M-5500 and 6880-001
Calculus of Variations

Spring 2018

### Instructor Andrej Cherkaev

Office: JWB 225
Telephone: 581-6822
E-mail: cherk@math.utah.edu

Every problem of the calculus of variations has a solution,
provided that the word `solution' is suitably understood.

David Hilbert

Syllabus

#### Notes:

I will work on the notes and edit them during the semester.

• Robert Weinstock. Calculus of Variations with Applications to Physics and Engineering. Dover Publications, 1974.
• I. M. Gelfand, S. V. Fomin Calculus of Variations Dover Publications, 2000
• Inequalities that Imply the Isoperimetric Inequality: an article by Andrejs Treibergs: http://www.math.utah.edu/~treiberg/isoperim/isop.pdf

Homework (will be updated)

HW1 2018
HW2 2018

HW3 2018
HW4 2018
Sources for Numerical methods
Shooting methods
https://en.wikipedia.org/wiki/Shooting_method
Lecture
https://www.mathworks.com/matlabcentral/fileexchange/32451-shooting-method?focused=5194030&tab=function&s_tid=gn_loc_drop
Matlab
https://www.mathworks.com/matlabcentral/fileexchange/32451-shooting-method?focused=5194030&tab=function&s_tid=gn_loc_drop
Matematica
https://www.mathworks.com/matlabcentral/fileexchange/32451-shooting-method?focused=5194030&tab=function&s_tid=gn_loc_drop

https://en.wikipedia.org/wiki/Rayleigh%E2%80%93Ritz_method
HW5 2018
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Ref for formulation of the control problems:
1. From Calculus of Variations to Optimal Control
by Daniel Liberzon
University of Illinois at Urbana-Champaign
http://liberzon.csl.illinois.edu/teaching/cvoc/node45.html

2. An Introduction to Mathematical Optimal Control Theory
by Lawrence C. Evans
University of California, Berkeley
math.berkeley.edu/~evans/control.course.pdf

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Relaxation of nonconvex variational problems:

http://www.math.utah.edu/~cherk/teach/12calcvar/150existance.pdf

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Math 5500-001 Review Session:
4/27/18 - 1:30PM - 3:30PM Scheduled LCB 121

Problem for the final exam
R
eturn your work at Monday, 4/29/18 before 5 pm.
Notice: an extra-credit problem is added.

Homework assignments from from the last year

HW2 - approximates

HW3 - constraints
HW3 - the new file
HW4 - numerical solutions
HW5 - Hamiltonian and Legendre transform

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HW5 - duality
NW6 - see the note
HW 8 (PDE)

Final HW 2017