Book contents
- Frontmatter
- Contents
- Preface to the second edition
- Preface to the first edition
- 1 Preliminary algebra
- 2 Preliminary calculus
- 3 Complex numbers and hyperbolic functions
- 4 Series and limits
- 5 Partial differentiation
- 6 Multiple integrals
- 7 Vector algebra
- 8 Matrices and vector spaces
- 9 Normal modes
- 10 Vector calculus
- 11 Line, surface and volume integrals
- 12 Fourier series
- 13 Integral transforms
- 14 First-order ordinary differential equations
- 15 Higher-order ordinary differential equations
- 16 Series solutions of ordinary differential equations
- 17 Eigenfunction methods for differential equations
- 18 Partial differential equations: general and particular solutions
- 19 Partial differential equations: separation of variables and other methods
- 20 Complex variables
- 21 Tensors
- 22 Calculus of variations
- 23 Integral equations
- 24 Group theory
- 25 Representation theory
- 26 Probability
- 27 Statistics
- 28 Numerical methods
- Appendix Gamma, beta and error functions
- Index
Preface to the second edition
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface to the second edition
- Preface to the first edition
- 1 Preliminary algebra
- 2 Preliminary calculus
- 3 Complex numbers and hyperbolic functions
- 4 Series and limits
- 5 Partial differentiation
- 6 Multiple integrals
- 7 Vector algebra
- 8 Matrices and vector spaces
- 9 Normal modes
- 10 Vector calculus
- 11 Line, surface and volume integrals
- 12 Fourier series
- 13 Integral transforms
- 14 First-order ordinary differential equations
- 15 Higher-order ordinary differential equations
- 16 Series solutions of ordinary differential equations
- 17 Eigenfunction methods for differential equations
- 18 Partial differential equations: general and particular solutions
- 19 Partial differential equations: separation of variables and other methods
- 20 Complex variables
- 21 Tensors
- 22 Calculus of variations
- 23 Integral equations
- 24 Group theory
- 25 Representation theory
- 26 Probability
- 27 Statistics
- 28 Numerical methods
- Appendix Gamma, beta and error functions
- Index
Summary
Since the publication of the first edition of this book, both through teaching the material it covers and as a result of receiving helpful comments from colleagues, we have become aware of the desirability of changes in a number of areas. The most important of these is that the mathematical preparation of current senior college and university entrants is now less thorough than it used to be. To match this, we decided to include a preliminary chapter covering areas such as polynomial equations, trigonometric identities, coordinate geometry, partial fractions, binomial expansions, necessary and sufficient condition and proof by induction and contradiction.
Whilst the general level of what is included in this second edition has not been raised, some areas have been expanded to take in topics we now feel were not adequately covered in the first. In particular, increased attention has been given to non-square sets of simultaneous linear equations and their associated matrices. We hope that this more extended treatment, together with the inclusion of singular value matrix decomposition, will make the material of more practical use to engineering students. In the same spirit, an elementary treatment of linear recurrence relations has been included. The topic of normal modes has been given a small chapter of its own, though the links to matrices on the one hand, and to representation theory on the other, have not been lost.
Elsewhere, the presentation of probability and statistics has been reorganised to give the two aspects more nearly equal weights.
- Type
- Chapter
- Information
- Mathematical Methods for Physics and EngineeringA Comprehensive Guide, pp. xix - xxPublisher: Cambridge University PressPrint publication year: 2002