Vector Analysis: A Physicist's Guide to the Mathematics of Fields in Three DimensionsVector analysis provides the language that is needed for a precise quantitative statement of the general laws and relationships governing such branches of physics as electromagnetism and fluid dynamics. The account of the subject is aimed principally at physicists but the presentation is equally appropriate for engineers. The justification for adding to the available textbooks on vector analysis stems from Professor Kemmer's novel presentation of the subject developed through many years of teaching, and in relating the mathematics to physical models. While maintaining mathematical precision, the methodology of presentation relies greatly on the visual, geometric aspects of the subject and is supported throughout the text by many beautiful illustrations that are more than just schematic. A unification of the whole body of results developed in the book - from the simple ideas of differentiation and integration of vector fields to the theory of orthogonal curvilinear coordinates and to the treatment of time-dependent integrals over fields - is achieved by the introduction from the outset of a method of general parametrisation of curves and surfaces. |
Contents
Summary of vector algebra | 1 |
Exercises A | 9 |
Metric properties of Euclidean space | 27 |
Scalar and vector fields | 37 |
Exercises C | 45 |
Further spatial integrals | 62 |
the gradient | 72 |
The fundamental property of a gradient field | 78 |
Exercises | 134 |
Second derivatives of vector fields elements | 145 |
Exercises G | 155 |
Exercises H | 171 |
Timedependent fields | 181 |
Exercises I | 191 |
Exercises C | 202 |
Exercises E | 208 |
the divergence | 93 |
A general notation | 100 |
Exercises | 107 |
Boundary behaviour of fields | 116 |
Exercises F | 218 |
Exercises H | 229 |
Exercises | 247 |
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Vector Analysis: A Physicist's Guide to the Mathematics of Fields in Three ... N. Kemmer No preview available - 1977 |
Common terms and phrases
arbitrary C₁ calculation cartesian coordinates chapter closed curve closed surface component const constant vector curl curl curl f defined derivatives differential dipole direction discontinuity div f divergence divergence theorem double layer equation Evaluate exercise expression f₁ f₂ field ƒ field lines fluid dynamics flux integral function generalisation given grad gradient Hence integrand irrotational field level surface mathematical normal notation orthogonal parameters parametrisation physical plane polar coordinates potential theory quasi-cube quasi-square r₁ result S₁ S₂ scalar field scalar potential Show sin² solenoidal field space sphere spherical polars Stokes stream function surface integral surface sources T-field theorem unit vector V₁ values vanish vector analysis vector area vector field vector potential Verify volume vorticity zero αλ δμ λ² λι µ² ду дф