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Calculus can test the limits of even the most advanced math students. This visual, easy-to-follow book deconstructs complex mathematical concepts in a way that’s infinitely easier to grasp. With clear, color-coded methods, you’ll get step-by-step instructions on solving problems using limits, derivatives, differentiation, curve sketching, and integrals. Easy access to concepts means you don’t have to sort through lengthy instructional text, and you can refer to the Appendix for a look at common differentiation rules, integration formulas, and trigonometric identities.
In 1947, as the integration of Major League Baseball began, the once-daring American League had grown reactionary, unwilling to confront postwar challenges--population shifts, labor issues and, above all, racial integration. The league had matured in the Jim Crow era, when northern cities responded to the Great Migration by restricting black access to housing, transportation, accommodations and entertainment, while blacks created their own institutions, including baseball's Negro Leagues. As the political climate changed and some major league teams realized the necessity of integration, the American League proved painfully reluctant. With the exception of the Cleveland Indians, integration was slow and often ineffective. This book examines the integration of baseball--widely viewed as a triumph--through the experiences of the American League and finds only a limited shift in racial values. The teams accepted few black players and made no effort to alter management structures, and organized baseball remained an institution governed by tradition-bound owners.
For many students, calculus can be the most mystifying and frustrating course they will ever take. Based upon Adrian Banner's popular calculus review course at Princeton University, this book provides students with the essential tools they need not only to learn calculus, but also to excel at it.
This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online. For errata and updates, visit https://measure.axler.net/
"Published by OpenStax College, Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates."--BC Campus website.
This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them.
This textbook focuses on one of the most valuable skills in multivariable and vector calculus: visualization. With over one hundred carefully drawn color images, students who have long struggled picturing, for example, level sets or vector fields will find these abstract concepts rendered with clarity and ingenuity. This illustrative approach to the material covered in standard multivariable and vector calculus textbooks will serve as a much-needed and highly useful companion. Emphasizing portability, this book is an ideal complement to other references in the area. It begins by exploring preliminary ideas such as vector algebra, sets, and coordinate systems, before moving into the core areas of multivariable differentiation and integration, and vector calculus. Sections on the chain rule for second derivatives, implicit functions, PDEs, and the method of least squares offer additional depth; ample illustrations are woven throughout. Mastery Checks engage students in material on the spot, while longer exercise sets at the end of each chapter reinforce techniques. An Illustrative Guide to Multivariable and Vector Calculus will appeal to multivariable and vector calculus students and instructors around the world who seek an accessible, visual approach to this subject. Higher-level students, called upon to apply these concepts across science and engineering, will also find this a valuable and concise resource.
Stewart's CALCULUS: CONCEPTS AND CONTEXTS, 3rd Edition focuses on major concepts and supports them with precise definitions, patient explanations, and carefully graded problems. Margin notes clarify and expand on topics presented in the body of the text. The Tools for Enriching Calculus CD-ROM contains visualizations, interactive modules, and homework hints that enrich your learning experience. iLrn Homework helps you identify where you need additional help, and Personal Tutor with SMARTHINKING gives you live, one-on-one online help from an experienced calculus tutor. In addition, the Interactive Video Skillbuilder CD-ROM takes you step-by-step through examples from the book. The new Enhanced Review Edition includes new practice tests with solutions, to give you additional help with mastering the concepts needed to succeed in the course.