| Description |
1 online resource (790 pages) |
| Contents |
Intro -- Preface -- Contents -- About the Author -- 1 Warming Up: Functions of a Real Variable -- 1.1 Sketching Functions -- 1.1.1 Features of Interest in a Function -- 1.1.2 Powers of x -- 1.1.3 A Family of Ovals -- 1.1.4 A Family of Spirals -- 1.2 Maps of the Unit Interval -- 2 Gaussian Integrals, Stirling's Formula, and Some Integrals -- 2.1 Gaussian Integrals -- 2.1.1 The Basic Gaussian Integral -- 2.1.2 A Couple of Higher Dimensional Examples -- 2.2 Stirling's Formula -- 2.3 The Dirichlet Integral and Its Descendants -- 2.4 Solutions -- 3 Some More Functions |
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5.3 Invariant Decomposition of a 2nd Rank Tensor -- 5.3.1 Spherical or Irreducible Tensors -- 5.3.2 Stress, Strain, and Stiffness Tensors -- 5.3.3 Moment of Inertia -- 5.3.4 The Euler Top -- 5.3.5 Multipole Expansion -- Quadrupole Moment -- 5.3.6 The Octupole Moment -- 5.4 Solutions -- 6 Vector Calculus -- 6.1 Orthogonal Curvilinear Coordinates -- 6.1.1 Cylindrical and Spherical Polar Coordinates -- 6.1.2 Elliptic and Parabolic Coordinates -- 6.1.3 Polar Coordinates in d Dimensions -- 6.2 Scalar and Vector Fields and Their Derivatives -- 6.2.1 The Gradient of a Scalar Field |
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6.2.2 The Flux and Divergence of a Vector Field -- 6.2.3 The Circulation and Curl of a Vector Field -- 6.2.4 Some Physical Aspects of the Curl of a Vector Field -- 6.2.5 Any Vector Field is the Sum of a Curl and a Gradient -- 6.2.6 The Laplacian Operator -- 6.2.7 Why Do div, curl, and del-Squared Occur so Frequently? -- 6.2.8 The Standard Identities of Vector Calculus -- 6.3 Solutions -- 7 A Bit of Fluid Dynamics -- 7.1 Equation of Motion of a Fluid Element -- 7.1.1 Hydrodynamic Variables -- 7.1.2 Equation of Motion -- 7.2 Flow When Viscosity Is Neglected -- 7.2.1 Euler's Equation |
| Summary |
This textbook is aimed at advanced undergraduate and graduate students interested in learning the fundamental mathematical concepts and tools widely used in different areas of physics. The author draws on a vast teaching experience, and presents a comprehensive and self-contained text which explains how mathematics intertwines with and forms an integral part of physics in numerous instances. Rather than emphasizing rigorous proofs of theorems, specific examples and physical applications (such as fluid dynamics, electromagnetism, quantum mechanics, etc.) are invoked to illustrate and elaborate upon the relevant mathematical techniques. The early chapters of the book introduce different types of functions, vectors and tensors, vector calculus, and matrices. In the subsequent chapters, more advanced topics like linear spaces, operator algebras, special functions, probability distributions, stochastic processes, analytic functions, Fourier series and integrals, Laplace transforms, Green's functions and integral equations are discussed. The book also features about 400 exercises and solved problems interspersed throughout the text at appropriate junctures, to facilitate the logical flow and to test the key concepts. Overall this book will be a valuable resource for a wide spectrum of students and instructors of mathematical physics |
| Bibliography |
Includes bibliographical references and index |
| Notes |
7.2.2 Barotropic Flow |
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Print version record |
| Subject |
Mathematical physics.
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Mathematical physics.
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Maths for engineers.
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Science -- Mathematical Physics.
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Technology & Engineering -- Engineering (General)
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Mathematical physics
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| Form |
Electronic book
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| ISBN |
9783030396800 |
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3030396800 |
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