Book contents
- Frontmatter
- Contents
- Preface
- Mathematical symbols
- 1 PRELIMINARY CALCULUS
- 2 VECTOR ALGEBRA
- 3 CALCULUS OF VECTORS
- 4 VECTOR OPERATORS
- 5 ORDINARY DIFFERENTIAL EQUATIONS
- 6 SERIES SOLUTIONS OF DIFFERENTIAL EQUATIONS
- 7 SUPERPOSITION METHODS
- 8 FOURIER METHODS
- 9 PARTIAL DIFFERENTIAL EQUATIONS
- 10 SEPARATION OF VARIABLES
- 11 NUMERICAL METHODS
- 12 CALCULUS OF VARIATIONS
- 13 GENERAL EIGENVALUE PROBLEM
- 14 MATRICES
- 15 CARTESIAN TENSORS
- 16 COMPLEX VARIABLES
- SOLUTIONS AND HINTS FOR EXERCISES AND EXAMPLES
- INDEX
1 - PRELIMINARY CALCULUS
Published online by Cambridge University Press: 05 February 2012
- Frontmatter
- Contents
- Preface
- Mathematical symbols
- 1 PRELIMINARY CALCULUS
- 2 VECTOR ALGEBRA
- 3 CALCULUS OF VECTORS
- 4 VECTOR OPERATORS
- 5 ORDINARY DIFFERENTIAL EQUATIONS
- 6 SERIES SOLUTIONS OF DIFFERENTIAL EQUATIONS
- 7 SUPERPOSITION METHODS
- 8 FOURIER METHODS
- 9 PARTIAL DIFFERENTIAL EQUATIONS
- 10 SEPARATION OF VARIABLES
- 11 NUMERICAL METHODS
- 12 CALCULUS OF VARIATIONS
- 13 GENERAL EIGENVALUE PROBLEM
- 14 MATRICES
- 15 CARTESIAN TENSORS
- 16 COMPLEX VARIABLES
- SOLUTIONS AND HINTS FOR EXERCISES AND EXAMPLES
- INDEX
Summary
Although the major part of this book is concerned with mathematics of direct value in describing situations arising in physical science and engineering, this opening chapter, although directed to the same end, is of a less obviously ‘applied’ nature. It is concerned with those techniques of mathematics, principally in the field of calculus, which are the nuts and bolts of the more particularly orientated methods presented in later chapters.
Two particular factors have to be taken into account in its presentation; firstly the various levels of previous knowledge which different readers will possess, and secondly the fact that the subjects to be treated in this chapter form a less coherent whole than do those in any other.
The first of these has been approached at the ‘highest common factor’ level, namely, knowledge has been presumed only of those topics which will normally be familiar to a student who, in his previous studies, has taken mathematics in conjunction with other science subjects, rather than as his main or only subject. As a result, although several parts of this chapter will almost certainly be unfamiliar to him, the reader with more than this presumed level of knowledge may in some sections find it sufficient to make sure he can solve the corresponding exercises, marked by the symbol ▸, and then pass on to the next section.
As a result of the rather diverse nature of the topics considered, the degree of difficulty of the material does not vary ‘monotonically’ throughout the chapter.
- Type
- Chapter
- Information
- Mathematical Methods for the Physical SciencesAn Informal Treatment for Students of Physics and Engineering, pp. 1 - 68Publisher: Cambridge University PressPrint publication year: 1974