AMATH 401  |  Schedule  |  Instructor  |  Assistant  |  Content  |  Textbooks  |  Prerequisites  |  Grading  |  Calendar  |  Notes  |  References  |  Homework  
  
     

AMATH 401

Vector Calculus and Complex Variables
Fall 2011

Schedule


SLN: 10198 A
Days: M, T, W, F
Time: 3:30-4:20 pm
Room: MGH 231 










Amath 401 is for undergraduates.



Graduate students should sign up for Amath 501.

Instructor








Name:

Mark Kot




Office:

415G Guggenheim Hall




Phone:

(206) 543-0908




Fax:

(206) 685-1440




Email:

mark_kot@comcast.net











Office Hours:

M, W, F






10:00-11:00 am






415G Guggenheim Hall









Assistant










Name:

Nicholas Cain




Office:

Guggenheim 407 (29)




Phone:

(206) 685-9395




Fax:

(206) 685-1440




Email:

nicain@u.washington.edu











Office Hours:
        



M       
3:00-4:00 pm    
Guggenheim 305
    



M       
4:30-5:30 pm    
Guggenheim 305
    



T       
3:00-4:00 pm    
Guggenheim 406
    



Th      
2:30-3:20 pm    
Guggehheim 406
    











Content



Course Catalog


Vector analysis (4 weeks)

  • 
Vector fields and vector calculus

  • 
Orthogonal curvilinear coordinates

  • 
Gradient, divergence, and curl

  • 
Line, surface, and volume integrals

  • 
Green's theorem, Stokes' theorem, and divergence theorem.

    



Complex analysis (6 weeks)

  • 
Complex numbers

  • 
Functions of a complex variable

  • 
Analyticity

  • 
Integration

  • 
Cauchy's theorem and the Cauchy integral formula

  • 
Taylor and Laurent series

  • 
Calculus of residues and contour integration

  • 
Fourier and Laplace transforms.



Textbooks



There are no required textbooks.



I will post lecture notes to the web page.


Lecture Notes





The mathematics library has a number of Springer ebooks that can be


downloaded and used as textbooks for the complex-variables portion of


the course.  For examples, please see:





Agarwal, R. P., Perera, K., and Pinelas, S.  2011.  An Introduction to Complex Analysis.  Springer, New York.


Link to Textbook


Cohen, H.  2007.  Complex Analysis with Aplications in Science and Engineering.  Springer, New York.


Link to Textbook


Ponnusamy, S. and Silverman, H.  2006.  Complex Variables with Applications.  Birkhauser, Boston.


Link to Textbook





Please see the references sections for other useful books.


References

Prerequisites



Math 324 used to be a prerequisite.  Although we have dropped this prerequisite,


you should already know some vector algebra and multivariate calculus.


You should also be familiar with infinite series and Taylor expansions.

Grading



There will be a midterm and a final.


Exams constitute 60% of the final grade.  


The final counts more than the midterm.


Homeworks count for 40% of your grade.

Calendar



Important Dates







September 28
-

Wednesday

-
First Lecture
      



October 31
-

Monday

-
Midterm (MGH 231)
      



November 11
-

Friday

-
Veterans Day (No Class)
      



November 24
-

Thursday

-
Thanksgiving (No Class)
      



November 25
-

Friday

-
Thanksgiving (No Class)
      



December 9
-

Friday

-
Last Class
      



December 15
-

Thursday

-
Final Exam  (MGH 231, 2:30-4:20 pm)
      








Notes






References



Vector Analysis:


Davis, H. F. and Snider, A. D. 1995.  Introduction to Vector Analysis. Wm. C. Brown Publishers, Dubuque, IA.


Rahman, M. 2001.  Applied Vector Analysis.  CRC Press, Boca Raton, FL.


Schwartz, M., Green, S. and Rutledge, W. A.  1960.  Vector Analysis with Applications to Geometry and Physics,
Harper & Brothers, New York, NY.


Young, E. C. 1993.  Vector and Tensor Analysis.  Marcel Dekker, New York, NY.










Complex Analysis:


Ablowitz, M. J. and Fokas, A. S.  1997.  Complex Variables: Introduction and Applications.  Cambridge University
Press, Cambridge, UK.


Brown, J. W. and Churchill, R. V.  1996. Complex Variables & Applications.  McGraw-Hill, New York, NY.


Kwok, Y. K.  2002.  Applied Complex Variables for Scientists and Engineers. Cambridge University Press, Cambridge, UK.


Marsden, J. E. and Hoffman, M. J.  1999.  Basic Complex Analysis.  W. H. Freeman, New York, NY.


Mathews, J. H. and Howell, R. W.  2001.  Complex Analysis for Mathematics and Engineering.  Jones and Bartlett, Sudbury, MA.


Saff, E. B. and Snider, A. D.  2003.  Fundamentals of Complex Analysis with Applications to Engineering and Science.  Prentice-Hall, Upper Saddle River, New Jersey.


Spiegel, M. R.  1968. Schaum's Outline of Complex Variables. McGraw-Hill, New York, NY.


Zill, D. G. and Shanahan, P. D.  2009.  A First Course in Complex Analysis with Applications.  Jones and Bartlett Publishers, Sudbury, MA.

Homework



I assign weekly problem sets.


Homeworks constitute 40% of the final grade.


Write up your homework alone, not as a group!



  • 
Homework #1

    
Due:  Wednesday, October 12, 2011

    
hw1.pdf

    


  • 
Homework #2

    
Due:  Wednesday, October 19, 2011

    
hw2.pdf

    


  • 
Homework #3

    
Due:  Wednesday, October 26, 2011	 

    
hw3.pdf

    


  • 
Stokes' Theorem & Divergence Theorem Practice Problems

    
practice.pdf

    


  • 
Homework #4

    
Due:  Monday, November 14, 2011 

    
hw4.pdf

    


  • 
Homework #5

    
Due:  Friday, November 18, 2011 

    
hw5.pdf

    


  • 
Homework #6

    
Due:  Monday, November 28, 2011

    
hw6.pdf

    


  • 
Homework #7

    
Due:  Monday, December 5, 2011 

    
hw7.pdf

    


  • 
Homework #8

    
Due:  Friday, December 9, 2011  (Due in class.)

    
hw8.pdf

    


  • 
Laplace Transform Practice Problems (Revised on 12/9)

    
laplace.pdf