Vector Analysis and Cartesian Tensors, Third editionThis is a comprehensive and self-contained text suitable for use by undergraduate mathematics, science and engineering students. Vectors are introduced in terms of cartesian components, making the concepts of gradient, divergent and curl particularly simple. The text is supported by copious examples and progress can be checked by completing the many problems at the end of each section. Answers are provided at the back of the book. |
Contents
Scalar and vector algebra | 21 |
Vector functions of a real variable Differential geometry | 55 |
34 | 76 |
55835 | 82 |
Scalar and vector fields | 89 |
Line surface and volume integrals | 147 |
Integral theorems | 195 |
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Common terms and phrases
a₁ axes Ox axes Oxyz axis b₁ b₂ cartesian tensor components constant continuously differentiable coordinate system curl F curvilinear coordinates cylindrical polar coordinates defined definition denote direction cosines div F divergence theorem double integral dt dt eigenvalues Evaluate example EXERCISES expressed F.dr F₁ field F follows geometrical grad gradient Hence isotropic Laplace's equation line integral magnitude matrix notation origin orthogonal parallel parametric equation perpendicular plane Poisson's equation position vector proof prove rectangular cartesian coordinate relative respectively rotation scalar field scalar invariant scalar product second order tensor Show simple closed surface sin² Solution sphere spherical polar coordinates suffixes symmetrical transformation unit normal unit tangent unit vector vector field vector product velocity verify xy-plane z-axis zero ΘΩ ΘΩ д д ди ди дх ду дл дхі