SYLLABUS
1. The name of course (in Vietnamese): Hàm biến số phức và phép biến đổi Laplace.
2. The name of course(in English): Complex variables functions and Laplace transforms
3. Course’s code:
4. Credit: 2 (30 sessions).
5. Education level: College
6. Course attending condition:
Requirement: advanced mathematics
7. Teaching staff in charge of course:
Main Teacher:
Master: Mr. Tống Minh Hải
Other teachers :
Mr. Bùi Minh Quân
Mr. Võ Sĩ Trọng Long
8. Participants:
The students of CTTC specialize in Electronic , Electrical and automatic technology, attending the 2nd semester of the 1st year .
9. Abstract:
- This course provides students with the basic knowledge and concepts of complex variable functions including complex numbers,analytic function, harmonic function , elementary function , integrals in the complex surface, Cauchy integrals , string theory, surplus theory , conformal transformation…
- The position of course: This course belongs to Culture and foreign language subdepartment , General Education Department.
- The role of course: This course provides students with the basic skills and concepts of complex variable functions and Laplace transforms
10. Aim – Outcomes of course:
10.1. Aim:
This course aims to provide students:
-
The knowledge: the concepts of complex variable functions and Laplace transforms
-
The skills: Solving the probleme of complex variable functions and laplace transforms.
-
The attitude: Forming a positive attitude in students’learning
10.2. Outcomes of course:
No
|
Outcomes of course
|
Outcomes of training
|
1
|
Understand how to survey the derivative of complex variable functions, to calcuate for the harmonic functions, to show the formulas and the nature of the elementary functions
|
|
2
|
Calculate the integrals in AB segment, the integrals in closed loop by Cauchy’s formula.
|
3
|
Show the basic nature of Laplace transforms, how to calculate the photo function and original function
|
-
The Contents and schedule of course :
No
|
Title
|
Time (session - 45 minutes)
|
Total
|
theory
|
exercise
|
discussion
|
test
|
1
|
1st chapter: the analytic function
|
10
|
5
|
5
|
0
|
0
|
2
|
2nd chapter:the integrals
|
10
|
4
|
4
|
0
|
2
|
3
|
3rd chapter: Laplace transforms
|
10
|
5
|
5
|
0
|
0
|
4
|
Total
|
30
|
14
|
14
|
0
|
2
| 12. Detailed contents:
13. Students’duties:
- Students’attendance: at least 80% of total sessions
- Students’ Prereading their lessons before arriving at school
- Students’self-study according to teacher’s instructions
14. School Materials:
Manual of complex variable function of CTTC in 2014
Reference Books:
[1] Complex variable function and its application written by Nguyễn Kim Đính – published by The National University of HCMC in 2000.
[2] Laplace operator and its application written by Nguyễn Kim Đính – published by The National University of HCMC in 2000.
[3] Complex variable function and Laplace operator written by Võ Đăng Thảo – published by The National University of HCMC in 2000.
[4] Introduction of complex analytics written by Nguyễn Hữu Anh – published by The University of natural sciences in 1999.
[5] Theory and problems of complex variables written by Spiegel Mr. Graw Hill in 1996
15. The percentage of point components and evaluation forms for students:
-
Description
|
Scale of point
|
Students’ attendance point
|
1
|
The average point of students’tests
|
4
|
The Point of Students’final test
|
5
|
Total
|
10
|
Scale of point for evaluation:
-
Grade
|
point
|
pretty
|
8 – 10
|
good
|
6 – 7.99
|
Average
|
5 – 5.99
|
Not good
|
Less than 5
|
16. Maximum point: 10
17. The Instructions:
Manipulate / apply the methodology for interpretive presentation
Review attentively the knowledge of complex numbers studied in the 1st semester so that students keep on studying in the next chapter .
Pay attention to mention the exponential, draw the figures of the domain on the surface
1st chapter: The analytic function
Manipulate / apply the methodology for interpretive presentation
Showing the new concepts especially Cauchy – Rienmann’s conditions to survey the derivative of the complex function ; the relationship between the analytic function and the harmonic function; The nature of the elementary functions
2nd chapter: the integrals on the complex surface
Manipulate / apply the methodology for interpretive presentation
Show the concepts and skills used for calculating the integrals on the complex surface
Calculate the integrals in AB segment, the integrals in closed loop by Cauchy’s formula.
3rd chapter: Laplace transform
Manipulate / apply the methodology for interpretive presentation
Show the nature of Laplace transform and concerned examples; the skills how to calculate the photo function and original function especially the functions shown by the charts so that students are easy to realize the practical applications of this course.
18. Confirmation
Date:……………….
Head of Department Head of Team Written by
Tống Minh Hải
1st time: updated content
|
Date:…………………
Implemented by
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MINISTRY OF INDUSTRY AND TRADE
CAO THANG TECHNICAL COLLEGE
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THE SOCIALIST REPUBLIC OF VIET NAM
Independence – Liberty - Happiness
|
THE CONTENTS OF TEST – EVALUATION
-
The analytic functions and the integrals on the complex surface
Test.1
form: writing
Contents:
-
Applying laplace equation for considering a function of two variables which is a harmonic function or not.
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Applying the Cauchy-Riemann conditions for considering a complex function which is an analytic function or not?
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Applying the Cauchy-Riemann conditions for looking for a conjugate harmonic function of the function harmonic given.
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Applying the Cauchy-Riemann conditions for calculating the derivative of a complexe function at a point z0 .
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Calculating the integral of the function of multiple variables on supply AB.
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Calculating the integral of the function of a complex variable on closed curve Cauchy integral formula.
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The final test
form: writing
Contents:
-
Finding image functions, original function using a function table image - common root function.
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Applying the linearity, image shift, shift the original.
B1.19 -
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