COMPLEX

LESSON PLAN

DEPARTMENT OF MATHEMATICS

FACULTY OF MATH AND SCIENCES STATE UNIVERSTIY OF MALANG

ODD SEMESTER 2012/2013

A.  COURSE DESCRIPTION

1.    Name                                          : Complex Function

2.    Code                                          : MAU 414

3.    Credit/hour semester                 : 3 / 3

4.    Level                                          : S-1

5.    Group                                                      :  Compulsary

6.    Pre-quested course                     :  Real analysis I

7.    Lecturer                                     :  Sukoriyanto

B.  STANDARD COMPETENCY

Understanding analysis concepts with complex variable and being able to solve applied problems which use complex variable

C.  BASIC COMPTENCES

1. Understanding and mastery complex number
2. Explaining exponential form to complex number
3. Determining roots of complex number
4. Determining regions in complex plane
5. Determining the value of function of complex number
6. Determining the transformation of a complex function
7. Understanding and mastering limit of function of complex variables
8. Understanding and mastering functions continuity of complex variables
9. Understanding and mastering the derivative of function of complex variable
10. Proving theorem that related to Cauchy-Riemann equations
11. Proving theorem that related to polar coordinates

12.  DETAIL ACTIVITIES

Session	Basic Competencies	Material	Activities	Task
1	1	Topic ·     Introduce, course material, agreement for courses, assessment, etc. ·     Sum and products of  complex number ·     Basic algebraic properties of complex number References: [1] and [2]	·         expository ·         answer and question ·         grup discussion ·         individual work	·    read handout ·    do exercise
2	1	Topic ·         Properties of complex number ·      Moduli in complex number ·      Do exercise References: [1] and [2]	·         expository ·         answer and question ·         grup discussion ·         individual work	·    read handout ·    do exercise
3	1	Topic ·      Complex conjugate ·      Exponintial form ·      Do exercise References: [1] and [2]	·         expository ·         answer and question ·         grup discussion ·         individual work	·    read handout ·    do exercise
4	2	Topic ·      Products and quotients in exponential form ·      Products and quotients in exponential form ·      Do exercise References: [1] and [2]	·         expository ·         answer and question ·         grup discussion ·         individual work	·    read handout ·    do exercise
5	3 and 4	Topic ·      Roots in complex numbers ·      Reagions in the complex plane ·      Do exercise References: [1] and [2]	·          expository ·          answer and question ·          grup discussion ·          individual work	·    read handout ·    do exercise
6		test 1	Individual work	study  BC 1 - 4
7	5	Topic ·      Function of complex variable ·      Transformation ·      Do exercise References: [1] and [2]	·          expository ·          answer and question ·          grup discussion ·          individual work	·    read handout ·    do exercise
8	6	Topic ·      Transformation by the exponential function ·      Do exercise References: [1] and [2]	·          expository ·          answer and question ·          grup discussion ·          individual work	·    read handout ·    do exercise
9	7	Topic ·      Limit ·      Theorem on limit ·      Do exercise References: [1] and [2]	·          expository ·          answer and question ·          grup discussion ·          individual work	·    read handout ·    do exercise
10	7	Topic ·      Limits involving the point at infinitly ·      Do exercise References: [1] and [2]	·          expository ·          answer and question ·          grup discussion ·          individual work	·    read handout ·    do exercise
11		test 2	Individual work	study  BC 5 - 7
12	8 and 9	Topic ·      Continuity ·      Derivatives ·      Do exercise References: [1] and [2]	·          expository ·          answer and question ·          grup discussion ·          individual work	·    read handout ·    do exercise
13	9	Topic ·      Diferentiation formulas ·      Do exercise References: [1] and [2]	·          expository ·          answer and question ·          grup discussion ·          individual work	·    read handout ·    do exercise
14	10	Topic ·      Cauchy-Riemann equations ·      Do exercise References: [1] and [2]	·          expository ·          answer and question ·          grup discussion ·          individual work	·    read handout ·    do exercise
15	10 and 11	Topic ·      Sufficient conditions for differentiability ·      Polar coordinates ·      Do exercise References: [1] and [2]	·          expository ·          answer and question ·          grup discussion ·          individual work	·    read handout ·    do exercise
16		Test  3	Individual work	study BC 8 - 11

F. Evaluation

Assesment is done comprehensively, not only test. It must pay ettention:

• Test tree times (k₁, k_2, dan k₃ )
• Activity (a)

F. Referencess

Main References:

[1]. Churchill R.V dan J.W.Brown, 1984.  “Complex Variables and Applications” USA: McGraw-Hill Book Company

Additional References: 

 [2]  Conway, J.D. 1973 “ Functions of One Complex Variable”New York : Springer- Verlag, Inc.

[3]  Muray  R  Spiegel  1990 “ Peubah Kompleks” Jakarta : Erlangga

[4]  Hauser A.A Jr., 1971. “Complex Variables with Physical Applications” New York: Simon and Schuster

[5]  Saff, E.B and A.D. Snieder, 1987 “ Fundamentals of Complex Analysis”New Jersey: Prentice-Hall, Inc