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Introduction to the calculus of variations

The Open University via OpenLearn

Description

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.

Tags

Economics

Syllabus

Introduction
Learning outcomes
Link to course PDF
Conclusion
Acknowledgements

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Online Courses

OpenLearn

Introduction to the calculus of variations

The Open University

Start Learning Find study partner

Affiliate notice

Type

Online Courses
Provider

OpenLearn

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.

Introduction
Learning outcomes
Link to course PDF
Conclusion
Acknowledgements

Tags

Economics

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