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401-3350-26L 4 Credits BSC , MSC D-MATH

Introduction to Calculus of Variations

Lecturers & Examiners: Prof. Dr. Francesca Da Lio
Number of participants limited to 18. Almost fully booked. [Late inquiries as to whether a place is still available must be directed to the seminar advisor.]
VVZ CR n/a

Last Updated: 2026-06-03 00:14:38

Abstract

Many problems in mathematics, physics, and engineering can be described as optimization problems: finding the best possible shape, path, or configuration among many alternatives. The Calculus of Variations is a branch of mathematics that studies such problems by analyzing quantities such as length, energy, or cost, and by understanding how they can be minimized or maximized.

Objective

The series is intended for bachelor/master students with a good background in calculus, measure theory and function spaces. Its aim is to introduce variational thinking and to show how these ideas appear in many areas of mathematics and science, while encouraging curiosity, independent learning, and clear mathematical communication.

Content

Many problems in mathematics, physics, and engineering can be described as optimization problems: finding the best possible shape, path, or configuration among many alternatives. The Calculus of Variations is a branch of mathematics that studies such problems by analyzing quantities such as length, energy, or cost, and by understanding how they can be minimized or maximized. This seminar series provides an introductory overview of the Calculus of Variations and some of its applications. Starting from classical examples such as shortest paths and minimal surfaces, we will see how variational ideas naturally lead to differential equations and useful mathematical tools. The emphasis will be on intuition and concrete examples rather than technical details, with connections to physics, geometry, and applied mathematics. The series is intended for bachelor/master students with a good background in calculus, measure theory and function spaces. Its aim is to introduce variational thinking and to show how these ideas appear in many areas of mathematics and science, while encouraging curiosity, independent learning, and clear mathematical communication.

Resources

Literature

Main References: 1. Buttazzo, Giuseppe(I-PISA); Giaquinta, Mariano(I-PISA); Hildebrandt, Stefan(D-BONN) One-dimensional variational problems.(English summary) An introduction Oxford Lecture Ser. Math. Appl., 15 The Clarendon Press, Oxford University Press, New York, 1998. viii+262 pp. ISBN:0-19-850465-9 2. Dacorogna, Bernard(CH-LSNP-NDM) Introduction to the calculus of variations. Fourth edition [of MR2162819] World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, [2025], ©2025. xiii+353 3. Appunti di Calcolo delle Variazioni Paperback – 27 Jan. 2019 by Carlo Mantegazza, Francesca Angrisani, Giacomo Ascione , Chiara Leone https://cvgmt.sns.it/HomePages/cm/other/Dida/intro1capCalcVar.pdf 4. Direct methods in the calculus of variations, Giusti, Enrico World Scientific Publishing Co., Inc., River Edge, NJ, 2003, viii+403 pp. ISBN: 981-238-043-4 5. Partial differential equations Evans, Lawrence C. Grad. Stud. Math., 19 American Mathematical Society, Providence, RI, 2010, xxii+749 pp. ISBN: 978-0-8218-4974-3 6. - Functional analysis, Sobolev spaces and partial differential equations Brezis, Haim Universitext Springer, New York, 2011, xiv+599 pp.

General Information

Language
English
Levels
BSC , MSC

Examination

Type
ungraded semester performance

Registration & Places

Limited places (Special selection)
Signup End
07.02.2026
Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type Title Time & Place Hours
seminar Introduction to Calculus of Variations
  • Wed 10:15-12:00 (HG F 26.5)
2 h weekly

Offered In

  • Mathematics Bachelor
    • Seminars (The number of seminar places is limited, and the special selection procedure should help to allocate the places not primarily according to the registration time. Everybody is waitlisted first when he/she tries to register for a seminar in myStudies. Moreover: Only one mathematics seminar can be chosen per semester. Notice also the course unit 401-0002-99L Generic Seminar - Second Priority / Third Priority.)
  • Mathematics Master
    • Seminars and Semester Papers
      • Seminars (The number of seminar places is limited, and the special selection procedure should help to allocate the places not primarily according to the registration time. Everybody is waitlisted first when he/she tries to register for a seminar in myStudies. Moreover: Only one mathematics seminar can be chosen per semester. In case you need to attend 2 seminars in this semester, please take contact with the Study Administration (email: ). Notice also the course unit 401-0002-99L Generic Seminar - Second Priority / Third Priority.)