Real Functions in Several Variables: Volume XII Vector Fields III
Publisher: Bookboon.com
Published: 2015
ISBN-13: 9788740309195
Table of contents: title: Content; title: 1. Preface; title: 2. Introduction to volume XII, Vector fields III; Potentials, Harmonic Functions and Green’s Identities; title: 3. Potentials; title: 3.1. Definitions of scalar and vectorial potentials; title: 3.2. A vector field given by its rotation and divergence; title: 3.3. Some applications in Physics; title: 3.4. Examples from Electromagnetism; title: 3.5. Scalar and vector potentials; title: 4. Harmonic functions and Green’s identities; title: 4.1. Harmonic functions; title: 4.2. Green’s first identity; title: 4.3. Green’s second identity; title: 4.4. Green’s third identity; title: 4.5. Green’s identities in the plane; title: 5. Gradient, divergence and rotation in semi-polar and spherical coordinates; title: 5.1. Examples of applications of Green’s identities; title: 5.2. Overview of Green’s theorems in the plane; title: 5.3. Miscellaneous examples; title: 6. Formulæ; title: 6.1. Squares etc; title: 6.2. Powers etc; title: 6.3. Differentiation; title: 6.4. Special derivatives; title: 6.5. Integration; title: 6.6. Special antiderivatives; title: 6.7. Trigonometric formulæ; title: 6.8. Hyperbolic formulæ; title: 6.9. Complex transformation formulæ; title: 6.10. Taylor expansions; title: 6.11. Magnitudes of functions; title: 7. Index