AMATH 507  |  Schedule  |  Instructor  |  Assistant  |  Flier  |  Handout  |  Content  |  Textbooks  |  Prerequisites  |  Grading  |  Homework  |  Meeting  |  Calendar  |  Videos  |  Notes  
  
     

AMATH 507

Calculus of Variations
Winter 2011

Schedule


SLN: 10201 (Section A)
10202 (Section B)
Days: M, W, F
Time: 10:30-11:20 am
Room: Loew Hall 216 










Section A is the regular, on-campus, in-class section for graduate students.





Section B is for students in the EDGE program. For more about EDGE, please see the



EDGE program




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, 11:30-12:20 pm









Assistant








Name:

Vishal Vasan




Office:

407 Guggenheim Hall




Phone:

(206) 685-9395




Fax:

(206) 685-1440




Email:

vvasan@amath.washington.edu











Office Hours:
T 9:00-10:30 am
  




Th 9:30-11:00 am
  




Guggenheim 406
  








Flier



Here is a



course flier



to help you remember this course.




Handout

Handout






Content



The calculus of variations is a branch of optimization theory.


It seeks to find curves and surfaces that maximize or minimize integrals.


I will cover core topics in the calculus of variations.


These include the Euler-Lagrange equation, constraints, the second


variaion, the Legendre condition, the Jacobi equation, homogeneous


problems, transversality conditions, broken extremals, the


Weierstrass excess function, sufficient conditions, the royal road,


and Hamilton-Jacobi theory.


Examples will include such classic gems as the brachistochrone, minimum surfaces


of revolution (soap films), and geodesics.  I will also include numerous examples


from classical mechanics, optics, and other applied areas.


Please see the class
notes
for further details regarding class content.










Course Catalog






Textbooks



There is no required textbook.   I will instead provide detailed, typeset lecture notes.















Optional Textbooks:









University Book Store:



Textbook Status




Prerequisites



You should be comfortable with differential equations.




Grading



Homeworks count for 2/3 of the final grade.



Your talk at the class conference counts for 1/3 of your grade.




Homework



Homeworks are due one week from when they are assigned.





  • 
Homework #1.1 (Due Monday, January 10, 2011)

    
hw_01_01.pdf

    


  • 
Homework #1.2 (Due Monday, January 10, 2011)

    
hw_01_02.pdf

    


  • 
Homework #1.4 (Due Wednesday, January 12, 2011)

    
hw_01_04.pdf

    


  • 
Homework #1.5 (Due Friday, January 14, 2011)

    
hw_01_05.pdf

    


  • 
Homework #3.1 (Due Wednesday, January 19, 2011)

    
hw_03_01.pdf

    


  • 
Homework #3.2 (Due Wednesday, January 26, 2011)

    
hw_03_02.pdf

    


  • 
Homework #3.3 (Due Wednesday, January 26, 2011)

    
hw_03_03.pdf

    


  • 
Homework #3.5 (Extra credit, by February 2, 2011 )

    
hw_03_05.pdf

    


  • 
Homework #4.6 (Due Wednesday, January 26, 2011)

    
hw_04_06.pdf

    


  • 
Homework #4.8 (Due Monday, January 31, 2011)

    
hw_04_08.pdf

    


  • 
Homework #4.9 (Due Monday, January 31, 2011)

    
hw_04_09.pdf

    


  • 
Homework #4.12 (Due Wednesday, February 2, 2011)

    
hw_04_12.pdf

    


  • 
Homework #4.13 (Due Wednesday, February 2, 2011)

    
hw_04_13.pdf

    


  • 
Homework #4.14 (Extra credit, by Wednesday, February 9, 2011)

    
hw_04_14.pdf

    


  • 
Homework #5.02 (Due Monday, February 7, 2011)

    
hw_05_02.pdf

    


  • 
Homework #5.04 (Due Wednesday, February 9, 2011)

    
hw_05_04.pdf

    


  • 
Homework #6.01 (Due Friday, February 18, 2011)

    
hw_06_01.pdf

    


  • 
Homework #6.02 (Due Wednesday, February 23, 2011)

    
hw_06_02.pdf

    


  • 
Homework #8.02 (Due, Wednesday, March 2, 2011)

    
hw_08_02.pdf

    


  • 
Homework #9.02 (Due, Friday, March 4, 2011)

    
hw_09_02.pdf

    


  • 
Homework #9.03 (Due, Monday, March 7, 2011)

    
hw_09_03.pdf

    


  • 
Homework #10.01 (Due, Friday, March 11, 2011)

    
hw_10_01.pdf

    




Meeting






We will hold an all-day conference on Saturday, February 26, 2011.


I will provide refreshments for the conference.


I will ask each of you to present a 15-25 minute talk summarizing


a recent paper from the scientific literature that uses the calculus of


variations.  Your talk counts for 1/3 of your grade.


Students wishing to give an M.S. presentation should plan on giving


a 25 minute talk.  If we have too many speakers, some of the M.S. talks


may be scheduled for the Master's Presentation Symposium. 


Students who are unable to attend the meeting may submit a 10-20 page


term paper.  The term paper is due the last day of lectures.










Questions





Frequently Asked Questions (FAQs)




Registration





Registration Form




Schedule





Schedule




Abstracts





Abstracts




Tasks





Tasks and Duties






Calendar



Important Dates








Monday
January 3, 2011
First Day of Classes




Monday
January 17, 2011
Martin Luther King Day (No Class)




Friday
February 18, 2011
FPCVM Registration Due Date




Monday
February 21, 2011
Presidents Day (No Class)




Saturday
February 26, 2011
FPC Variational Meeting




Friday
March 11, 2011
Last Day of Lectures









Videos



You may download videos of the lectures from this class's





To read more about streaming video see the





Notes