Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing the mathematical model) and how to solve the equation (along with initial and boundary conditions). Written for advanced undergraduate and graduate students, as well as professionals working in the applied sciences, this clearly written book offers realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, and numerical and approximate methods. Each chapter contains a selection of relevant problems (answers are provided) and suggestions for further reading.

    The story of information begins in a time profoundly unlike our own, when every thought and utterance vanishes as soon as it is born. From the invention of scripts and alphabets to the long-misunderstood talking drums of Africa, Gleick tells the story of information technologies that changed the very nature of human consciousness. He provides portraits of the key figures contributing to the inexorable development of our modern understanding of information: Charles Babbage, the idiosyncratic inventor of the first great mechanical computer; Ada Byron, the brilliant and doomed daughter of the poet, who became the first true programmer; pivotal figures like Samuel Morse and Alan Turing; and Claude Shannon, the creator of information theory itself. And then the information age arrives. Citizens of this world become experts willy-nilly: aficionados of bits and bytes. And we sometimes feel we are drowning, swept by a deluge of signs and signals, news and images, blogs and tweets. The Information is the story of how we got here and where we are heading.

    In the four main sections of the book, Stein tells the stories of the mathematical thinkers who discerned some of the most fundamental aspects of our universe. From their successes and failures, delusions, and even duels, the trajectories of their innovations—and their impact on society—are traced in this fascinating narrative. Quantum mechanics, space-time, chaos theory and the workings of complex systems, and the impossibility of a "perfect" democracy are all here. Stein's book is both mind-bending and practical, as he explains the best way for a salesman to plan a trip, examines why any thought you could have is imbedded in the number π , and—perhaps most importantly—answers one of the modern world's toughest questions: why the garage can never get your car repaired on time.Friendly, entertaining, and fun, How Math Explains the World is the first book by one of California's most popular math teachers, a veteran of both "math for poets" and Princeton's Institute for Advanced Studies. And it's perfect for any reader wanting to know how math makes both science and the world tick.

    The brief volume of the first 37 chapters focuses on Western (or Classical) music, which includes the first 6 parts of LISTENING TO MUSIC, 5th Edition, and omits all end-of-chapter "Cultural Context" boxes.

    Learn You a Haskell for Great Good! introduces programmers familiar with imperative languages (such as C++, Java, or Python) to the unique aspects of functional programming. Packed with jokes, pop culture references, and the author's own hilarious artwork, Learn You a Haskell for Great Good! eases the learning curve of this complex language, and is a perfect starting point for any programmer looking to expand his or her horizons. The well-known web tutorial on which this book is based is widely regarded as the best way for beginners to learn Haskell, and receives over 30,000 unique visitors monthly.

    Even when dealing with standard material, Stillwell manages to dramatize it and to make it worth rethinking. In short, his book is a splendid addition to the genre of works that build royal roads to mathematical culture for the many." (Mathematical Intelligencer)This second edition includes new chapters on Chinese and Indian number theory, on hypercomplex numbers, and on algebraic number theory. Many more exercises have been added, as well as commentary to the exercises explaining how they relate to the preceding section, and how they foreshadow later topics.

     Learning is the key to bettering your circumstances and becoming the person you want to be. Skills, information, and abilities will never come to you - it’s up to you to seek them out, and this book shows you how to do so in the most effective and efficient manner. Applicable and actionable advice - not just theory and description. Work smarter, not harder. The Science of Rapid Skill Acquisition is the definitive resource to get you where you want to be in terms of a new talent, skill, or ability. You may not realize it, but each day is a set of skills and tasks that we repeat. Each hobby and interest is also a set of skills and tasks. This book focuses on what matters in processing information and being able to use it effectively to your advantage. Rapid skill acquisition is how you get ahead in life professionally and personally. Learn to rapidly train your brain and develop muscle memory. Understand the underlying psychology and biology. Peter Hollins has studied psychology and peak human performance for over a dozen years and is a bestselling author. He has worked with a multitude of individuals to unlock their potential and path towards success. His writing draws on his academic, coaching, and research experience. Tactics that top 1% performers and competitors use. • Theories and principles of learning and what we are doing wrong. • How your expectations matter more than your amount of talent. • How to make a plan to strategically deconstruct and analyze information and skills. How to get better results while working less. • Surprising methods to utilize the people and environment around you. • The art of practicing, pivoting, and correcting yourself. • How to stack your skills and become a unique resource. • Take advantage of learning science to best absorb info. Learning slowly and inefficiently will lead to your downfall -- or even worse, being average. We live in a fast-paced world. Will you fall behind or take the lead? The choice is yours -- learning unlocks the doors to everything we want in life. Accelerating that process makes your life easier and more fulfilled. Personally, your intersts and hobbies will grow at a quick pace for more enjoyment. Professionally, your career opportunities will skyrocket because of your newfound proficiencies. Start your journey rapidly by clicking the BUY NOW BUTTON at the top of this page!

    In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature - from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world. With admirable clarity, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples). In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the "golden ratio." And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal's triangle, to name a few.Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings.

    These efforts evolved into a general theory of expectation that will prove informative to readers interested in cognitive science and evolutionary psychology as well as those interested in music. The book describes a set of psychological mechanisms and illustrates how these mechanisms work in the case of music. All examples of notated music can be heard on the Web.Huron proposes that emotions evoked by expectation involve five functionally distinct response systems: reaction responses (which engage defensive reflexes); tension responses (where uncertainty leads to stress); prediction responses (which reward accurate prediction); imagination responses (which facilitate deferred gratification); and appraisal responses (which occur after conscious thought is engaged). For real-world events, these five response systems typically produce a complex mixture of feelings. The book identifies some of the aesthetic possibilities afforded by expectation, and shows how common musical devices (such as syncopation, cadence, meter, tonality, and climax) exploit the psychological opportunities. The theory also provides new insights into the physiological psychology of awe, laughter, and spine-tingling chills. Huron traces the psychology of expectations from the patterns of the physical/cultural world through imperfectly learned heuristics used to predict that world to the phenomenal qualia we experienced as we apprehend the world.

    Looking at practices, concepts, tools and mixing instruments the author provides a comprehensive insight to the art and science of mixing.Whether a hobbyist of professional this book covers basic concepts to advanced techniques as well as tips and tricks and is a vital read for anyone wanting to succeed in the field of mixing.The book is accompanied by the website www.mixingaudio.com, featuring a sample chapter, illustrations, audio and a user forum. * Rounded, extensive and complete coverage of music mixing* Includes a DVD with over 700 audio samples and 4 sample mixes. The DVD is not included with the E-book. Please visit http://www.mixingaudiodvd.com/ to access the DVD content.* Covers new topics and mixing trends such as computer centred mixing

    We have Mindstorms to thank for that. In this book, pioneering computer scientist Seymour Papert uses the invention of LOGO, the first child-friendly programming language, to make the case for the value of teaching children with computers. Papert argues that children are more than capable of mastering computers, and that teaching computational processes like de-bugging in the classroom can change the way we learn everything else. He also shows that schools saturated with technology can actually improve socialization and interaction among students and between students and teachers.

    This logic extends far beyond the realm of computer science and into the wide and entertaining world of puzzles. In Algorithmic Puzzles, Anany and Maria Levitin use many classic brainteasers as well as newer examples from job interviews with major corporations to show readers how to apply analytical thinking to solve puzzles requiring well-defined procedures.The book's unique collection of puzzles is supplemented with carefully developed tutorials on algorithm design strategies and analysis techniques intended to walk the reader step-by-step through the various approaches to algorithmic problem solving. Mastery of these strategies--exhaustive search, backtracking, and divide-and-conquer, among others--will aid the reader in solving not only the puzzles contained in this book, but also others encountered in interviews, puzzle collections, and throughout everyday life. Each of the 150 puzzles contains hints and solutions, along with commentary onthe puzzle's origins and solution methods. The only book of its kind, Algorithmic Puzzles houses puzzles for all skill levels. Readers with only middle school mathematics will develop their algorithmic problem-solving skills through puzzles at the elementary level, while seasoned puzzle solvers will enjoy the challenge of thinking throughmore difficult puzzles.

    

     Learn the essential concepts using concrete analogies and vivid diagrams, not mechanical definitions. Calculus isn't a set of rules, it's a specific, practical viewpoint we can apply to everyday thinking. Frustrated With Abstract, Mechanical Lessons? I was too. Despite years of classes, I didn't have a strong understanding of calculus concepts. Sure, I could follow mechanical steps, but I had no lasting intuition. The classes I've seen are too long, taught in the wrong order, and without solid visualizations. Here's how this course is different: 1) It gets to the point. A typical class plods along, saving concepts like Integrals until Week 8. I want to see what calculus can offer by Minute 8. Each compact, tightly-written lesson can be read in 15 minutes. 2) Concepts are taught in their natural order. Most classes begin with the theory of limits, a technical concept discovered 150 years after calculus was invented. That's like putting a new driver into a Formula-1 racecar on day 1. We can begin with the easy-to-grasp concepts discovered 2000 years ago. 3) It has vivid analogies and visualizations. Calculus is usually defined as the "study of change"... which sounds like history or geology. Instead of an abstract definition, we'll see calculus a step-by-step viewpoint to explore patterns. 4) It's written by a human, for humans. I'm not a haughty professor or strict schoolmarm. I'm a friend who saw a fun way to internalize some difficult ideas. This course is a chat over coffee, not a keep-your-butt-in-your-seat lecture. The goal is to help you grasp the Aha! moments behind calculus in hours, not a painful semester (or a decade, in my case). Join Thousands Of Happy Readers Here's a few samples of anonymous feedback as people went through the course. The material covers a variety of levels, whether you're looking for intuitive appreciation or the specifics of the rules. "I've done all of this stuff before, and I do understand calculus intuitively, but this was the most fun I've had going through this kind of thing. The informal writing and multitude of great analogies really helps this become an enjoyable read and the rest is simple after that - you make this seem easy, but at the same time, you aren't doing it for us…This is what math education is supposed to be like :)" "I have psychology and medicine background so I relate your ideas to my world. To me the most useful idea was what each circle production feels like. Rings are natural growth…Slices are automatable chunks and automation cheapens production… Boards in the shape on an Arch are psychologically most palatable for work (wind up, hard part, home stretch). Brilliant and kudos, from one INTP to another." "I like how you're introducing both derivatives and integrals at the same time - it's really helps with understanding the relationship between them. Also, I appreciate how you're coming from such a different angle than is traditionally taken - it's always interesting to see where you decide to go next." "That was breathtaking. Seriously, mail my air back please, I've grown used to it. Beautiful work, thank you. Lesson 15 was masterful. I am starting to feel calculus. "d/dx is good" (sorry, couldn't resist!)."

    The Third Edition retains the elements that have made the book a classic while embracing new technology and responding to the needs of today's students and teachers.