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The Physical WorldAn Inspirational Tour of Fundamental Physics$
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Nicholas Manton and Nicholas Mee

Print publication date: 2017

Print ISBN-13: 9780198795933

Published to Oxford Scholarship Online: July 2017

DOI: 10.1093/oso/9780198795933.001.0001

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Fundamental Ideas

Fundamental Ideas

Chapter:
(p.4) 1 Fundamental Ideas
Source:
The Physical World
Author(s):

Nicholas Manton

Nicholas Mee

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198795933.003.0002

Chapter 1 offers a simple introduction to the use of variational principles in physics. This approach to physics plays a key role in the book. The chapter starts with a look at how we might minimize a journey by car, even if this means taking a longer route. Soap films are also discussed. It then turns to geometrical optics and uses Fermat’s principle to explain the reflection and refraction of light. There follows a discussion of the significance of variational principles throughout physics. The chapter also covers some introductory mathematical ideas and techniques that will be used in later chapters. These include the mathematical representation of space and time and the use of vectors; partial differentiation, which is necessary to express all the fundamental equations of physics; and Gaussian integrals, which arise in many physical contexts. These mathematical techniques are illustrated by their application to waves and radioactive decay.

Keywords:   Fermat’s principle, geometrical optics, variational principle, Gaussian integral, waves, vectors, radioactive decay, soap films

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