Spring 2011 - Math 463 Section 0201
                                                                            Complex Variables for Scientists and Engineers

Instructor: Suleyman Ulusoy                                             

Office: 4123 CSIC Building

Classes: TuTh 09:30am-10:45pm (MTH 0409)

Office Hours: TuTh. 11:30am-12:30pm, or by appointment

Teaching Assistant (TA) info:

Name: Mr. Bradford A. Sanders

Office: Meetings with students will take place in Math Tutoring Room: Math 0301

Email address: brad@math.umd.edu

Office hours: Tue & Wed, 11:00am-12:00noon


First day Hand-out

Textbook:
Complex Variables and Applications, Eighth Edition. James W. Brown and Ruel V. Churchill. Published by McGraw-Hill. ISBN 978-0-07-305194-9

Dates:

Lectures Schedule and Assignments:

Lecture dates

Sections

Assignment

1. Tue. Jan. 25

1-4

Basic definitions; The complex plane
Algebra of complex numbers; Modulus; Triangle inequality

Homework #1 Due Tue. Feb. 8th   Solutions

2. Thu. Jan. 27

(Class was cancelled due to snow)

4-6

CLASS  CANCELLED DUE TO SNOW!

3. Tue. Feb. 1 

7-10

Complex conjugates;
Exponential form of complex numbers; Using the exponential form to compute products, powers and fractions  n-th roots of a complex number

4. Thu. Feb. 3

10-12

Neighborhood of a point, open sets, closed sets, boundary of a set
Functions of a complex variable

Homework #2 Due Tue. Feb. 15’th    Solutions

5. Tue. Feb. 8

13-15

Complex functions as transformations of the complex plane.
Mappings by the exponential function
Limits: Definition and first properties

6. Thu. Feb. 10

16-19

Further properties of limits; Point at infinity; Stereographic projection.
Continuity: Definition and properties
Derivatives: Definition. First examples

 

7. Tue. Feb. 15

19-23

Derivatives: Further examples, formulas and properties.
Cauchy-Riemann equations in rectangular and polar coordinates.

Homework #3 Due Thu. Feb. 24’th

8. Thu. Feb. 17

24-26

Analytic functions, singular points, entire functions.
Connected set.
Harmonic functions, harmonic conjugates

 

9. Tue. Feb. 22

Review                               Practice Midterm #1   

          Additional Review Class Wed. Feb. 23 at 5.30 PM,   CSIC Bldg (#406) Room 4122

10. Thu. Feb. 24

                                                             Midterm #1        Solutions

11. Tue. Mar. 1

29-33

Elementary functions: The exponential function, the logarithmic function
Branches of a multiple valued function
Complex exponents

12. Thu. Mar. 3

34-36

Trigonometric functions, Inverse trigonometric functions Hyperbolic functions
Application of harmonic conjugate function to electrostatic

Homework #4 Due Thu. March 10th

13. Tue. Mar. 8

37-39

Calculus for complex valued functions of a real variable.
Arc, Simple Closed Curve (Jordan Curve), smooth arc, contour.

14. Thu. Mar. 10

40-45

Contour integrals: Definition, properties and examples
Contour integrals and antiderivatives

Homework #5 Due March 17th

15. Tue. Mar. 15

46-49

Cauchy Theorem, Cauchy-Goursat Theorem
Simply connected domain; Multiply connected domain: Principle of deformation

16. Thu. Mar. 17

50

First Cauchy integral formula and applications

 

17. Tue. Mar. 29

51

Cauchy integral formula for the derivatives.
Applications to the computation of complex integrals

Homework # 6 Due  March 31st

18. Thu. Mar. 31

52-55

Consequences of Cauchy's formula:
Cauchy's inequality, Liouville theorem, Fundamental theorem of Algebra.
Computing a complex integral: Review.
Sequences of complex numbers.

 

19. Tue. Apr. 5

56

Infinite series - Geometric series

Homework #7 Due  April 12th

20. Thu. Apr. 7

Review                       

                                                 Practice Midterm # 2   

          Additional Review Class Mon. Apr. 11 at 5.30 PM,   CSIC Bldg (#406) Room 4122

21. Tue. Apr. 12

                                                                  Midterm #2

22. Thu. Apr. 14

57-59 (64-66)

Power series. Radius and circle of convergence. Properties of power series
Taylor's Theorem

 

23. Tue. Apr. 19

60,62

Laurent series. Laurent's Theorem. Examples.

24. Thu. Apr. 21

68-70, 72

Residues. Cauchy's residues theorem.
Removable singularity/pole/essential singularities.

Homework #8 Due May 3rd

25. Tue. Apr. 26

73-76

Poles and zeroes of an analytic function

26. Thu. Apr. 28

78-82

Application of residue: Evaluating improper integrals

 

27. Tue. May 3

Review                       Some Review Problems for  Midterm #3

   

                                             Practice Midterm # 3   

          Additional Review Class Wed. May 4 at 5.00 PM,   CSIC Bldg (#406) Room 4122

28. Thu. May 5

                                                                Midterm #3

29. Tue. May 10

Review                        Some Review Problems for  Final                 Practice Final

Additional Review Class Thu. May 12 at 5.30 PM,   CSIC Bldg (#406) Room 4122

 Homework #9
Additional Practice Problems can be found in the testbank