One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.

    

    We start counting our fingers and toes and end up balancing checkbooks and calculating risk. So powerful is the appeal of numbers that many people ascribe to them a mystical significance. Other numbers go beyond the supernatural, working to explain our universe and how it behaves. In Cosmic Numbers, mathematics professor James D. Stein traces the discovery, evolution, and interrelationships of the numbers that define our world. Everyone knows about the speed of light and absolute zero, but numbers like Boltzmann’s constant and the Chandrasekhar limit are not as well known, and they do far more than one might imagine: They tell us how this world began and what the future holds. Much more than a gee-whiz collection of facts and figures, Cosmic Numbers illuminates why particular numbers are so important—both to the scientist and to the rest of us.

    Bestselling authors and acclaimed astrophysicists Neil deGrasse Tyson, Michael A. Strauss, and J. Richard Gott take readers on an unforgettable journey of exploration to reveal how our universe actually works.Propelling you from our home solar system to the outermost frontiers of space, this book builds your cosmic insight and perspective through a marvelously entertaining narrative. How do stars live and die? What are the prospects of intelligent life elsewhere in the universe? How did the universe begin? Why is it expanding and accelerating? Is our universe alone or part of an infinite multiverse? Exploring these and many other questions, this pocket-friendly book is your passport into the wonders of our evolving cosmos.

    The author successfully introduces Maxwell's equations, wave propagation, network analysis, and design principles as applied to modern microwave engineering. A considerable amount of material in this book is related to the design of specific microwave circuits and components, for both practical and motivational value. It also presents the analysis and logic behind these designs so that the reader can see and understand the process of applying the fundamental concepts to arrive at useful results. The derivations are well laid out and the majority of each chapter's formulas are displayed in a nice tabular format every few pages. This Third Edition offers greatly expanded coverage with new material on: Noise; Nonlinear effects; RF MEMs; transistor power amplifiers; FET mixers; oscillator phase noise; transistor oscillators and frequency multiplier.

    This work includes differential forms and the elegant forms of Maxwell's equations, and a chapter on probability and statistics. It also illustrates and proves mathematical relations.

    in this book, once more, her heart is laid bare' Giovanna Fletcher 'I didn't want to put it down' Jools Oliver 'Raw and honest... like a letter from a friend' Sarah Turner, The Unmumsy Mum 'Beautifully emotional and healing' Genelle Aldred 'Heartbreaking yet uplifting... I was truly holding my breath' Cat Strawbridge, The Finally Pregnant podcast ***** 'It turns out there are plenty of us: the unlucky ones. The women whose journey into motherhood, or whose yearning for more children, has yet to be fulfilled by the universe. I am certain that in so many parts of my story I really am not the only one to have gone through it, so it makes sense to write it all down. For all of us - and for any parents who might go through some of what we did in the future too. So here it is, our journey to a rainbow. A story of fertility, trying again and, above all, hope.' After the death of her three-day-old son Teddy in 2016, Elle Wright never expected what came next - that the path to bringing home a living child could be so winding. Elle's loss was followed by three and a half years of endless waiting. She and her husband waited for test results, hospital appointments and so many new procedures to help with their experience of secondary infertility. This wait included friends announcing their happy news whilst Elle was experiencing three rounds of IVF and the loss of three more babies. Months and years slipped by, of immense physical and emotional toll, and still those two lines were just out of reach. Faced with constant questions, drugs, negative tests, tears, loss, frustration and so many more tears, throughout it all Elle managed to still believe that one day it would happen for her, somehow... A Bump in the Road reflects the reality of becoming a parent for thousands of people like Elle who have difficulty conceiving in the UK today. It captures Elle's journey to a rainbow, comforting through her beautifully written words with a story of fertility that might just reflect yours, too.

    Known for its carefully developed, thoroughly integrated, step-by-step approach to problem solving, General Chemistry helps students master quantitative skills and build a lasting conceptual understanding of key chemical concepts. The Ninth Edition retains this hallmark approach and builds upon the conceptual focus through key new features and revisions.

    Chapter topics include atomic structure, molecular orbitals, organometallic chemistry, simple bonding theory, symmetry and group theory, and more. For chemists and other professionals who want to update or improve their background in the field.

    From the sudden expansion of a cloud of gas to the cooling of hot metal--everything is moved or restrained by four simple laws. Written by Peter Atkins, one of the world's leading authorities on thermodynamics, this powerful and compact introduction explains what these four laws are and how they work, using accessible language and virtually no mathematics. Guiding the reader a step at a time, Atkins begins with Zeroth (so named because the first two laws were well established before scientists realized that a third law, relating to temperature, should precede them--hence the jocular name zeroth), and proceeds through the First, Second, and Third Laws, offering a clear account of concepts such as the availability of work and the conservation of energy. Atkins ranges from the fascinating theory of entropy (revealing how its unstoppable rise constitutes the engine of the universe), through the concept of free energy, and to the brink, and then beyond the brink, of absolute zero. About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam.

    It was a sea in name only. It was actually a bone dry, ancient dusty basin pockmarked with craters and littered with rocks and boulders. Somewhere in that 500 mile diameter basin, the astronauts would attempt to make Mankind’s first landing on the Moon. Neil Armstrong would pilot the Lunar Module “Eagle” during its twelve minute descent from orbit down to a landing. Col. Edwin “Buzz” Aldrin would assist him. On the way down they would encounter a host of problems, any one of which could have potentially caused them to have to call off the landing, or, even worse, die making the attempt. The problems were all technical-communications problems, computer problems, guidance problems, sensor problems. Armstrong and Aldrin faced the very real risk of dying by the very same technical sword that they had to live by in order to accomplish the enormous task of landing on the Moon for the first time. Yet the human skills Armstrong and Aldrin employed would be more than equal to the task. Armstrong’s formidable skills as an aviator, honed from the time he was a young boy, would serve him well as he piloted Eagle down amidst a continuing series of systems problems that might have fatally distracted a lesser aviator. Armstrong’s brilliant piloting was complemented by Aldrin’s equally remarkable discipline and calmness as he stoically provided a running commentary on altitude and descent rate while handling systems problems that threatened the landing. Finally, after a harrowing twelve and a half minutes, Armstrong gently landed Eagle at “Tranquility Base”, a name he had personally chosen to denote the location of the first Moon landing. In “Landing Eagle-Inside the Cockpit During the First Moon Landing”, author Mike Engle gives a minute by minute account of the events that occurred throughout Eagle’s descent and landing on the Moon. Engle, a retired NASA engineer and Mission Control flight controller, uses NASA audio files of actual voice recordings made inside Eagle’s cockpit during landing to give the reader an “inside the cockpit” perspective on the first Moon landing. Engle’s transcripts of these recordings, along with background material on the history and technical details behind the enormous effort to accomplish the first Moon landing, give a new and fascinating insight into the events that occurred on that remarkable day fifty years ago.

    Written By Two Of Today'S Most Respected Computer Science Educators, Nell Dale And John Lewis, The Text Provides A Broad Overview Of The Many Aspects Of The Discipline From A Generic View Point. Separate Program Language Chapters Are Available As Bundle Items For Those Instructors Who Would Like To Explore A Particular Programming Language With Their Students. The Many Layers Of Computing Are Thoroughly Explained Beginning With The Information Layer, Working Through The Hardware, Programming, Operating Systems, Application, And Communication Layers, And Ending With A Discussion On The Limitations Of Computing. Perfect For Introductory Computing And Computer Science Courses, Computer Science Illuminated, Third Edition's Thorough Presentation Of Computing Systems Provides Computer Science Majors With A Solid Foundation For Further Study, And Offers Non-Majors A Comprehensive And Complete Introduction To Computing.

    This beginning aviator's guide is intended for pilots wishing to improve their flying proficiency and aeronautical knowledge, and flyers preparing for additional certificates or ratings, and others.

    Perform this genius seemingly-mathematical feat on any napkin, any receipt, or even on your friend's arm.You can learn the famous Magic Square, and you can learn it in under 10 minutes.You will have a magician's Grand Finale, in your hands at any moment. This gets audible gasps, and you can wow people with this for the rest of your life...**************************THE PERFORMANCE:**************************Your friend will name a random number. You then speedily write 16 different numbers into a 4x4 grid. With a smug flourish, you then reveal that all combinations and directions within the grid add up to their chosen number. It is simply mind-blowing.Effortlessly perform a trick that it seems only a computer could perform, and learn how in 10 minutes from right now.

    In "Physics Demystified" best-selling author Stan Gibilisco offers a fun, effective, and totally painless way to learn the fundamentals and general concepts of physics.With "Physics Demystified" you master the subject one simple step at a time – at your own speed. Unlike most books on physics, general principles are presented first – and the details follow. In order to make the learning process as clear and simple as possible, heavy-duty math, formulas, and equations are kept to a minimum. This unique self-teaching guide offers questions at the end of each chapter and section to pinpoint weaknesses, and a 100-question final exam to reinforce the entire book.Simple enough for a beginner but challenging enough for an advanced student, "Physics Demystified" is your direct route to learning or brushing up on physics.HERE’S EVERYTHING YOU NEED TO: * Understand the math used in physical science* Solve mass/force/acceleration problems* Create mathematical models of physical phenomena* Perform distance vs. time calculations* Determine potential and kinetic energy* Calculate the wavelength of sounds and radio signals* Understand visible light interference patterns* Calculate the energy and frequency of a moving particle* Understand atomic structure* Learn about electric current, voltage, resistance, power, and energy