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.
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