Book contents
- Frontmatter
- Contents
- Dedication
- Preface
- Introduction
- 1 Summary of vector algebra
- Exercises A
- 2 The geometrical background to vector analysis
- 3 Metric properties of Euclidean space
- Exercises B
- 4 Scalar and vector fields
- Exercises C
- 5 Spatial integrals of fields
- 6 Further spatial integrals
- Exercises D
- 7 Differentiation of fields. Part 1: the gradient
- 8 Differentiation of fields. Part 2: the curl
- 9 Differentiation of fields. Part 3: the divergence
- 10 Generalisation of the three principal theorems and some remarks on notation
- Exercises E
- 11 Boundary behaviour of fields
- Exercises F
- 12 Differentiation and integration of products of fields
- 13 Second derivatives of vector fields; elements of potential theory
- Exercises G
- 14 Orthogonal curvilinear coordinates
- Exercises H
- 15 Time-dependent fields
- Exercises I
- Answers and comments
- Index
- Frontmatter
- Contents
- Dedication
- Preface
- Introduction
- 1 Summary of vector algebra
- Exercises A
- 2 The geometrical background to vector analysis
- 3 Metric properties of Euclidean space
- Exercises B
- 4 Scalar and vector fields
- Exercises C
- 5 Spatial integrals of fields
- 6 Further spatial integrals
- Exercises D
- 7 Differentiation of fields. Part 1: the gradient
- 8 Differentiation of fields. Part 2: the curl
- 9 Differentiation of fields. Part 3: the divergence
- 10 Generalisation of the three principal theorems and some remarks on notation
- Exercises E
- 11 Boundary behaviour of fields
- Exercises F
- 12 Differentiation and integration of products of fields
- 13 Second derivatives of vector fields; elements of potential theory
- Exercises G
- 14 Orthogonal curvilinear coordinates
- Exercises H
- 15 Time-dependent fields
- Exercises I
- Answers and comments
- Index
Summary
The material of chapters 7–9 is so interrelated that it would not have been practical to provide separate exercises for each, or even to arrange the exercises in an order that relates strictly to the topics of the individual chapters. The student should, however, find little difficulty in identifying questions that require the understanding of earlier material only. An attempt at logical progress has been made except that the first three questions clearly relate to chapters 7, 8 and 9 separately. Sections 2 and 3 of chapter 10 do not call for illustration by exercises, but the last few questions in the following relate in part to section 1 of chapter 10.
At this stage in the book the idea behind the quasi-square and quasi-cube technique can be taken for granted. The technique is still relevant to some of the exercises, but many are now independent of it – and particular fields that are of importance in physics are now introduced when possible. However, some of the exercises still deal with quite artificial constructs. As before, these serve to illustrate general ideas by non-trivial particular examples. In some case the work is saved from being intolerably cumbersome only by the symmetries built in. Artificial though this may be, training in the exploitation of symmetries is of value in itself.
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- Chapter
- Information
- Vector AnalysisA Physicist's Guide to the Mathematics of Fields in Three Dimensions, pp. 107 - 114Publisher: Cambridge University PressPrint publication year: 1977