Essential mathematics for the physical sciences.

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"Version: 20171001"--Title page verso."A Morgan & Claypool publication as part of IOP Concise Physics"--Title page verso.Includes bibliographical references.1. Partial differential equations -- 2. Separation of variables -- 2.1. Helmholtz equation -- 2.2. Helmholtz equation in rectangular coordinates -- 2.3. Helmholtz equation in cylindrical coordinates -- 2.4. Helmholtz equation in spherical coordinates -- 2.5. Roadmap : where we are headed3. Power-series solutions of ODEs -- 3.1. Analytic functions and the Frobenius method -- 3.2. Ordinary points -- 3.3. Regular singular points -- 3.4. Wronskian method for obtaining a second solution -- 3.5. Bessel and Neumann functions -- 3.6. Legendre polynomials4. Sturm-Liouville theory -- 4.1. Differential equations as operators -- 4.2. Sturm-Liouville systems -- 4.3. The SL eigenvalue problem, L[y] = -[lambda]wy -- 4.4. Dirac delta function -- 4.5. Completeness -- 4.6. Hilbert space : a brief introduction5. Fourier series and integrals -- 5.1. Fourier series -- 5.2. Complex form of Fourier series -- 5.3. General intervals -- 5.4. Parseval's theorem -- 5.5. Back to the delta function -- 5.6. Fourier transform -- 5.7. Convolution integral6. Spherical harmonics and friends -- 6.1. Properties of the Legendre polynomials, Pl(x) -- 6.2. Associated Legendre functions, Pl m(x) -- 6.3. Spherical harmonic functions, Yl m([theta], [phi]) -- 6.4. Addition theorem for Yl m([theta], [phi]) -- 6.5. Laplace equation in spherical coordinates7. Bessel functions and friends -- 7.1. Small-argument and asymptotic forms -- 7.2. Properties of the Bessel functions, Jn(x) -- 7.3. Orthogonality -- 7.4. Bessel series -- 7.5. Fourier-Bessel transform -- 7.6. Spherical Bessel functions -- 7.7. Expansion of plane waves in spherical coordinatesAppendices -- A. Topics in linear algebra -- B. Vector calculus -- C. Power series -- D. Gamma function, [Gamma](x).Physics is expressed in the language of mathematics; it is deeply ingrained in how physics is taught and how it's practiced. A study of the mathematics used in science is thus a sound intellectual investment for training as scientists and engineers. This first volume of two is centered on methods of solving partial differential equations and the special functions introduced. This text is based on a course offered at the Naval Postgraduate School (NPS) and while produced for NPS needs, it will serve other universities well.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.Brett Borden in a Professor of Physics at the Naval Postgraduate School in Monterey, California. Dr. Borden joined the faculty of NPS in 2002, after 22 years as a Research Physicist at The Naval Weapons Center. His research has centered on inverse problems with particular concentration in radar-based imaging and remote sensing. He is a fellow of the Institute of Physics, a member of the editorial board for the journal Inverse Problems, and received China Lake's TD award for Technical Achievement in 1995. James Luscombe is a Professor of Physics at the Naval Postgraduate School in Monterey, California. Dr. Luscombe joined the faculty of NPS in 1994. He is active in theoretical condensed matter physics research, with more than 60 journal articles published and more than 100 conference presentations made. His current research interests are in the electronic and magnetic properties of nano-scale systems, quantum computing, and statistical physics for networked computers.Title from PDF title page (viewed on November 18, 2017).

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: .,

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1 online resource (various pagings) :illustrations (some color).

Language

English

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9781681744858

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530.15

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SCIENCE / Physics / Mathematical & Computational.
Mathematical physics.

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Brett Borden, James Luscombe.

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