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This book—unique in the literature—provides readers with the mathematical background needed to design many of the optical combinations that are used in astronomical telescopes and cameras. The results presented in the work were obtained by using a different approach to third-order aberration theory as well as the extensive use of the software package Mathematica®. The newly presented approach to third-order aberration theory adopted is based on Fermat’s principle and the use of particular optical paths—not rays—termed stigmatic paths, allowing for easy derivation of third-order formulae. This approach enables readers to understand and handle the formulae required to design optical combinations without resorting to the much more complex Hamiltonian formalism and Seidel's relations. Additional features and topics: * Presentation of the third-order design of cameras and telescopes with the aid of Mathematica eliminates the need for tedious computer calculations * Mathematica notebooks accompanying each optical combination analyzed in the book are available for download at http://extra.springer.com/978-0-8176-4871-8 * Discussion and analysis of specific optical devices: Newtonian and Cassegrain telescopes; Schmidt, Wright, Houghton, and Maksutov cameras; and other optical combinations, such as the Klevtsov telescope and the Baker–Schmidt flat-field camera * Additional supplementary material available at the publisher's website * Many worked-out examples and exercises Geometric Optics is an excellent reference for advanced graduate students, researchers, and practitioners in applied mathematics, engineering, astronomy, and astronomical optics. The work may be used as a supplementary textbook for graduate-level courses in astronomical optics, optical design, optical engineering, programming with Mathematica, or geometric optics.

Astronomical instruments -- Design and construction. --- Geometrical optics -- Mathematics. --- Mathematica (Computer program language). --- Optical instruments -- Design and construction. --- Geometrical optics --- Astronomical instruments --- Optical instruments --- Mathematica (Computer program language) --- Physics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Light & Optics --- Applied Mathematics --- Mathematics --- Design and construction --- Mathematics. --- Design and construction. --- Astronomy --- Instruments, Astronomical --- Optics, Geometrical --- Instruments --- Physics. --- Mathematical models. --- Geometry. --- Astronomy. --- Astrophysics. --- Cosmology. --- Microwaves. --- Optical engineering. --- Optics, Lasers, Photonics, Optical Devices. --- Astronomy, Astrophysics and Cosmology. --- Physics, general. --- Mathematical Modeling and Industrial Mathematics. --- Microwaves, RF and Optical Engineering. --- Optical engineering --- Domain-specific programming languages --- Physical instruments --- Scientific apparatus and instruments --- Space optics --- Optics --- Euclid's Elements --- Hertzian waves --- Electric waves --- Electromagnetic waves --- Geomagnetic micropulsations --- Radio waves --- Shortwave radio --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Lasers. --- Photonics. --- Mechanical engineering --- Models, Mathematical --- Simulation methods --- Astronomical physics --- Cosmic physics --- New optics --- Light amplification by stimulated emission of radiation --- Masers, Optical --- Optical masers --- Light amplifiers --- Light sources --- Optoelectronic devices --- Nonlinear optics --- Optical parametric oscillators

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This book—unique in the literature—provides readers with the mathematical background needed to design many of the optical combinations that are used in astronomical telescopes and cameras. The results presented in the work were obtained by using a different approach to third-order aberration theory as well as the extensive use of the software package Mathematica®. The newly presented approach to third-order aberration theory adopted is based on Fermat’s principle and the use of particular optical paths—not rays—termed stigmatic paths, allowing for easy derivation of third-order formulae. This approach enables readers to understand and handle the formulae required to design optical combinations without resorting to the much more complex Hamiltonian formalism and Seidel's relations. Additional features and topics: * Presentation of the third-order design of cameras and telescopes with the aid of Mathematica eliminates the need for tedious computer calculations * Mathematica notebooks accompanying each optical combination analyzed in the book are available for download at http://extra.springer.com/978-0-8176-4871-8 * Discussion and analysis of specific optical devices: Newtonian and Cassegrain telescopes; Schmidt, Wright, Houghton, and Maksutov cameras; and other optical combinations, such as the Klevtsov telescope and the Baker–Schmidt flat-field camera * Additional supplementary material available at the publisher's website * Many worked-out examples and exercises Geometric Optics is an excellent reference for advanced graduate students, researchers, and practitioners in applied mathematics, engineering, astronomy, and astronomical optics. The work may be used as a supplementary textbook for graduate-level courses in astronomical optics, optical design, optical engineering, programming with Mathematica, or geometric optics.

Geometry --- Mathematics --- Space research --- Cosmology --- Astrophysics --- Fluid mechanics --- Optics. Quantum optics --- Physics --- Spectrometric and optical chemical analysis --- Electronics --- Planning (firm) --- astrofysica --- photonics --- lasers (technologie) --- mathematische modellen --- telecommunicatie --- wiskunde --- fysica --- ruimte (astronomie) --- kosmologie --- geometrie --- spectrometrie --- optica

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This text, now in its second edition, presents the mathematical background needed to design many optical combinations that are used in astronomical telescopes and cameras. It uses a novel approach to third-order aberration theory based on Fermat’s principle and the use of particular optical paths (called stigmatic paths) instead of rays, allowing for easier derivation of third-order formulae. Each optical combination analyzed is accompanied by a downloadable Mathematica® notebook that automates its third-order design, eliminating the need for lengthy calculations. The essential aspects of an optical system with an axis of rotational symmetry are introduced first, along with a development of Gaussian optics from Fermat’s principal. A simpler approach to third-order monochromatic aberrations based on both Fermat’s principle and stigmatic paths is then described, followed by a new chapter on fifth-order aberrations and their classification. Several specific optical devices are discussed and analyzed, including the Newtonian and Cassegrain telescopes; the Schmidt, Wright, Houghton, and Maksutov cameras; the Klevtsov telescope; the Baker-Schmidt flat-field camera; the Buchroeder camera; and, new in this edition, the Baker-Nunn camera and optical combinations with sub-corrector and Petzval objectives. Finally, the Lagrangian and Hamiltonian formulations of geometric optics and Seidel’s third-order aberration theory are presented, and a new chapter considers optics in anisotropic media. Numerous diagrams, worked-out examples, and exercises for further practice of key concepts are included throughout the book. Geometric Optics is an excellent reference for advanced graduate students, researchers, and practitioners in applied mathematics, engineering, astronomy, and astronomical optics. It can also be used as a supplementary textbook for graduate-level courses in astronomical optics, optical design, optical engineering, programming with Mathematica®, or geometric optics.

Mathematics. --- Mathematical physics. --- Mathematical models. --- Microwaves. --- Optical engineering. --- Mathematical Modeling and Industrial Mathematics. --- Optics, Lasers, Photonics, Optical Devices. --- Microwaves, RF and Optical Engineering. --- Mathematical Applications in the Physical Sciences. --- Geometrical optics --- Optics, Geometrical --- Optics --- Hertzian waves --- Electric waves --- Electromagnetic waves --- Geomagnetic micropulsations --- Radio waves --- Shortwave radio --- Lasers. --- Photonics. --- Physical mathematics --- Physics --- Mechanical engineering --- New optics --- Light amplification by stimulated emission of radiation --- Masers, Optical --- Optical masers --- Light amplifiers --- Light sources --- Optoelectronic devices --- Nonlinear optics --- Optical parametric oscillators --- Models, Mathematical --- Simulation methods --- Mathematics

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Christian hagiography --- History --- Lupus --- Hagiographie chrétienne --- Christian hagiography - Early works to 1800 --- Christian hagiography - History - To 1500 --- Maximinus ep. Treverensis --- Wigbertus ab. Friteslariensis --- Hagiographie medievale --- Lupus de ferrieres

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This textbook's methodological approach familiarizes readers with the mathematical tools required to correctly define and solve problems in continuum mechanics. Covering essential principles and fundamental applications, this second edition of Continuum Mechanics using Mathematica® provides a solid basis for a deeper study of more challenging and specialized problems related to nonlinear elasticity, polar continua, mixtures, piezoelectricity, ferroelectricity, magneto-fluid mechanics, and state changes (see A. Romano, A. Marasco, Continuum Mechanics: Advanced Topics and Research Trends, Springer (Birkhäuser), 2010, ISBN 978-0-8176-4869-5). Key topics and features: * Concise presentation strikes a balance between fundamentals and applications * Requisite mathematical background carefully collected in two introductory chapters and one appendix * Recent developments highlighted through coverage of more significant applications to areas such as wave propagation, fluid mechanics, porous media, linear elasticity. This second edition expands the key topics and features to include: * Two new applications of fluid dynamics: meteorology and navigation * New exercises at the end of the existing chapters * The packages are rewritten for Mathematica 9 Continuum Mechanics using Mathematica®: Fundamentals, Methods, and Applications is aimed at advanced undergraduates, graduate students, and researchers in applied mathematics, mathematical physics, and engineering. It may serve as a course textbook or self-study reference for anyone seeking a solid foundation in continuum mechanics.

Physics. --- Applied mathematics. --- Engineering mathematics. --- Mathematical models. --- Mechanics. --- Mechanics, Applied. --- Continuum mechanics. --- Continuum Mechanics and Mechanics of Materials. --- Theoretical and Applied Mechanics. --- Applications of Mathematics. --- Theoretical, Mathematical and Computational Physics. --- Mathematical Modeling and Industrial Mathematics. --- Mechanics, applied. --- Mathematics. --- Classical Mechanics. --- Solid Mechanics. --- Math --- Science --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Continuum mechanics --- Data processing. --- Mathematica (Computer file) --- Mathematical physics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Models, Mathematical --- Simulation methods --- Physical mathematics --- Mathematics