Ellipsoidal Harmonics

Ellipsoidal Harmonics

Author: George Dassios

Publisher: Cambridge University Press

Published: 2012-07-12

Total Pages: 475

ISBN-13: 1139510134

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The sphere is what might be called a perfect shape. Unfortunately nature is imperfect and many bodies are better represented by an ellipsoid. The theory of ellipsoidal harmonics, originated in the nineteenth century, could only be seriously applied with the kind of computational power available in recent years. This, therefore, is the first book devoted to ellipsoidal harmonics. Topics are drawn from geometry, physics, biosciences and inverse problems. It contains classical results as well as new material, including ellipsoidal bi-harmonic functions, the theory of images in ellipsoidal geometry and vector surface ellipsoidal harmonics, which exhibit an interesting analytical structure. Extended appendices provide everything one needs to solve formally boundary value problems. End-of-chapter problems complement the theory and test the reader's understanding. The book serves as a comprehensive reference for applied mathematicians, physicists, engineers and for anyone who needs to know the current state of the art in this fascinating subject.


An Elementary Treatise on Fourier's Series

An Elementary Treatise on Fourier's Series

Author: William Elwood Byerly

Publisher:

Published: 2021-04-13

Total Pages: 292

ISBN-13:

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William Elwood Byerly was an American mathematician at Harvard University where he was the "Perkins Professor of Mathematics". He was noted for his excellent teaching and textbooks


Foundations of Potential Theory

Foundations of Potential Theory

Author: Oliver Dimon Kellogg

Publisher: Courier Corporation

Published: 1953-01-01

Total Pages: 404

ISBN-13: 9780486601441

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Introduction to fundamentals of potential functions covers the force of gravity, fields of force, potentials, harmonic functions, electric images and Green's function, sequences of harmonic functions, fundamental existence theorems, the logarithmic potential, and much more. Detailed proofs rigorously worked out. 1929 edition.


Partial Differential Equations of Mathematical Physics

Partial Differential Equations of Mathematical Physics

Author: Arthur Godon Webster

Publisher: Courier Dover Publications

Published: 2016-06-20

Total Pages: 465

ISBN-13: 0486805158

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A classic treatise on partial differential equations, this comprehensive work by one of America's greatest early mathematical physicists covers the basic method, theory, and application of partial differential equations. In addition to its value as an introductory and supplementary text for students, this volume constitutes a fine reference for mathematicians, physicists, and research engineers. Detailed coverage includes Fourier series; integral and elliptic equations; spherical, cylindrical, and ellipsoidal harmonics; Cauchy's method; boundary problems; the Riemann-Volterra method; and many other basic topics. The self-contained treatment fully develops the theory and application of partial differential equations to virtually every relevant field: vibration, elasticity, potential theory, the theory of sound, wave propagation, heat conduction, and many more. A helpful Appendix provides background on Jacobians, double limits, uniform convergence, definite integrals, complex variables, and linear differential equations.


Geometric Applications of Fourier Series and Spherical Harmonics

Geometric Applications of Fourier Series and Spherical Harmonics

Author: H. Groemer

Publisher: Cambridge University Press

Published: 1996-09-13

Total Pages: 343

ISBN-13: 0521473187

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This book provides a comprehensive presentation of geometric results, primarily from the theory of convex sets, that have been proved by the use of Fourier series or spherical harmonics. An important feature of the book is that all necessary tools from the classical theory of spherical harmonics are presented with full proofs. These tools are used to prove geometric inequalities, stability results, uniqueness results for projections and intersections by hyperplanes or half-spaces and characterisations of rotors in convex polytopes. Again, full proofs are given. To make the treatment as self-contained as possible the book begins with background material in analysis and the geometry of convex sets. This treatise will be welcomed both as an introduction to the subject and as a reference book for pure and applied mathematics.


Mathematical Modeling in Biomedical Imaging I

Mathematical Modeling in Biomedical Imaging I

Author: Habib Ammari

Publisher: Springer Science & Business Media

Published: 2009-10-21

Total Pages: 244

ISBN-13: 3642034438

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This volume gives an introduction to a fascinating research area to applied mathematicians. It is devoted to providing the exposition of promising analytical and numerical techniques for solving challenging biomedical imaging problems, which trigger the investigation of interesting issues in various branches of mathematics.


Theory of the Earth's Shape

Theory of the Earth's Shape

Author: V.C. Dragomir

Publisher: Elsevier

Published: 2017-01-31

Total Pages: 705

ISBN-13: 1483291898

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Theory of the Earth's Shape considers the physical-mathematical problems raised by the determination of the form of the planet, thereby making a significant contribution to the technological scientific literature in this field. This book is organized into six parts encompassing 29 chapters. The first part, entitled Physical Geodesy, presents the theory of the determination of the gravitational field, in the definition of which preference was given to the method of expansion in spherical harmonics recommended by the International Union of Geodesy and Geophysics in establishing the international "Geodetic Reference System 1967". Part II deals with the principal aspects of Ellipsoidal Geodesy, such as the methods of solving the geodetic problems on the reference ellipsoid. Part III considers the main problems associated with Astro-geodetic Triangulation, particularly with the conception of materialization and the necessary measurements as the required adjustment procedures. This part also provides approaches regarding the controlled analysis of angular measurements and the description of some original calculation and measurement methods. Part IV concerns one of the methods of determining the spatial coordinates of the geodetic points in a unitary system, such as the three-dimensional geodesy, which has had more concrete applications since the launching of the Earth's first artificial satellites. Part V describes the methods for determining the terrestrial ellipsoid and the geoid, as well as the conventional methods and the methods of Dynamical Geodesy. Part VI discusses the geodetic methods for the determination of the movements of the Earth's crust, along with an overall examination of the theoretical and practical aspects which in principle constitute the object of such activities.