Cao thang technical college the socialist republic of viet nam



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MINISTRY OF INDUSTRY AND TRADE

CAO THANG TECHNICAL COLLEGE

THE SOCIALIST REPUBLIC OF VIET NAM

Independence – Liberty - Happiness

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



  1. 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






MINISTRY OF INDUSTRY AND TRADE

CAO THANG TECHNICAL COLLEGE

THE SOCIALIST REPUBLIC OF VIET NAM

Independence – Liberty - Happiness

THE CONTENTS OF TEST – EVALUATION

  1. 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.

  • Applying the Cauchy-Riemann conditions for considering a complex function which is an analytic function or not?

  • Applying the Cauchy-Riemann conditions for looking for a conjugate harmonic function of the function harmonic given.

  • Applying the Cauchy-Riemann conditions for calculating the derivative of a complexe function at a point z0 .

  • Calculating the integral of the function of multiple variables on supply AB.

  • Calculating the integral of the function of a complex variable on closed curve Cauchy integral formula.

  1. The final test

form: writing

Contents:

  • Finding image functions, original function using a function table image - common root function.

  • Applying the linearity, image shift, shift the original.



B1.19 -


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