Electricity and Magnetism for Mathematicians

Author: Thomas A. Garrity

Publisher: Cambridge University Press

ISBN: 1107078202

Category: Mathematics

Page: 304

View: 2731

Maxwell's equations have led to many important mathematical discoveries. This text introduces mathematics students to some of their wonders.

Exterior Analysis

Using Applications of Differential Forms

Author: Erdogan Suhubi

Publisher: Elsevier

ISBN: 0124159281

Category: Mathematics

Page: 779

View: 9022

Exterior analysis uses differential forms (a mathematical technique) to analyze curves, surfaces, and structures. Exterior Analysis is a first-of-its-kind resource that uses applications of differential forms, offering a mathematical approach to solve problems in defining a precise measurement to ensure structural integrity. The book provides methods to study different types of equations and offers detailed explanations of fundamental theories and techniques to obtain concrete solutions to determine symmetry. It is a useful tool for structural, mechanical and electrical engineers, as well as physicists and mathematicians. Provides a thorough explanation of how to apply differential equations to solve real-world engineering problems Helps researchers in mathematics, science, and engineering develop skills needed to implement mathematical techniques in their research Includes physical applications and methods used to solve practical problems to determine symmetry

Masters of Theory

Cambridge and the Rise of Mathematical Physics

Author: Andrew Warwick

Publisher: University of Chicago Press

ISBN: 9780226873749

Category: Science

Page: 572

View: 9685

Winner of the the Susan Elizabeth Abrams Prize in History of Science. When Isaac Newton published the Principia three centuries ago, only a few scholars were capable of understanding his conceptually demanding work. Yet this esoteric knowledge quickly became accessible in the nineteenth and early twentieth centuries when Britain produced many leading mathematical physicists. In this book, Andrew Warwick shows how the education of these "masters of theory" led them to transform our understanding of everything from the flight of a boomerang to the structure of the universe. Warwick focuses on Cambridge University, where many of the best physicists trained. He begins by tracing the dramatic changes in undergraduate education there since the eighteenth century, especially the gradual emergence of the private tutor as the most important teacher of mathematics. Next he explores the material culture of mathematics instruction, showing how the humble pen and paper so crucial to this study transformed everything from classroom teaching to final examinations. Balancing their intense intellectual work with strenuous physical exercise, the students themselves—known as the "Wranglers"—helped foster the competitive spirit that drove them in the classroom and informed the Victorian ideal of a manly student. Finally, by investigating several historical "cases," such as the reception of Albert Einstein's special and general theories of relativity, Warwick shows how the production, transmission, and reception of new knowledge was profoundly shaped by the skills taught to Cambridge undergraduates. Drawing on a wealth of new archival evidence and illustrations, Masters of Theory examines the origins of a cultural tradition within which the complex world of theoretical physics was made commonplace.

Modern Methods in Topological Vector Spaces

Author: Albert Wilansky

Publisher: Courier Corporation

ISBN: 0486493539

Category: Mathematics

Page: 298

View: 8242

"Designed for a one-year course in topological vector spaces, this text is geared toward beginning graduate students of mathematics. Topics include Banach space, open mapping and closed graph theorems, local convexity, duality, equicontinuity, operators,inductive limits, and compactness and barrelled spaces. Extensive tables cover theorems and counterexamples. Rich problem sections throughout the book. 1978 edition"--


Author: John C. Slater,Nathaniel H. Frank

Publisher: Courier Corporation

ISBN: 0486150402

Category: Science

Page: 256

View: 5114

A basic introduction to electromagnetism, supplying the fundamentals of electrostatics and magnetostatics, in addition to a thorough investigation of electromagnetic theory. Numerous problems and references. Calculus and differential equations required. 1947 edition.

Basic Training in Mathematics

A Fitness Program for Science Students

Author: R. Shankar

Publisher: Springer

ISBN: 1489967982

Category: Science

Page: 366

View: 5536

Based on course material used by the author at Yale University, this practical text addresses the widening gap found between the mathematics required for upper-level courses in the physical sciences and the knowledge of incoming students. This superb book offers students an excellent opportunity to strengthen their mathematical skills by solving various problems in differential calculus. By covering material in its simplest form, students can look forward to a smooth entry into any course in the physical sciences.

Classical Electricity and Magnetism

Second Edition

Author: Wolfgang K. H. Panofsky,Melba Phillips

Publisher: Courier Corporation

ISBN: 0486132250

Category: Science

Page: 512

View: 5584

Compact and precise coverage of the electrostatic field in vacuum; general methods for solution of potential problems; radiation reaction and covariant formulation of conservation laws of electrodynamics; much more. 1962 edition.

Einstein's Heroes

Imagining the World Through the Language of Mathematics

Author: Robyn Arianrhod

Publisher: Oxford University Press

ISBN: 9780195308907

Category: Biography & Autobiography

Page: 336

View: 9010

Blending science, history, and biography, this book reveals the mysteries of mathematics, focusing on the life and work of three of Albert Einstein's heroes: Isaac Newton, Michael Faraday, and James Clerk Maxwell.

Quantum Theory

A Mathematical Approach

Author: Peter Bongaarts

Publisher: Springer

ISBN: 3319095617

Category: Science

Page: 445

View: 7046

This book was inspired by the general observation that the great theories of modern physics are based on simple and transparent underlying mathematical structures – a fact not usually emphasized in standard physics textbooks – which makes it easy for mathematicians to understand their basic features. It is a textbook on quantum theory intended for advanced undergraduate or graduate students: mathematics students interested in modern physics, and physics students who are interested in the mathematical background of physics and are dissatisfied with the level of rigor in standard physics courses. More generally, it offers a valuable resource for all mathematicians interested in modern physics, and all physicists looking for a higher degree of mathematical precision with regard to the basic concepts in their field.

The Theory of Electromagnetism

Author: D. S. Jones

Publisher: Elsevier

ISBN: 1483279049

Category: Science

Page: 824

View: 2550

The Theory of the Electomagnetism covers the behavior of electromagnetic fields and those parts of applied mathematics necessary to discover this behavior. This book is composed of 11 chapters that emphasize the Maxwell's equations. The first chapter is concerned with the general properties of solutions of Maxwell's equations in matter, which has certain macroscopic properties. The succeeding chapters consider specific problems in electromagnetism, including the determination of the field produced by a variable charge, first in isolation and then in the surface distributions of an antenna. The next two chapters are concerned with the effects of surrounding the medium by a perfectly conducting boundary as in a cavity resonator and as in a waveguide. Other chapters are devoted to discussions on the effect of a plane interface where the properties of the medium change discontinuously; the propagation along cylindrical surfaces; the study of the waves scattered by objects both with and without edges. This book further reviews the harmonic waves and the difficulties involved in going from harmonic waves to those with a more general time dependence. The final chapter provides some information about the classical theory of electrons, magneto-hydrodynamics and waves in a plasma. This book will prove useful to physicists, and physics teachers and students.

In Pursuit of the Unknown

17 Equations That Changed the World

Author: Ian Stewart

Publisher: Basic Books

ISBN: 0465029744

Category: Mathematics

Page: 360

View: 9995

In In Pursuit of the Unknown, celebrated mathematician Ian Stewart uses a handful of mathematical equations to explore the vitally important connections between math and human progress. We often overlook the historical link between mathematics and technological advances, says Stewart—but this connection is integral to any complete understanding of human history. Equations are modeled on the patterns we find in the world around us, says Stewart, and it is through equations that we are able to make sense of, and in turn influence, our world. Stewart locates the origins of each equation he presents—from Pythagoras's Theorem to Newton's Law of Gravity to Einstein's Theory of Relativity—within a particular historical moment, elucidating the development of mathematical and philosophical thought necessary for each equation's discovery. None of these equations emerged in a vacuum, Stewart shows; each drew, in some way, on past equations and the thinking of the day. In turn, all of these equations paved the way for major developments in mathematics, science, philosophy, and technology. Without logarithms (invented in the early 17th century by John Napier and improved by Henry Briggs), scientists would not have been able to calculate the movement of the planets, and mathematicians would not have been able to develop fractal geometry. The Wave Equation is one of the most important equations in physics, and is crucial for engineers studying the vibrations in vehicles and the response of buildings to earthquakes. And the equation at the heart of Information Theory, devised by Claude Shannon, is the basis of digital communication today. An approachable and informative guide to the equations upon which nearly every aspect of scientific and mathematical understanding depends, In Pursuit of the Unknown is also a reminder that equations have profoundly influenced our thinking and continue to make possible many of the advances that we take for granted.

Algebraic Geometry

A Problem Solving Approach

Author: Thomas A. Garrity

Publisher: American Mathematical Soc.

ISBN: 0821893963

Category: Mathematics

Page: 335

View: 4627

Algebraic Geometry has been at the center of much of mathematics for hundreds of years. It is not an easy field to break into, despite its humble beginnings in the study of circles, ellipses, hyperbolas, and parabolas. This text consists of a series of ex

Calculus of Several Variables

Author: Serge Lang

Publisher: Springer Science & Business Media

ISBN: 1461210682

Category: Mathematics

Page: 619

View: 8387

This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green’s theorem, multiple integrals, surface integrals, Stokes’ theorem, and the inverse mapping theorem and its consequences. It includes many completely worked-out problems.

Second Year Calculus

From Celestial Mechanics to Special Relativity

Author: David M. Bressoud

Publisher: Springer Science & Business Media

ISBN: 1461209595

Category: Mathematics

Page: 404

View: 9678

Second Year Calculus: From Celestial Mechanics to Special Relativity covers multi-variable and vector calculus, emphasizing the historical physical problems which gave rise to the concepts of calculus. The book guides us from the birth of the mechanized view of the world in Isaac Newton's Mathematical Principles of Natural Philosophy in which mathematics becomes the ultimate tool for modelling physical reality, to the dawn of a radically new and often counter-intuitive age in Albert Einstein's Special Theory of Relativity in which it is the mathematical model which suggests new aspects of that reality. The development of this process is discussed from the modern viewpoint of differential forms. Using this concept, the student learns to compute orbits and rocket trajectories, model flows and force fields, and derive the laws of electricity and magnetism. These exercises and observations of mathematical symmetry enable the student to better understand the interaction of physics and mathematics.