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An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
American Military History provides the United States Army-in particular, its young officers, NCOs, and cadets-with a comprehensive but brief account of its past. The Center of Military History first published this work in 1956 as a textbook for senior ROTC courses. Since then it has gone through a number of updates and revisions, but the primary intent has remained the same. Support for military history education has always been a principal mission of the Center, and this new edition of an invaluable history furthers that purpose. The history of an active organization tends to expand rapidly as the organization grows larger and more complex. The period since the Vietnam War, at which point the most recent edition ended, has been a significant one for the Army, a busy period of expanding roles and missions and of fundamental organizational changes. In particular, the explosion of missions and deployments since 11 September 2001 has necessitated the creation of additional, open-ended chapters in the story of the U.S. Army in action. This first volume covers the Army's history from its birth in 1775 to the eve of World War I. By 1917, the United States was already a world power. The Army had sent large expeditionary forces beyond the American hemisphere, and at the beginning of the new century Secretary of War Elihu Root had proposed changes and reforms that within a generation would shape the Army of the future. But world war-global war-was still to come. The second volume of this new edition will take up that story and extend it into the twenty-first century and the early years of the war on terrorism and includes an analysis of the wars in Afghanistan and Iraq up to January 2009.
Each vol. is divided into 2 parts 1st-7th ed.: Dictionary catalog and Classified catalog; 8th-9th ed. have 3rd. part: Directory of publishers.
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
The implicit function theorem is one of the most important theorems in analysis and its many variants are basic tools in partial differential equations and numerical analysis. This second edition of Implicit Functions and Solution Mappings presents an updated and more complete picture of the field by including solutions of problems that have been solved since the first edition was published, and places old and new results in a broader perspective. The purpose of this self-contained work is to provide a reference on the topic and to provide a unified collection of a number of results which are currently scattered throughout the literature. Updates to this edition include new sections in almost all chapters, new exercises and examples, updated commentaries to chapters and an enlarged index and references section.
"I too am not a bit tamed—I too am untranslatable / I sound my barbaric yawp over the roofs of the world."—Walt Whitman, "Song of Myself," Leaves of Grass The American Yawp is a free, online, collaboratively built American history textbook. Over 300 historians joined together to create the book they wanted for their own students—an accessible, synthetic narrative that reflects the best of recent historical scholarship and provides a jumping-off point for discussions in the U.S. history classroom and beyond. Long before Whitman and long after, Americans have sung something collectively amid the deafening roar of their many individual voices. The Yawp highlights the dynamism and conflict inherent in the history of the United States, while also looking for the common threads that help us make sense of the past. Without losing sight of politics and power, The American Yawp incorporates transnational perspectives, integrates diverse voices, recovers narratives of resistance, and explores the complex process of cultural creation. It looks for America in crowded slave cabins, bustling markets, congested tenements, and marbled halls. It navigates between maternity wards, prisons, streets, bars, and boardrooms. The fully peer-reviewed edition of The American Yawp will be available in two print volumes designed for the U.S. history survey. Volume I begins with the indigenous people who called the Americas home before chronicling the collision of Native Americans, Europeans, and Africans.The American Yawp traces the development of colonial society in the context of the larger Atlantic World and investigates the origins and ruptures of slavery, the American Revolution, and the new nation's development and rebirth through the Civil War and Reconstruction. Rather than asserting a fixed narrative of American progress, The American Yawp gives students a starting point for asking their own questions about how the past informs the problems and opportunities that we confront today.
A comprehensive and rigorous introduction for graduate students and researchers, with applications in sequential decision-making problems.
The Book of R is a comprehensive, beginner-friendly guide to R, the world’s most popular programming language for statistical analysis. Even if you have no programming experience and little more than a grounding in the basics of mathematics, you’ll find everything you need to begin using R effectively for statistical analysis. You’ll start with the basics, like how to handle data and write simple programs, before moving on to more advanced topics, like producing statistical summaries of your data and performing statistical tests and modeling. You’ll even learn how to create impressive data visualizations with R’s basic graphics tools and contributed packages, like ggplot2 and ggvis, as well as interactive 3D visualizations using the rgl package. Dozens of hands-on exercises (with downloadable solutions) take you from theory to practice, as you learn: –The fundamentals of programming in R, including how to write data frames, create functions, and use variables, statements, and loops –Statistical concepts like exploratory data analysis, probabilities, hypothesis tests, and regression modeling, and how to execute them in R –How to access R’s thousands of functions, libraries, and data sets –How to draw valid and useful conclusions from your data –How to create publication-quality graphics of your results Combining detailed explanations with real-world examples and exercises, this book will provide you with a solid understanding of both statistics and the depth of R’s functionality. Make The Book of R your doorway into the growing world of data analysis.
Since the publication of its first edition, this book has served as one of the few available on the classical Adams spectral sequence, and is the best account on the Adams-Novikov spectral sequence. This new edition has been updated in many places, especially the final chapter, which has been completely rewritten with an eye toward future research in the field. It remains the definitive reference on the stable homotopy groups of spheres. The first three chapters introduce the homotopy groups of spheres and take the reader from the classical results in the field though the computational aspects of the classical Adams spectral sequence and its modifications, which are the main tools topologists have to investigate the homotopy groups of spheres. Nowadays, the most efficient tools are the Brown-Peterson theory, the Adams-Novikov spectral sequence, and the chromatic spectral sequence, a device for analyzing the global structure of the stable homotopy groups of spheres and relating them to the cohomology of the Morava stabilizer groups. These topics are described in detail in Chapters 4 to 6. The revamped Chapter 7 is the computational payoff of the book, yielding a lot of information about the stable homotopy group of spheres. Appendices follow, giving self-contained accounts of the theory of formal group laws and the homological algebra associated with Hopf algebras and Hopf algebroids. The book is intended for anyone wishing to study computational stable homotopy theory. It is accessible to graduate students with a knowledge of algebraic topology and recommended to anyone wishing to venture into the frontiers of the subject.