Calculus of Variations is given by the Department of Mathematics LTH. The course is also available for students enrolled in the Bachelor´s or Master´s Programme in Mathematics at the Faculty of Science who can take this course as an optional course on upper basic level within their programme. Also, an extended version of the course can be taken of Ph.D students from both faculties.

The course codes are as follows for the different student categories:

FMAN25, 7,5 credits, for students at Faculty of Engineering
MATC25, 7.5 credits, for students at Faculty of Science
FMA201F, 7.5 credits, for Ph.D students

Course Contents
The aim of the course is to present the basic theory for, and applications of, the calculus of variations, i.e., optimization problems for "functions of functions". A classical example is the isoperimetric problem, to find which closed curve of a given length encloses maximal area. Many physical laws can be formulated as variational principles, i.e. the law of refraction. The calculus of variations is also a cornerstone in classical mechanics, and has many other technological applications e.g. in systems theory and optimal control.

Teaching
The teaching consists of lectures and compulsory assignments.

Assessment
The course is assessed through an oral examination and the assignments.

Course literature

Both books are available electronically on the LU library.

[1] Mark Kot, A First Course in the Calculus of Variations, 2014, ISBN 978-1-4704-1495-5 (Course Book)

[2] Mesterton-Gibbons, A Primer on the Calculus of Variations and Optimal Control Theory (Optional), 2009, ISBN 978-0-8218-4772-5 (Optional)

Schedule
The schedule for the first half of the semester is here.