This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

This short primer, geared towards students with a strong interest in mathematically rigorous approaches, introduces the essentials of classical physics, briefly points out its place in the history of physics and its relation to modern physics, and explains what benefits can be gained from a mathematical perspective. As a starting point, Newtonian mechanics is introduced and its limitations are discussed. This leads to and motivates the study of different formulations of classical mechanics, such as Lagrangian and Hamiltonian mechanics, which are the subjects of later chapters. In the second part, a chapter on classical field theories introduces more advanced material. Numerous exercises are collected in the appendix.

Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.

This book is intended to provide an adequate background for various theortical physics courses, especially those in classical mechanics, electrodynamics, quatum mechanics and statistical physics. Each topic is dealt with in a generally self-contained manner and the text is interspersed with a number of solved examples ad a large number of exercise problems.

This classic book helps students learn the basics in physics by bridging the gap between mathematics and the basic fundamental laws of physics. With supplemental material such as graphs and equations, Mathematical Methods for Physics creates a strong, solid anchor of learning. The text has three parts: Part I focuses on the use of special functions in solving the homogeneous partial differential equations of physics, and emphasizes applications to topics such as electrostatics, wave guides, and resonant cavities, vibrations of membranes, heat flow, potential flow in fluids, plane and spherical waves. Part II deals with the solution of inhomogeneous differential equations with particular emphasis on problems in electromagnetism, Green's functions for Poisson's equation, the wave equation and the diffusion equation, and the solution of integral equations by iteration, eigenfunction expansion and the Fredholm series. Finally, Part II explores complex variable techniques, including evalution of itegrals, dispersion relations, special functions in the complex plane, one-sided Fourier transforms, and Laplace transforms.

As a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arnold-Moser) theory and asymptotic completeness in classical scattering. Including a wealth of fascinating examples in physics, it offers not only an excellent selection of basic topics, but also an introduction to a number of current areas of research in the field of classical mechanics. Thanks to the didactic structure and concise appendices, the presentation is self-contained and requires only knowledge of the basic courses in mathematics. The book addresses the needs of graduate and senior undergraduate students in mathematics and physics, and of researchers interested in approaching classical mechanics from a modern point of view.

From classical mechanics and classical electrodynamics to modern quantum mechanics many physical phenomena are formulated in terms of similar partial differential equations while boundary conditions determine the specifics of the problem. This 45th anniversary edition of the advanced book classic Mathematical Methods for Physics demonstrates how many physics problems resolve into similar inhomogeneous partial differential equations and the mathematical techniques for solving them. The text has three parts: Part I establishes solving the homogenous Laplace and Helmholtz equations in the three main coordinate systems, rectilinear, cylindrical, and spherical and develops the solution space for series solutions to the Sturm-Liouville equation, indicial relations, and the expansion of orthogonal functions including spherical harmonics and Fourier series, Bessel, and Spherical Bessel functions. Many examples with figures are provided including electrostatics, wave guides and resonant cavities, vibrations of membranes, heat flow, potential flow in fluids, and plane and spherical waves. In Part II the inhomogeneous equations are addressed where source terms are included for Poisson's equation, the wave equation, and the diffusion equation. Coverage includes many examples from averaging approaches for electrostatics and magnetostatics, from Green function solutions for time independent and time dependent problems, and from integral equation methods. In Part III complex variable techniques are presented for solving integral equations involving Cauchy Residue theory, contour methods, analytic continuation, and transforming the contour; for addressing dispersion relations; for revisiting special functions in the complex plane; and for transforms in the complex plane including Green’s functions and Laplace transforms. Key Features: · Mathematical Methods for Physics creates a strong, solid anchor of learning and is useful for reference. · Lecture note style suitable for advanced undergraduate and graduate students to learn many techniques for solving partial differential equations with boundary conditions · Many examples across various subjects of physics in classical mechanics, classical electrodynamics, and quantum mechanics · Updated typesetting and layout for improved clarity This book, in lecture note style with updated layout and typesetting, is suitable for advanced undergraduate, graduate students, and as a reference for researchers. It has been edited and carefully updated by Gary Powell.