**Auteur :** Jesper Lützen

**la langue :** en

**Éditeur:** Springer Science & Business Media

**Date de sortie :** 2012-12-06

**Auteur :** Ioan James

**la langue :** en

**Éditeur:** Cambridge University Press

**Date de sortie :** 2002

This 2003 book contains portrayals of sixty mathematicians, which collectively convey how mathematics developed into its modern form.

**Auteur :** Kenneth S. Williams

**la langue :** en

**Éditeur:** Cambridge University Press

**Date de sortie :** 2010-10-21

A gentle introduction to Liouville's powerful method in elementary number theory. Suitable for advanced undergraduate and beginning graduate students.

**Auteur :** Mariano Giaquinta

**la langue :** en

**Éditeur:** Springer Science & Business Media

**Date de sortie :** 2010-07-25

This superb and self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables. The wide range of topics covered include the differential calculus of several variables, including differential calculus of Banach spaces, the relevant results of Lebesgue integration theory, and systems and stability of ordinary differential equations. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis. This text motivates the study of the analysis of several variables with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.

**Auteur :** Paul Blaise

**la langue :** en

**Éditeur:** John Wiley & Sons

**Date de sortie :** 2011-08-24

An invaluable reference for an overall but simple approach to the complexity of quantum mechanics viewed through quantum oscillators Quantum oscillators play a fundamental role in many areas of physics; for instance, in chemical physics with molecular normal modes, in solid state physics with phonons, and in quantum theory of light with photons. Quantum Oscillators is a timely and visionary book which presents these intricate topics, broadly covering the properties of quantum oscillators which are usually dispersed in the literature at varying levels of detail and often combined with other physical topics. These properties are: time-independent behavior, reversible dynamics, thermal statistical equilibrium and irreversible evolution toward equilibrium, together with anharmonicity and anharmonic couplings. As an application of these intricate topics, special attention is devoted to infrared lineshapes of single and complex (undergoing Fermi resonance or Davydov coupling) damped H-bonded systems, providing key insights into this rapidly evolving area of chemical science. Quantum Oscillators is a long overdue update in the literature surrounding quantum oscillators, and serves as an excellent supplementary text in courses on IR spectroscopy and hydrogen bonding. It is a must-have addition to the library of any graduate or undergraduate student in chemical physics.

**Auteur :** Chjan Lim

**la langue :** en

**Éditeur:** Springer Science & Business Media

**Date de sortie :** 2007-07-28

This book is drawn from across many active fields of mathematics and physics. It has connections to atmospheric dynamics, spherical codes, graph theory, constrained optimization problems, Markov Chains, and Monte Carlo methods. It addresses how to access interesting, original, and publishable research in statistical modeling of large-scale flows and several related fields. The authors explicitly reach around the major branches of mathematics and physics, showing how the use of a few straightforward approaches can create a cornucopia of intriguing questions and the tools to answer them.

**Auteur :** William Dunham

**la langue :** en

**Éditeur:** Princeton University Press

**Date de sortie :** 2005

More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway into higher mathematics. This book charts its growth and development by sampling from the work of some of its foremost practitioners, beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri Lebesgue at the dawn of the twentieth--mathematicians whose achievements are comparable to those of Bach in music or Shakespeare in literature. William Dunham lucidly presents the definitions, theorems, and proofs. "Students of literature read Shakespeare; students of music listen to Bach," he writes. But this tradition of studying the major works of the "masters" is, if not wholly absent, certainly uncommon in mathematics. This book seeks to redress that situation. Like a great museum, The Calculus Gallery is filled with masterpieces, among which are Bernoulli's early attack upon the harmonic series (1689), Euler's brilliant approximation of pi (1779), Cauchy's classic proof of the fundamental theorem of calculus (1823), Weierstrass's mind-boggling counterexample (1872), and Baire's original "category theorem" (1899). Collectively, these selections document the evolution of calculus from a powerful but logically chaotic subject into one whose foundations are thorough, rigorous, and unflinching--a story of genius triumphing over some of the toughest, most subtle problems imaginable. Anyone who has studied and enjoyed calculus will discover in these pages the sheer excitement each mathematician must have felt when pushing into the unknown. In touring The Calculus Gallery, we can see how it all came to be.