This textbook presents the theory of Metric Spaces necessary for studying analysis beyond one real variable. Rich in examples, exercises and motivation, it provides a careful and clear exposition at a pace appropriate to the material. The book covers the main topics of metric space theory that the student of analysis is likely to need. Starting with an overview defining the principal examples of metric spaces in analysis (chapter 1), it turns to the basic theory (chapter 2) covering open and closed sets, convergence, completeness and continuity (including a treatment of continuous linear mappings). There is also a brief dive into general topology, showing how metric spaces fit into a wider theory. The following chapter is devoted to proving the completeness of the classical spaces. The text then embarks on a study of spaces with important special properties. Compact spaces, separable spaces, complete spaces and connected spaces each have a chapter devoted to them. A particular feature of the book is the occasional excursion into analysis. Examples include the Mazur–Ulam theorem, Picard’s theorem on existence of solutions to ordinary differential equations, and space filling curves. This text will be useful to all undergraduate students of mathematics, especially those who require metric space concepts for topics such as multivariate analysis, differential equations, complex analysis, functional analysis, and topology. It includes a large number of exercises, varying from routine to challenging. The prerequisites are a first course in real analysis of one real variable, an acquaintance with set theory, and some experience with rigorous proofs.
Rome 51 AD. When a secretive astrologer is found murdered, Marcus Salvius Magnus, leader of the South Quirinal Crossroads Brotherhood, suspects that there is more to the brutal slaughter in his district than it seems. As Magnus pieces together the motives behind the plot, it emerges that the astrologer had been drawing up illegal horoscopes for the powerful and wealthy in Rome, including Magnus' patron, Senator Gaius Vespasius Pollo. But knowledge of this kind can be deadly. With Magnus' enemies closing in, danger from both within the Brotherhood's ranks and from rival gang the West Viminal threatens everything he has fought for. Magnus must use every trick known to him to survive, and to try to come out on top... ______________________________________________ Don't miss Robert Fabbri's epic new series Alexander's Legacy
This textbook offers a comprehensive undergraduate course in real analysis in one variable. Taking the view that analysis can only be properly appreciated as a rigorous theory, the book recognises the difficulties that students experience when encountering this theory for the first time, carefully addressing them throughout. Historically, it was the precise description of real numbers and the correct definition of limit that placed analysis on a solid foundation. The book therefore begins with these crucial ideas and the fundamental notion of sequence. Infinite series are then introduced, followed by the key concept of continuity. These lay the groundwork for differential and integral calculus, which are carefully covered in the following chapters. Pointers for further study are included throughout the book, and for the more adventurous there is a selection of "nuggets", exciting topics not commonly discussed at this level. Examples of nuggets include Newton's method, the irrationality of π, Bernoulli numbers, and the Gamma function. Based on decades of teaching experience, this book is written with the undergraduate student in mind. A large number of exercises, many with hints, provide the practice necessary for learning, while the included "nuggets" provide opportunities to deepen understanding and broaden horizons.
In the year 4000, the human race is threatened by robots bent on enslaving mankind, and only one man has the power to fight back--Magnus, Robot Fighter!"--Volume 1 cover.
This textbook offers an engaging account of the theory of ordinary differential equations intended for advanced undergraduate students of mathematics. Informed by the author’s extensive teaching experience, the book presents a series of carefully selected topics that, taken together, cover an essential body of knowledge in the field. Each topic is treated rigorously and in depth. The book begins with a thorough treatment of linear differential equations, including general boundary conditions and Green’s functions. The next chapters cover separable equations and other problems solvable by quadratures, series solutions of linear equations and matrix exponentials, culminating in Sturm–Liouville theory, an indispensable tool for partial differential equations and mathematical physics. The theoretical underpinnings of the material, namely, the existence and uniqueness of solutions and dependence on initial values, are treated at length. A noteworthy feature of this book is the inclusion of project sections, which go beyond the main text by introducing important further topics, guiding the student by alternating exercises and explanations. Designed to serve as the basis for a course for upper undergraduate students, the prerequisites for this book are a rigorous grounding in analysis (real and complex), multivariate calculus and linear algebra. Some familiarity with metric spaces is also helpful. The numerous exercises of the text provide ample opportunities for practice, and the aforementioned projects can be used for guided study. Some exercises have hints to help make the book suitable for independent study.fsfsfsscs
In the year 4,000, the human race is threatened by robots bent to enslave mankind, and only one man has the power to fight back, Magnus, Robot Fighter! Join Magnus on his quest, as he proclaims, 'My task will not be completed until I have smashed every evil robot that is hurting mankind in body and soul'.
More died in one day than in any other day until Hiroshima, and only one man was responsible; not Caesar, Genghis Khan, not even Hitlert-but Hannibal! In Hannibal Magus: Book I, go back in time to join the great Carthaginian military leader as a treasure of collected writings by a member of Hannibal's staff is discovered in modern times in the Italian Alps. A compelling historical fiction novel that gives detail and voice to a tumultuous epoch in both ancient and military history, these eyewitness accounts of the Second Punic War chronicle Hannibal's decent into Italy as he defeats the Roman legions and sends Rome into a crisis. Will the Roman leadership's unorthodox solution to the military genius of Hannibal-defeating him by not fighting-save the army and preserve the Republic? Or will it set the stage for an epic showdown between Hannibal and his forty thousand mercenaries and the Roman legions?
He's lethal with a sword. She's deadly with her bow. But will it be enough in the coming war? Erroh must return to Spark City to warn of the approaching army. Growing ever stronger, the reluctant warrior and his fierce companion must elude bandits and soldiers in a mad dash against time. Across the map his father, Magnus, rallies his troops to march for the first time in two decades as he seeks to avenge his son, presumed dead. But with unrest and injustice exploding within Spark City, and their foes marching towards its gates, they may already be too late. The Spark City Cycle continues with The March of Magnus; the eagerly awaited sequel to #1 bestselling Spark City, from top fantasy author Robert J Power.
An epic work of historical and military fiction. . . a prime work for Roman history lovers." - InD'Tale Magazine Caesar and Brutus. Marius and Sulla. Cicero, Antony, Clodius and Augustus. The century before the current era gave us a host of larger-than-life characters hailing from Rome. Only one was named Great. In the year 90 B.C.E., chaos and unrest erupts across the Italian peninsula. Rome's allies have rebelled and taken up arms against the most powerful military on earth. Leading Rome's legions - and his only son - to the city's defense, an unproven and unloved commander will taste victory and defeat outside the capital's gates. The name Pompey had yet to be praised and revered, but fate would soon alter the course of one man's life. RISING SUN is the first book in Robert Allen Johnson's captivating MAGNUS trilogy. Narrated by the last living son of Gnaeus Pompey, RISING SUN sets the stage for the man historians would later name the Roman Alexander.
In 1665 an anonymous treatise on magic, by magicians, was added to a book skeptical of witchcraft, "The Discoverie of Witchcraft". The "Magitians Discovered" series examines that anonymous material. This volume contains texts that are foundational for understanding that material, plus texts that are related to the arguments about the material made in the first volume. These texts include selections from Henry Cornelius Agrippa's "Three Books of Occult Philosophy", about the theory and practice of magic; selections from his "Fourth Book"; selections from Olaus Magnus' "Description of the Northern Peoples" about pagan customs, giants, standing stones, witches, and related topics; selections from Robert Burton's "Anatomy of Melancholy" that deal with magic; selections from Isaac La Peyrère's "Prae-Adamitae" which deal with magic and hermeticism; selections from John Dee's writings from "A True and Faithful Relation" that deal with the nature of the aerial spirits; selections from Robert Kirk's "Secret Commonwealth of Elves, Fauns, and Fairies", and more.
In Replacement Parts, internationally recognized bioethicist Arthur L. Caplan and coeditors James J. McCartney and Daniel P. Reid assemble seminal writings from medicine, philosophy, economics, and religion that address the ethical challenges raised by organ transplantation. Caplan's new lead essay explains the shortfalls of present policies. From there, book sections take an interdisciplinary approach to fundamental issues like the determination of death and the dead donor rule; the divisive case of using anencephalic infants as organ donors; the sale of cadaveric or live organs; possible strategies for increasing the number of available organs, including market solutions and the idea of presumed consent; and questions surrounding transplant tourism and "gaming the system" by using the media to gain access to organs. Timely and balanced, Replacement Parts is a first-of-its-kind collection aimed at surgeons, physicians, nurses, and other professionals involved in this essential lifesaving activity that is often fraught with ethical controversy.
Rome, AD 34: Marcus Salvius Magnus, leader of the Crossroads Brotherhood, is searching for the resin of an eastern flower that can unlock the realm of Morpheus. His patron, Senator Pollo, needs it for the city's most powerful woman, the Lady Antonia, in order to recoup a considerable debt. Meanwhile, rebellion is in the air and as the Ides of October festival dawns to celebrate the completion of agricultural and military campaigns, a violent riot erupts. Can Magnus help right the wrongs that have been perpetrated upon the stirred-up crowd? A VESPASIAN NOVELLA ______________________________________________ Don't miss Robert Fabbri's epic new series Alexander's Legacy
An ebook-exclusive short story from the bestselling Vespasian series. Marcus Salvius Magnus is a fanatical supporter of the Green Racing Faction and expects a wager to be honoured. Although he does not presume honesty from anyone, he does believe that a bookmaker at the Circus Maximus should record each bet scrupulously and pay the full amount due. But Ignatius, the bookmaker, is foolish enough to attempt to cheat Magnus out of his winnings, incurring not only his wrath but that also of the South Quirinal Crossroads Brotherhood of which Magnus is the leader. In the shady realm of Rome's underworld Magnus will use the full resources of his criminal fraternity to exact appropriate vengeance. But Magnus also has a problem: his patron, Gaius Vespasius Pollo, is attempting to get his nephew, Sabinus, elected as a quaestor. To do this he feels that the support of the senior consul, Gnaeus Domitius Ahenobarbus, would be more than useful. He asks Magnus to ease the consul - a man known for his extreme violence - in the right direction. Ahenobarbus has a passion: the Red Faction at the circus. Could it be that Magnus might wash two tunics in the same tub, bringing Ignatius down and securing Ahenobarbus' support by attempting to fix a chariot race in a manner that has never been done before?
Rome, AD 25: Marcus Salvius Magnus, Patron of the Crossroads Brotherhood, has a problem. In fact, he has two. One of the brothels under his protection has been raided by a rival Brotherhood, and valuable merchandise has been stolen. He can't lose face and let the attack go unpunished, but how can he retaliate without igniting a gang war? At the other end of the social spectrum, Lady Antonia - the emperor's sister-in-law - has let Senator Gaius Vespasius Pollo know that she has a score that only blood will settle, and Magnus owes the Senator a favour. Now, a simple assassination wouldn't be a problem for a man like Magnus, but the instruction is that this death has to be a little more... inventive... than the usual knife-in-the-back-in-a-dark-alley. Perhaps the Patronus of the Crossroads Brotherhood can kill two birds with one stone? A VESPASIAN NOVELLA ______________________________________________ Don't miss Robert Fabbri's epic new series Alexander's Legacy
Starring characters from the bestselling Vespasian series, The Crossroads Brotherhood, The Racing Factions and The Dreams of Morpheus delve into Rome's criminal underworld. In each of these exclusive e-novellas, Marcus Salvius Magnus, leader of the Crossroads Brotherhood, must overcome his own problems whilst battling his way through Rome's savage and corrupt political arena. THREE VESPASIAN NOVELLAS ______________________________________________ Don't miss Robert Fabbri's epic new series Alexander's Legacy
A new supplement from Ranger Games for the Dice & Glory game system containing specialist (traditional) character classes. This book is a great resource for both Players and Game Masters introducing classic archetype specialist classes as well as new and strange hybrids. Requires the Dice & Glory Core Rulebook This book contains: Over 70 Fantasy Specialist Classes with full descriptions of class abilities and level progression tables! Of these, there are 4 Brick classes, 16 Fighter classes, 7 Adventurer classes, 5 Rogue classes, 6 Psychic classes, 19 mage classes, 7 Clergy classes and 13 NPC classes! NPC tables which can be applied to NPC's to easily apply specialist class levels! Multiple forms of stylized Martial Arts forms! ...And advice on how and why to pick a specialist class, advice for Game Masters about NPC's and monsters with specialist classes. This book is an invaluable resource for any player or GM of the D&G system.
Rome 44 AD, Marcus Salvius Magnus has returned from three years fighting for the emperor Claudius in Britannia. As the leader of the South Quirinal Crossroads Brotherhood he must quickly re-establish his command. But he is beset with problems. Who is evicting tenants in his territory? How can he settle a debt to his patron's sister Vespasia Polla? How can he best his rivals, the West Viminal Brotherhood, who thwart him at every turn? Meanwhile Magnus' patron, Senator Gaius Vespasius Pollo is trying to broker a deal to illegally benefit from the booty looted from the war in Britannia, and he needs Magnus' help to carry out such an illicit task. Magnus, who doesn't leave anything up to Fortuna, is the perfect man for the job. He must use the resources of Rome's criminal underworld to find a way to regain control, appease his patrons, and of course, to make a profit. ______________________________________________ Don't miss Robert Fabbri's epic new series Alexander's Legacy
They don't fight for Spark City anymore. But they fight. They are The Outcasts. Hiding in The Wastes, Erroh and his band of exiles must find a way to defend a city that they can never return to. But with Magnus adrift, his warriors decimated, all appears lost as Uden begins his march. A world away, the deadly assassin, Aurora, is hunting down the man who stole her god's eye. Meanwhile, Spark City's fall has already begun from within its own walls. As war bears down on them all, The Outcasts are running out of time and options. Can they survive long enough to stop Uden's war before it burns them all, or will this be their final battle? Spark City Cycle continues with The Outcasts; the eagerly awaited third installment to #1 bestselling Spark City, from fantasy author Robert J Power.
Rome, AD 39: Rome. Marcus Salvius Magnus, leader of the Crossroads Brotherhood, is buying a dangerous cargo of illegal weaponry. When a deal which will ensure Magnus's dominance over Rome's criminal underworld goes sour, Magnus must regain the shipment by any means necessary... As the rival West Viminal Brotherhood threatens his whole operation, Magnus fights to outwit his opponents whilst juggling the threat of the law and the demands of his patron. With enemies, plots and intrigue on all sides, can Magnus manage to evade death long enough to emerge victorious? A VESPASIAN NOVELLA ______________________________________________ Don't miss Robert Fabbri's epic new series Alexander's Legacy
In this timely volume emanating from the National Bureau of Economic Research's program in international economics, leading economists address recent developments in three important areas. The first section of the book focuses on international comparisons of output and prices, and includes papers that present new measures of product market integration, new methodology to infer relative factor price changes from quantitative data, and an ongoing capital stock measurement project. The next section features articles on international trade, including such significant issues as deterring child labor exploitation in developing countries, exchange rate regimes, and mapping U. S. comparative advantage across various factors. The book concludes with research on multinational corporations and includes a discussion of the long-debated issue of whether growth of production abroad substitutes for or is complementary to production growth at home. The papers in the volume are dedicated to Robert E. Lipsey, who for more than a half century at the NBER, contributed significantly to the broad field of empirical international economics.
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