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The Open University

Introduction to the calculus of variations

The Open University via OpenLearn

Overview

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This free course concerns the calculus of variations. Section 1 introduces some key ingredients by solving a seemingly simple problem – finding the shortest distance between two points in a plane. The section also introduces the notions of a functional and of a stationary path. Section 2 describes basic problems that can be formulated in terms of functionals. Section 3 looks at partial and total derivatives. Section 4 contains a derivation of the Euler-Lagrange equation. In Section 5 the Euler-Lagrange equation is used to solve some of the earlier problems, as well as one arising from a new topic, Fermat’s principle.

Syllabus

  • Introduction
  • Learning outcomes
  • Link to course PDF
  • Conclusion
  • Acknowledgements

Reviews

4.4 rating at OpenLearn based on 8 ratings

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