Vector Analysis and Cartesian TensorsTaylor & Francis, 1992 - 304 pages This 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 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 |
Scalar and vector fields | 89 |
Copyright | |
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a₁ angle axes Ox₁ x2 axes Oxyz b₁ b₂ cartesian tensor components constant continuously differentiable coordinate system curl F curvilinear coordinates cylindrical polar coordinates defined denote direction cosines div F divergence theorem double integral dt dt Evaluate example EXERCISES expressed F₁ field F follows geometrical grad gradient h₁ h₂ Hence isotropic Laplace's equation line integral numbers origin orthogonal Ox₁ x2 x3 parallel parametric equation perpendicular plane Poisson's equation position vector proof prove rectangular cartesian coordinate relative respectively rotation scalar field scalar invariant second order tensor Show simple closed surface sin² Solution spherical polar coordinates suffixes symmetrical transformation unit normal unit tangent unit vector vector field vector product velocity verify xy-plane ΘΩ ΘΩ д д д ди ди дх ду дл дхі