YoVDO

Introduction to the calculus of variations

Offered By: The Open University via OpenLearn

Tags

Calculus Courses Partial Derivatives Courses Theoretical Physics Courses Calculus of Variation Courses

Course Description

Overview

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

Tags

Related Courses

Optimal control
Indian Institute of Technology Roorkee via Swayam
Calculus of Variations and Integral Equations
NPTEL via YouTube
Finite Element Method
Indian Institute of Technology, Kharagpur via Swayam
Mathematics
NIOS via YouTube
Optimal Control, Guidance and Estimation
NPTEL via YouTube