Dear students,
Next spring I will be teaching an introductory course on calculus of variations, Math 534. The course will follow the book "Introduction to Calculus of Variations" by Dacorogna.
Calculus of variations is one of the classical fields of mathematics with one of its oldest problems, Dido’s problem, dating back to the 9th century BC. According to a legend about the foundation of Carthage (today's Tunisia), queen Dido, the daughter of a Phoenician king, fled to the coast of Tunisia after the assassination of her husband by her brother. There, she asked a local leader for as much land as could be enclosed by the hide of an ox and since the request was so modest he agreed. Dido cut the hide into narrow strips, tied them together and encircled a large tract of land which became the city of Carthage. Dido faced a mathematical problem closely related to what is known today as the isoperimetric problem: Find among all curves of given length the one which encloses maximal area. The solution to the isoperimetric problem is given by a circle and was known already in ancient Greece. The isoperimetric problem is a problem of minimization which is the core of calculus of variations. The first systematic way of dealing with such problems is due to Euler and Lagrange in the 18th century who introduced what is know today as the Euler-Lagrange equation and which will be covered at the beginning of this course. Another famous problem of calculus of variations and one that will be discussed in this course is Plateau's problem, which is the problem of showing the existence of a minimal surface (a surface that locally minimizes its area) with a given boundary. This problem was raised by Lagrange, however, it is named after the Belgian physicist Plateau who experimented with soap films.
Feel free to contact me if you have any questions or concerns about the class.
Theodora Bourni
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