Books — Mathematical Physics

Mathematical Physics

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Author: Biman Das

A supplementary text for introductory courses in Calculus-Based Physics.

Designed for students who plan to take or who are presently taking calculus-based physics courses. This book will develop necessary mathematical skills and help students gain the competence to use precalculus, calculus, vector algebra, vector calculus, and the statistical analysis of experimental data. Students taking intermediate physics, engineering, and other science courses will also find the book useful–and will be able to use the book as a mathematical resource for these intermediate level courses. The book emphasizes primarily the use of mathematical techniques and mathematical concepts in Physics and does not go into their rigorous developments.

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Quantum Gravity (Cambridge Monographs on Mathematical Physics)

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Author: Carlo Rovelli

Quantum gravity poses the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time.

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Sync: The Emerging Science of Spontaneous Order

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Author: Steven H. Strogatz

t the heart of the universe is a steady, insistent beat, the sound of cycles in sync. Along the tidal rivers of Malaysia, thousands of fireflies congregate and flash in unison; the moon spins in perfect resonance with its orbit around the earth; our hearts depend on the synchronous firing of ten thousand pacemaker cells. While the forces that synchronize the flashing of fireflies may seem to have nothing to do with our heart cells, there is in fact a deep connection. Synchrony is a science in its infancy, and Strogatz is a pioneer in this new frontier in which mathematicians and physicists attempt to pinpoint just how spontaneous order emerges from chaos. From underground caves in Texas where a French scientist spent six months alone tracking his sleep-wake cycle, to the home of a Dutch physicist who in 1665 discovered two of his pendulum clocks swinging in perfect time, this fascinating book spans disciplines, continents, and centuries. Engagingly written for readers of books such as Chaos and The Elegant Universe, Sync is a tour-de-force of nonfiction writing.

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Sphere Packing, Lewis Carroll and Reversi (New Martin Gardner Mathematical Library)

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Author: Martin Gardner

Packing spheres, Reversi, braids, polyominoes, board games, and the puzzles of Lewis Carroll. These and other mathematical diversions return to readers with updates to all the chapters, including new game variations, proofs, and other developments and discoveries. Read about Knuth's Word Ladders program and the latest developments in the digits of pi. Once again these timeless puzzles will charm readers while demonstrating principles of logic, probability, geometry, and other fields of mathematics. It's the perfect stocking stuffer for the puzzle wizard on your list.

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Time Traveler: A Scientist's Personal Mission to Make Time Travel a Reality

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Author: Dr. Ronald L. Mallett

This is the dramatic and inspirational first-person story of theoretical physicist, Dr. Ronald Mallett, who recently discovered the basic equations for a working time machine that he believes can be used as a transport vehicle to the past.

Combining elements of Rocket Boys and Elegant Universe, Time Traveler follows Mallett's discovery of Einstein's work on space-time, his study of Godel's work on a solution of Einstein's equation that might allow for time travel, and his own research in theoretical physics spanning thirty years that culminated in his recent discovery of the effects of circulating laser light and its application to time travel.

The foundation for Mallett's historic time-travel work is Einstein's theory of general relativity, a sound platform for any physicist. Through his years of reading and studying Einstein, Mallett became a buff well before he had any notion of the importance of the grand old relativist's theories to his own career. One interesting subtext to the story is Mallett's identification with, and keen interest in, Einstein. Mallett provides easy-to-understand explanations of the famous physicist's seminal work.

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Fourier Series (Mathematical Association of America Textbooks)

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Author: Rajendra Bhatia

This is a concise introduction to Fourier series covering history, major themes, theorems, examples, and applications. It can be used for self study, or to supplement undergraduate courses on mathematical analysis. Beginning with a brief summary of the rich history of the subject over three centuries, the reader will appreciate how a mathematical theory develops in stages from a practical problem (such as conduction of heat) to an abstract theory dealing with concepts such as sets, functions, infinity, and convergence. The abstract theory then provides unforeseen applications in diverse areas. Exercises of varying difficulty are included throughout to test understanding. A broad range of applications are also covered, and directions for further reading and research are provided, along with a chapter that provides material at a more advanced level suitable for graduate students.

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A Student's Guide to Fourier Transforms: With Applications in Physics and Engineering

Generalized Coherent States and Their Applications (Texts and Monographs in Physics)

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Author: A. Perelomov

Fundamentals of the Finite Element Method

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Author: Hartley, Jr. Grandin

The basic concepts of the finite element method are presented in a clear and logical manner. The first chapter offers a brief discussion of matrix analysis of structures and is designed to establish a working knowledge of the matrix operations common to finite element solution procedures. The finite element method is then introduced as a discretized application of the Rayleigh-Ritz method using the energy functional of the uniaxial elasticity problem. The method's applicability to other physical problems is set forth with an introduction to variational calculus and the derivation of the functionals corresponding to the differential equations of these problems. Finally, the Galerkin weighted residual method is developed as an alternative technique.

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The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (Dover Civil and Mechanical Engineering)

From Pythagoras to Einstein

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Author: K. O. Friedrichs

The main thread running through this somewhat unorthodox approach to the special theory of relativity is the Pythagorean theorem. It appears in its most elementary geometric form in the very beginning of this monograph. Then it reappears in algebraic garb, is further modified and finally reinterpreted to play the role of one of the main characters in the special theory of relativity.

The first four chapters are easily accessible to high school sophmores or juniors. the remaining part of the book may be a little difficult for students who never studied physics, although the author actually employs only the notion of impact and presupposes no background in physics. With the aid of the vector geometry introduced earlier, he leads the reader from the impact conversation laws to the famous formula e=mc2.

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Data Reduction and Error Analysis for the Physical Sciences

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Author: Philip R. Bevington

The purpose of this book is to provide an introduction to the concepts of statistical analysis of data for students at the undergraduate and graduate level, and to provide tools for data reduction and error analysis commonly required in the physical sciences. The presentation is developed from a practical point of view, including enough derivation to justify the results, but emphasizing methods of handling data more than theory. This text provides a variety of numerical and graphical techniques. Computer programs that support these techniques will be available on an accompanying website in both Fortran and C++.

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