The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included. This text is part of the Walter Rudin Student Series in Advanced Mathematics.

     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!)."

    Argues that recent developments in quantum physics, astronomy, and chaos theory have forced a reconsideration of the concepts of space, time, and matter.

    Their quest: to be the first to detect gravitational waves, infinitesimal quakes that stretch and compress space-time and could add a brand-new dimension to our universal knowledge-allowing us to hear a sun going supernova, black holes colliding, and perhaps one day, the remnant rumble of the Big Bang itself...

    They'll also find the related analytic geometry much easier. The clear review of algebra and geometry in this edition will make calculus easier for students who wish to strengthen their knowledge in these areas. Updated to meet the emphasis in current courses, this new edition of a popular guide--more than 104,000 copies were bought of the prior edition--includes problems and examples using graphing calculators..

    Gordon strips engineering of its confusing technical terms, communicating its founding principles in accessible, witty prose.For anyone who has ever wondered why suspension bridges don't collapse under eight lanes of traffic, how dams hold back--or give way under--thousands of gallons of water, or what principles guide the design of a skyscraper, a bias-cut dress, or a kangaroo, this book will ease your anxiety and answer your questions.Structures: Or Why Things Don't Fall Down is an informal explanation of the basic forces that hold together the ordinary and essential things of this world--from buildings and bodies to flying aircraft and eggshells. In a style that combines wit, a masterful command of his subject, and an encyclopedic range of reference, Gordon includes such chapters as "How to Design a Worm" and "The Advantage of Being a Beam," offering humorous insights in human and natural creation.Architects and engineers will appreciate the clear and cogent explanations of the concepts of stress, shear, torsion, fracture, and compression. If you're building a house, a sailboat, or a catapult, here is a handy tool for understanding the mechanics of joinery, floors, ceilings, hulls, masts--or flying buttresses.Without jargon or oversimplification, Structures opens up the marvels of technology to anyone interested in the foundations of our everyday lives.

    Using illustrations and examples from science fiction pulp magazines and comic books, The Amazing Story of Quantum Mechanics explains the fundamental principles of quantum mechanics that underlie the world we live in.Watch a Video

    

    Focusing on the ideas, this book considers relativity and quantum ideas to provide a framework for understanding the physics of atoms and nuclei.

    He asks how today's scientists can claim to predict future climate events when even three-day forecasts prove a serious challenge. Can we predict and control epidemics? Can we accurately foresee our financial future? Or will we only find out about tomorrow when tomorrow arrives?

    It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

    Can you believe that physical reality is created by our observation of it? Physicists were forced to this conclusion, the quantum enigma, by what they observed in their laboratories.Trying to understand the atom, physicists built quantum mechanics and found, to their embarrassment, that their theory intimately connects consciousness with the physical world. Quantum Enigma explores what that implies and why some founders of the theory became the foremost objectors to it. Schr�dinger showed that it absurdly allowed a cat to be in a superposition simultaneously dead and alive. Einstein derided the theory's spooky interactions. With Bell's Theorem, we now know Schr�dinger's superpositions and Einstein's spooky interactions indeed exist.Authors Bruce Rosenblum and Fred Kuttner explain all of this in non-technical terms with help from some fanciful stories and bits about the theory's developers. They present the quantum mystery honestly, with an emphasis on what is and what is not speculation.Physics' encounter with consciousness is its skeleton in the closet. Because the authors open the closet and examine the skeleton, theirs is a controversial book. Quantum Enigma's description of the experimental quantum facts, and the quantum theory explaining them, is undisputed. Interpreting what it all means, however, is controversial.Every interpretation of quantum physics encounters consciousness. Rosenblum and Kuttner therefore turn to exploring consciousness itself--and encounter quantum physics. Free will and anthropic principles become crucial issues, and the connection of consciousness with the cosmos suggested by some leading quantum cosmologists is mind-blowing.Readers are brought to a boundary where the particular expertise of physicists is no longer a sure guide. They will find, instead, the facts and hints provided by quantum mechanics and the ability to speculate for themselves.

    The book is also ideal for university and third-level physics or engineering courses on solar photovoltaics, with exercises to check students' understanding and reinforce learning. It is the perfect companion to the Massive Open Online Course (MOOC) on Solar Energy (DelftX, ET.3034TU) presented by co-author Arno Smets. The course is available in English on the nonprofit open source edX.org platform, and in Arabic on edraak.org. Over 100,000 students have already registered for these MOOCs.

    C. Fields, and Woody Allen."Jokes, paradoxes, riddles, and the art of non-sequitur are revealed with great perception and insight in this illuminating account of the relationship between humor and mathematics."—Joseph Williams, New York Times"'Leave your mind alone,' said a Thurber cartoon, and a really complete and convincing analysis of what humour is might spoil all jokes forever. This book avoids that danger. What it does. . .is describe broadly several kinds of mathematical theory and apply them to throw sidelights on how many kinds of jokes work."—New Scientist"Many scholars nowadays write seriously about the ludicrous. Some merely manage to be dull. A few—like Paulos—are brilliant in an odd endeavor."—Los Angeles Times Book Review

    It resurrects from the vaults of neglect the polymath Jerome Cardano, a Milanese of the sixteenth century. Who is he? A gambler and blasphemer, inventor and chancer, plagued by demons and anxieties, astrologer to kings, emperors and popes. This stubborn and unworldly man was the son of a lawyer and a brothel keeper, but also a gifted physician and the unacknowledged discoverer of the mathematical foundations of quantum physics. That is the argument of this charming and intoxicatingly clever book, which is truly original in its style, and in the manner of the modernists embodies in its very form its theories about the world.'The Quantum Astrologer’s Handbook' is a science book with the panache of a novel, for readers of Carlo Rovelli or Umberto Eco. It is a work of and about genius.