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Calculus of Variations and Integral Equations


Topics in the calculus of variations, integral equations and applications.


Calculus of Variations - Mechanics, Control and other applications, MacCluer, Prentice-Hall, 2004.


MATH 220 , MATH 223 and MATH 290, or MATH 320.

Credit Hours: 

This course will cover the following topics:

  1. Basic concepts of calculus of variations - convexity and Lagrange multipliers
  2. Formulating variational problems and examples: geodesics, the catenary, the brahistochrone, shapes of minimum resistance
  3. Euler Lagrange equations, the Hamiltonian point of view
  4. Constrained optimization problems - integral and nonintegral constraints. Euler Lagrange equations and applications
  5. Extremal surfaces - soap films, the Schrodinger equation
  6. Uniqueness for variational problems, first and second variations of functionals 
  7. Weierstrass E function and Erdmann corner conditions

(Oh 2010 )

Every Spring Semester

Events Calendar

Using Math

CTE course transformation grant helps Emily Witt, assistant professor of math, develop active learning with student groups in calculus.  Positive results using modules developed with Justin Lyle and Amanda Wilkens, math graduate students, were attained.  Read more

Math and COVID-19: Sources on how math is being used to track the virus and its spread.  AMS link.

A mathematician-musician's breakthrough melds East, West. Read more.

Researcher's innovative approach to flood mapping support emergency management and water officials. Read more.

Nicole Johnson found a way to express her baton twirling using math. See video.