Book contents
- Frontmatter
- Contents
- Preface to Second Edition
- Acknowledgements
- 1 Introduction
- 2 Dimensional analysis
- 3 Power series
- 4 Spherical and cylindrical coordinates
- 5 Gradient
- 6 Divergence of a vector field
- 7 Curl of a vector field
- 8 Theorem of Gauss
- 9 Theorem of Stokes
- 10 Laplacian
- 11 Conservation laws
- 12 Scale analysis
- 13 Linear algebra
- 14 Dirac delta function
- 15 Fourier analysis
- 16 Analytic functions
- 17 Complex integration
- 18 Green's functions: principles
- 19 Green's functions: examples
- 20 Normal modes
- 21 Potential theory
- 22 Cartesian tensors
- 23 Perturbation theory
- 24 Asymptotic evaluation of integrals
- 25 Variational calculus
- 26 Epilogue, on power and knowledge
- References
- Index
1 - Introduction
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface to Second Edition
- Acknowledgements
- 1 Introduction
- 2 Dimensional analysis
- 3 Power series
- 4 Spherical and cylindrical coordinates
- 5 Gradient
- 6 Divergence of a vector field
- 7 Curl of a vector field
- 8 Theorem of Gauss
- 9 Theorem of Stokes
- 10 Laplacian
- 11 Conservation laws
- 12 Scale analysis
- 13 Linear algebra
- 14 Dirac delta function
- 15 Fourier analysis
- 16 Analytic functions
- 17 Complex integration
- 18 Green's functions: principles
- 19 Green's functions: examples
- 20 Normal modes
- 21 Potential theory
- 22 Cartesian tensors
- 23 Perturbation theory
- 24 Asymptotic evaluation of integrals
- 25 Variational calculus
- 26 Epilogue, on power and knowledge
- References
- Index
Summary
The topic of this book is the application of mathematics to physical problems. Mathematics and physics are often taught separately. Despite the fact that education in physics relies on mathematics, it turns out that students consider mathematics to be disjoint from physics. Although this point of view may strictly be correct, it reflects an erroneous opinion when it concerns an education in the sciences. The reason for this is that mathematics is the only language at our disposal for quantifying physical processes. One cannot learn a language by just studying a textbook. In order to truly learn how to use a language one has to go abroad and start using that language. By the same token one cannot learn how to use mathematics in the physical sciences by just studying textbooks or attending lectures; the only way to achieve this is to venture into the unknown and apply mathematics to physical problems.
It is the goal of this book to do exactly that; problems are presented in order to apply mathematical techniques and knowledge to physical concepts. These examples are not presented as well-developed theory. Instead, they are presented as a number of problems that elucidate the issues that are at stake. In this sense this book offers a guided tour: material for learning is presented but true learning will only take place by active exploration. In this process, the interplay of mathematics and physics is essential; mathematics is the natural language for physics while physical insight allows for a better understanding of the mathematics that is presented.
- Type
- Chapter
- Information
- A Guided Tour of Mathematical MethodsFor the Physical Sciences, pp. 1 - 2Publisher: Cambridge University PressPrint publication year: 2004