Music is, in one sense, merely a series of fleeting vibrations that arise and subside. How could it be that something so insubstantial fills us, and calms us, and makes us weep? Because, says W. A. Mathieu, music bridges mind and heart, self and other, and affirms our place in the world. Everyone uses the bridge of music, from casual listeners to devoted professionals. Mathieu's delightful and trenchant prose asks you to question what music is, how it works, and how to understand its value in your life, in the life of your community, and in the evolution of the cosmos.
This book is based on an undergraduate course taught at the IAS/Park City Mathematics Institute (Utah) on linear and nonlinear waves. The first part of the text overviews the concept of a wave, describes one-dimensional waves using functions of two variables, provides an introduction to partial differential equations, and discusses computer-aided visualization techniques. The second part of the book discusses traveling waves, leading to a description of solitary waves and soliton solutions of the Klein-Gordon and Korteweg-deVries equations. The wave equation is derived to model the small vibrations of a taut string, and solutions are constructed via d'Alembert's formula and Fourier series.The last part of the book discusses waves arising from conservation laws. After deriving and discussing the scalar conservation law, its solution is described using the method of characteristics, leading to the formation of shock and rarefaction waves. Applications of these concepts are then given for models of traffic flow. The intent of this book is to create a text suitable for independent study by undergraduate students in mathematics, engineering, and science. The content of the book is meant to be self-contained, requiring no special reference material. Access to computer software such as MathematicaR, MATLABR, or MapleR is recommended, but not necessary. Scripts for MATLAB applications will be available via the Web. Exercises are given within the text to allow further practice with selected topics.
It's the summer of 1994. O.J. Simpson is chased in his white Bronco, the Beastie Boys have just released Ill Communication, and the Major League Baseball strike is looming. For 19-year-old Colin Brennan living in Silver Shores Cape Cod, Summertime should be one of the best times of his young life. But the beautiful scenery is instead a constant reminder of what happened the previous year. Colin is haunted by the memory of a tragic accident that took the lives of his two best friends, in a story of unresolved grief, substance abuse, break-ups, baseball, brotherly love, and the thorny road to redemption.
The Bestselling Classic Updated for Surfers, Sailors, Oceanographers, Climate Activists, and Those Who Love the Sea First published in 1963 and updated in 1979, this classic was an essential handbook for anyone who studies, surfs, protects, or is fascinated by the ocean. The original author, Willard Bascom, was a master of the subject and included a wealth of information, based on theory and statistics, but also anecdotal observation and personal experience. It brought to the general public understanding of the awesome and complex power of the waves. This revision from Kim McCoy adds recent facts and anecdotes to update the book's relevance in the time of climate change. One of the most significant effects of global warming will be sea-level rise. What will this mean to waves and beaches, and what effects are we already seeing? New text and photos cover events such as the Indian Ocean tsunami of 2004, Hurricane Katrina flooding of 2005, and the 2011 earthquake and resulting devastation in Fukishima. As well as students, surfers, and the general public, this updated edition of a beloved classic is an essential handbook for climate scientists and ocean activists, providing clear explanations and detailed resources for the constant battle to preserve the shore.
Matter: Physical Science for Kids from the Picture Book Science series gets kids excited about science! What’s the matter? Everything is matter! Everything you can touch and hold is made up of matter—including you, your dog, and this book! Matter is stuff that you can weigh and that takes up space, which means pretty much everything in the world is made of matter. In Matter: Physical Science for Kids, kids ages 5 to 8 explore the definition of matter and the different states of matter, plus the stuff in our world that isn’t matter, such as sound and light! In this nonfiction picture book, children are introduced to physical science through detailed illustrations paired with a compelling narrative that uses fun language to convey familiar examples of real-world science connections. By recognizing the basic physics concept of matter and identifying the different ways matter appears in real life, kids develop a fundamental understanding of physical science and are impressed with the idea that science is a constant part of our lives and not limited to classrooms and laboratories. Simple vocabulary, detailed illustrations, easy science experiments, and a glossary all support exciting learning for kids ages 5 to 8. Perfect for beginner readers or as a read aloud nonfiction picture book! Part of a set of four books in a series called Picture Book Science that tackles different kinds of physical science (waves, forces, energy, and matter), Matter offers beautiful pictures and simple observations and explanations. Quick STEM activities such as weighing two balloons to test if air is matter help readers cross the bridge from conceptual to experiential learning and provide a foundation of knowledge that will prove invaluable as kids progress in their science education. Perfect for children who love to ask, “Why?” about the world around them, Matter satisfies curiosity while encouraging continual student-led learning.
An exploration of musical harmony from its ancient fundamentals to its most complex modern progressions, addressing how and why it resonates emotionally and spiritually in the individual. W. A. Mathieu, an accomplished author and recording artist, presents a way of learning music that reconnects modern-day musicians with the source from which music was originally generated. As the author states, "The rules of music--including counterpoint and harmony--were not formed in our brains but in the resonance chambers of our bodies." His theory of music reconciles the ancient harmonic system of just intonation with the modern system of twelve-tone temperament. Saying that the way we think music is far from the way we do music, Mathieu explains why certain combinations of sounds are experienced by the listener as harmonious. His prose often resembles the rhythms and cadences of music itself, and his many musical examples allow readers to discover their own musical responses.
“Why do you always write magic in the sand of every beach you go to?” he asked as he watched her finger move through the sand in a rhythm writing the word. She smiled and said, “Because there is magic in the sand.” “What do you mean?” he further asked. “When you feel the sand under your feet,” she scrunched up her toes in the sand as she spoke. “And feel every granule of it, the noise of your thoughts suddenly sound like the waves. Just like magic.” Me
This is the second edition of the textbook that was first published by Elsevier Science. Professor Slawinski has the copyright to the textbook and the second edition is significantly extended. The present book emphasizes the interdependence of mathematical formulation and physical meaning in the description of seismic phenomena. Herein, we use aspects of continuum mechanics, wave theory and ray theory to explain phenomena resulting from the propagation of seismic waves. The book is divided into three main sections: elastic continua, waves and rays and variational formulation of rays. There is also a fourth part, which consists of appendices. In Part 1, we use continuum mechanics to describe the material through which seismic waves propagate, and to formulate a system of equations to study the behaviour of such a material. In Part 2, we use these equations to identify the types of body waves propagating in elastic continua as well as to express their velocities and displacements in terms of the properties of these continua. To solve the equations of motion in anisotropic inhomogeneous continua, we use the high-frequency approximation and, hence, establish the concept of a ray. In Part 3, we show that, in elastic continua, a ray is tantamount to a trajectory along which a seismic signal propagates in accordance with the variational principle of stationary traveltime. Consequently, many seismic problems in elastic continua can be conveniently formulated and solved using the calculus of variations. In Part 4, we describe two mathematical concepts that are used in the book; namely, homogeneity of a function and Legendre's transformation. This section also contains a list of symbols.
Since Einstein first described them nearly a century ago, gravitational waves have been the subject of more sustained controversy than perhaps any other phenomenon in physics. These as yet undetected fluctuations in the shape of space-time were first predicted by Einstein's general theory of relativity, but only now, at the dawn of the twenty-first century, are we on the brink of finally observing them. Daniel Kennefick's landmark book takes readers through the theoretical controversies and thorny debates that raged around the subject of gravitational waves after the publication of Einstein's theory. The previously untold story of how we arrived at a settled theory of gravitational waves includes a stellar cast from the front ranks of twentieth-century physics, including Richard Feynman, Hermann Bondi, John Wheeler, Kip Thorne, and Einstein himself, who on two occasions avowed that gravitational waves do not exist, changing his mind both times. The book derives its title from a famously skeptical comment made by Arthur Stanley Eddington in 1922--namely, that "gravitational waves propagate at the speed of thought." Kennefick uses the title metaphorically to contrast the individual brilliance of each of the physicists grappling with gravitational-wave theory against the frustratingly slow progression of the field as a whole. Accessibly written and impeccably researched, this book sheds new light on the trials and conflicts that have led to the extraordinary position in which we find ourselves today--poised to bring the story of gravitational waves full circle by directly confirming their existence for the very first time.
