****ytic function and harmonic functions
(4) series (6 credit hours)
Plural term series; power series; * Taylor series; △ Laurent series
(5) residues (3 credit hours)
Isolated singularity; △ residue; the use of residue in the definite integral calculation (self)
(6) Conformal mapping (3 credit hours)
The concept of conformal mapping; fractional linear maps; the conditions of the only decision of fractional linear maps
2. Integral transformation (12 hours)
(1) Fourier transform (6 hours)
Fourier integral; * Fourier transform; the nature of Fourier transform; △ convolution and correlation function
(2) Laplace transform (6 credit hours)
The concept of Laplace transform; * the nature of Laplace transform; Laplace inverse transform; convolution; △ Application of Laplace transform
5、Evaluation Approaches
6、Performance Appraisal