Introduction to Physical Mathematics

P.G. Harper; D. L. Weaire

doi:10.1017/CBO9780511564277

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Reid, Jane M. Arcese, Peter and Keller, Lukas F. 2003. Inbreeding depresses immune response in song sparrows (Melospiza melodia): direct and inter–generational effects. Proceedings of the Royal Society of London. Series B: Biological Sciences, Vol. 270, Issue. 1529, p. 2151.

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Amiri, Iraj Sadegh and Ghadiry, Mahdiar 2018. Analytical Modelling of Breakdown Effect in Graphene Nanoribbon Field Effect Transistor. p. 45.

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P.G. Harper, D. L. Weaire

Publisher:: Cambridge University Press
Online publication date:: October 2009
Print publication year:: 1985
Online ISBN:: 9780511564277
DOI:: https://doi.org/10.1017/CBO9780511564277

Subjects:: Physics and Astronomy, Mathematical Methods

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Directed primarily at college and university undergraduates, this book covers at basic level the essential applications of mathematics to the physical sciences. It contains all the usual topics covered in a first-year course such as vectors, matrices, differential equations, basic mathematical functions and their analysis, and power series. There is a strong emphasis on qualitative understanding (such as curve sketching) and practical methods of solution. The latter take due account of the impact of computers on the subject. The principles of mathematical expression are illustrated by copious examples taken from a wide range of topics in physics and chemistry. Each of the short chapters concludes with a summary and a large number of problems.

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Introduction to Physical Mathematics

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

Some notes on notation
pp ix-xii

1 - Introduction
pp 1-4

2 - Errors
pp 5-16

3 - Cartesian coordinates
pp 17-22

4 - Vectors
pp 23-28

5 - The scalar product
pp 29-34

6 - The vector product and rotation
pp 35-42

7 - Matrices in physics
pp 43-49

8 - The transformation of matrices
pp 50-56

9 - The matrix eigenvalue equation
pp 57-61

10 - Exponential and logarithm functions
pp 62-68

11 - Sine and cosine functions
pp 69-75

12 - Graph plotting and curve sketching
pp 76-86

13 - Differentiation
pp 87-93

14 - Approximations
pp 94-98

15 - Power series and Taylor's expansion
pp 99-107

16 - Partial differentiation
pp 108-117

17 - Integration
pp 118-127

18 - The differential equation
pp 128-133

19 - Solving first-order differential equations
pp 134-140

20 - Second-order differential equations
pp 141-146

21 - Solving second-order differential equations
pp 147-152

22 - The complex exponential
pp 153-158

23 - The circuit equation
pp 159-164

24 - Harmonics and Fourier series
pp 165-172

25 - The diffusion equation
pp 173-183

26 - Waves
pp 184-193

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Introduction to Physical Mathematics

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