William Paterson University of New Jersey College of Science and Health

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10 Οκτ 2013 (πριν από 3 χρόνια και 10 μήνες)

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William Paterson University of New Jersey

College of Science and Health

Department of Mathematics

Course Outline


1.

Title of Course, Course Number and Credits:

Complex Analysis


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Effectively write mathematical solutions in a clear and con
cise manner. This will
be assessed through class assignments and exams.



Effectively locate and use the information needed to prove theorems and
establish mathematical results. This will be assessed through assignments and
exams.



Demonstrate the ability to

integrate knowledge and ideas of complex
differentiation and complex integration in a coherent and meaningful manner and
use appropriate techniques for solving related problems and for establishing
theoretical results. This will be assessed through assign
ments and exams.



Demonstrate ability to think critically by proving mathematical conjectures and
establishing theorems from complex analysis. This will be assessed through tests
and a final exam.



In addition, students will be able to:
Operate with complex
numbers
, u
se the
complex derivatives function
, u
se and operate analytic functions
, d
emonstrate
knowledge of integration in the complex plane
, u
se the Cauchy integral theorem
and Cauchy integral formula
, m
anipulate and use power series
, understand
residues
and their u
se in integration
, d
emonstrate the understanding of conformal
mappings
.

6.

Topical Outline of the Course Content
:


1.

Complex Numbers

1

week


2.

The Complex Function and Its Derivative

1.5

weeks


3.

The Basic Transcendental Functions

2

weeks


4.

Integration in the Complex Plane

2

weeks


5.

Infinite Series Involving a Complex Variable

2

weeks

Complex Analysis


Math 422
0

Page
2

of
2


6.

Residues and Their Use in Integration

2

weeks


7.

Conformal Mapping and Some of Its Applications

2

weeks

7.

Guidelines/Suggestions for Teaching
Methods and Student Learning Activities:

This course is taught as a lecture course with student participation and use of computers
.



8.

Guidelines/Suggestions for Methods of Student Assessment (Student Learning Outcomes)

1.

Two or three
examinations which
m
ay include in
-
class parts and take
-
home parts.

2.

Short quizzes, graded homework and computer lab assignments
.

3.

C
umulative final exam
.


9.

Suggested Reading, Texts and Objects of Study:

Wunsch, A. David, Complex Variables and Applications, Second Edition, Add
ison
-
Wesley
Publishing Company, Inc, 1994.


10.

Bibliography of Supportive Texts and Other Materials:

1.

Churchill, Ruel V. and James Ward Brown, Complex Variables and Applications. Fifth
Edition, McGraw
-
Hill, Inc., 1990.

2.

Lang, Serge, Complex Analysis, Add
ison Wesley Publishing Co., 1977.

3.

Silverman, Richard, Complex Analysis with Applications, Prentice Hall Publishing Co.,
1974.

11.

Preparer’s Name and Date:

12.

Original Department Approval Date
:

13.

Reviser’s Name and Date
:

Prof. M. Llarull


Fall 199
6

Prof. M. Rosar


Spring 2005

14.

Departmental Revision Approval Date
:

Spring 2005