This new edition of Lax, Burstein, and Lax's Calculus with Applications and Computing offers meaningful explanations of the important theorems of single variable calculus. Written with students in mathematics, the physical sciences, and engineering in mind, and revised with their help, it shows that the themes of calculation, approximation, and modeling are central to mathematics and the main ideas of single variable calculus. This edition brings the innovation of the first edition to a new generation of students. New sections in this book use simple, elementary examples to show that when applying calculus concepts to approximations of functions, uniform convergence is more natural and easier to use than point-wise convergence. As in the original, this edition includes material that is essential for students in science and engineering, including an elementary introduction to complex numbers and complex-valued functions, applications of calculus to modeling vibrations and population dynamics, and an introduction to probability and information theory."

This volume of the Encyclopaedia is a survey of stochastic calculus, an increasingly important part of probability, authored by well-known experts in the field. The book addresses graduate students and researchers in probability theory and mathematical statistics, as well as physicists and engineers who need to apply stochastic methods.

This is a serious - but not solemn - textbook that attempts to make a clear, conceptual understanding of calculus accessible to all liberal arts students. It presents mathematics as growing out of the classical liberal arts to form a natural bridge between the humanities and the sciences, integrating the history and pedagogy of mathematics in a way that may be of interest to prospective teachers as well. Instead of a pre-calculus review, this book offers an historical development of much of the geometry and algebra needed, emphasizing the fundamental need for students to develop a clear style of writing. Calculus is here largely restricted to the study of algebraic functions, but all the usual aspects of the interplay between functions and derivatives are covered: optimization, instantaneous rates, Newton's method, freely falling bodies, antiderivatives, integrals, areas, volumes, etc. The fundamental theorem is prominently featured and carefully treated. A brief final chapter about the intellectual climate surrounding the development of calculus offers students further insight into the place of mathematics as an element in the history of thought.

Another Calculus book? As long as students find calculus scary, the failure rate in mathematics is higher than in all other subjects, and as long as most people mistakenly believe that only geniuses can learn and understand mathematics, there will always be room for a new book of Calculus. We call it Calculus Light.

This book is designed for a one semester course in "light" calculus - mostly single variable, meant to be used by undergraduate students without a wide mathematical background and who do not major in mathematics but study subjects such as engineering, biology or management information systems.

The first chapter contains a historical background of calculus. Every scientific achievement involves people and therefore characterized by victories and disappointments, intrigues and hope. All of these elements exist in the story behind calculus and when you add the time dimension, starting 2400 years ago, it is a saga. We hope the reader enjoys reading this chapter as much as we enjoyed the writing.

In addition to classic calculus the book provides tools for practical applications such as Fourier series, Lagrange multipliers and elementary numerical methods.

In this book the details of many calculations are provided for access to work in quantum groups, algebraic differential calculus, noncommutative geometry, fuzzy physics, discrete geometry, gauge theory, quantum integrable systems, braiding, finite topological spaces, some aspects of geometry and quantum mechanics and gravity.

This is a text for students who have had a three-course calculus sequence and who are ready to explore the logical structure of analysis as the backbone of calculus. It begins with a development of the real numbers, building this system from more basic objects (natural numbers, integers, rational numbers, Cauchy sequences), and it produces basic algebraic and metric properties of the real number line as propositions, rather than axioms. The text also makes use of the complex numbers and incorporates this into the development of differential and integral calculus. For example, it develops the theory of the exponential function for both real and complex arguments, and it makes a geometrical study of the curve (expit)(expit), for real tt, leading to a self-contained development of the trigonometric functions and to a derivation of the Euler identity that is very different from what one typically sees. Further topics include metric spaces, the Stone–Weierstrass theorem, and Fourier series.

Learn everything you need to know about Calculus and practice your reasoning and practical skills with a high-end textbook suitable for a wide range of course levels. Calculus: A Complete Course, 10th Edition by Robert Adams and Christopher Essex is the ultimate guide written by two leading authors in the field that continues to build its solid core following the successful pattern of its previous editions. With its reader-friendly language, the textbook holds a reputation for excellent accuracy and mathematical rigour, offering you study material suitable to cover a standard semester course, as well as high-end content that will help you further explore some of the unique topics and approaches in the landscape of Mathematics. Adding important, but overlooked topics while clarifying old ones, this edition will help you develop and practice your reasoning skills and apply techniques you have learned to concrete situations. Some of the topics this edition explores include: Sufficient conditions for maxima and minima in higher dimensions: this is the only mainstream textbook that covers the topic sufficiently. The fuzzy topic of metrics: the text explores and addresses any issues and questions, leading to new gateway topics, including spherical geometry (as in navigation) and special relativity, which emerge rather effortlessly once the metric concept is in place properly. Computers and mathematics through Maple and now Python: there is no other Calculus book that deals better with the topic while treating unique but important applications from information theory to Levy distributions. With a wide variety of exercises and useful features to support your learning, this unique edition continues to aspire to the definition of its subtitle of "A Complete Course." Also available with MyLab (R) Math MyLab is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLabMath personalises the learning experience and improves results for each student. If you would like to purchase both the physical text and MyLab (R) Math, search for: 9780135732595 Calculus: A Complete Course, 10th Edition plus MyLab Math with Pearson eText -- Access Card Package Package consists of: 9780135732588 Calculus: A Complete Course, 10th Edition 9780135732526 Calculus: A Complete Course, 10th Edition MyLab (R) Math -- Standalone Access Card MyLab (R) Math is not included. Students, if MyLab is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN. MyLab should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

Discover an accessible and easy-to-use guide to calculus fundamentals In Quick Calculus: A Self-Teaching Guide, 3rd Edition, a team of expert MIT educators delivers a hands-on and practical handbook to essential calculus concepts and terms. The author explores calculus techniques and applications, showing readers how to immediately implement the concepts discussed within to help solve real-world problems. In the book, readers will find: An accessible introduction to the basics of differential and integral calculus An interactive self-teaching guide that offers frequent questions and practice problems with solutions. A format that enables them to monitor their progress and gauge their knowledge This latest edition provides new sections, rewritten introductions, and worked examples that demonstrate how to apply calculus concepts to problems in physics, health sciences, engineering, statistics, and other core sciences. Quick Calculus: A Self-Teaching Guide, 3rd Edition is an invaluable resource for students and lifelong learners hoping to strengthen their foundations in calculus.

From one of today's most accomplished and trusted mathematics authors comes a new textbook that offers unmatched support for students taking the AP (R) Calculus exam, and comes with additional resources for the teachers helping them prepare for it.Sullivan and Miranda's Calculus for the AP Course covers every Big Idea, Essential Knowledge statement, Learning Objective, and Math Practice described in the 2016-2017 redesigned College Board (TM) Curriculum Framework. It is concise and its focused narrative and integrated conceptual and problem-solving tools give students just the help they need as they learn calculus and prepare for the redesigned AP (R) Exam. Its accompanying Teacher's Edition provides an in depth correlation and abundant tips, examples, projects, and resources to ensure close adherence the new Curriculum Framework.

This book presents what in our opinion constitutes the basis of the theory of the mu-calculus, considered as an algebraic system rather than a logic. We have wished to present the subject in a unified way, and in a form as general as possible. Therefore, our emphasis is on the generality of the fixed-point notation, and on the connections between mu-calculus, games, and automata, which we also explain in an algebraic way.
This book should be accessible for graduate or advanced undergraduate students both in mathematics and computer science. We have designed this book especially for researchers and students interested in logic in computer science, comuter aided verification, and general aspects of automata theory. We have aimed at gathering in a single place the fundamental results of the theory, that are currently very scattered in the literature, and often hardly accessible for interested readers.
The presentation is self-contained, except for the proof of the Mc-Naughton's Determinization Theorem (see, e.g., 97]. However, we suppose that the reader is already familiar with some basic automata theory and universal algebra. The references, credits, and suggestions for further reading are given at the end of each chapter.

Calculus For Dummies, 2nd Edition (9781119293491) was previously published as Calculus For Dummies, 2nd Edition (9781118791295). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product. Slay the calculus monster with this user-friendly guide Calculus For Dummies, 2nd Edition makes calculus manageable even if you're one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. This user-friendly math book leads you step-by-step through each concept, operation, and solution, explaining the "how" and "why" in plain English instead of math-speak. Through relevant instruction and practical examples, you'll soon learn that real-life calculus isn't nearly the monster it's made out to be. Calculus is a required course for many college majors, and for students without a strong math foundation, it can be a real barrier to graduation. Breaking that barrier down means recognizing calculus for what it is simply a tool for studying the ways in which variables interact. It's the logical extension of the algebra, geometry, and trigonometry you've already taken, and Calculus For Dummies, 2nd Edition proves that if you can master those classes, you can tackle calculus and win. * Includes foundations in algebra, trigonometry, and pre-calculus concepts * Explores sequences, series, and graphing common functions * Instructs you how to approximate area with integration * Features things to remember, things to forget, and things you can't get away with Stop fearing calculus, and learn to embrace the challenge. With this comprehensive study guide, you'll gain the skills and confidence that make all the difference. Calculus For Dummies, 2nd Edition provides a roadmap for success, and the backup you need to get there.

Discover the relevance of mathematics in your own life as you master important concepts and skills in Waner/Costenoble’s APPLIED CALCULUS, 8th Edition. Updated, numerous examples and applications use real data from well-known businesses, current economic and life events -- from cryptocurrency to COVID -- to demonstrate how the principles you are learning impact you. Readable, streamlined content clearly presents concepts while numerous learning features and tools help you review and practice. Spreadsheet and TI graphing calculator instructions appear where needed. In addition, WebAssign online tools and an interactive eTextbook include teaching videos by an award-winning instructor. You can refine your skills in the necessary math prerequisites with additional examples and powerful adaptive practice sessions. A helpful website from the authors also offers online tutorials and videos on every topic to support your learning, no matter what your learning style.

This book is an introductory text that charts the recent developments in the area of Whitney-type extension problems and the mathematical aspects of interpolation of data. It provides a detailed tour of a new and active area of mathematical research. In each section, the authors focus on a different key insight in the theory. The book motivates the more technical aspects of the theory through a set of illustrative examples. The results include the solution of Whitney's problem, an efficient algorithm for a finite version, and analogues for Hoelder and Sobolev spaces in place of C m . The target audience consists of graduate students and junior faculty in mathematics and computer science who are familiar with point set topology, as well as measure and integration theory. The book is based on lectures presented at the CBMS regional workshop held at the University of Texas at Austin in the summer of 2019.

This book discusses advances in maximal function methods related to Poincare and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary values. The authors consider several uniform quantitative conditions that are self-improving, such as Hardy's inequalities, capacity density conditions, and reverse Hoelder inequalities. They also study Muckenhoupt weight properties of distance functions and combine these with weighted norm inequalities; notions of dimension are then used to characterize density conditions and to give sufficient and necessary conditions for Hardy's inequalities. At the end of the book, the theory of weak solutions to the p -Laplace equation and the use of maximal function techniques is this context are discussed. The book is directed to researchers and graduate students interested in applications of geometric and harmonic analysis in Sobolev spaces and partial differential equations.

The author's goal for the book is that it's clearly written, could be read by a calculus student and would motivate them to engage in the material and learn more. Moreover, to create a text in which exposition, graphics, and layout would work together to enhance all facets of a student's calculus experience. They paid special attention to certain aspects of the text: 1. Clear, accessible exposition that anticipates and addresses student difficulties.2. Layout and figures that communicate the flow of ideas. 3. Highlighted features that emphasize concepts and mathematical reasoning including Conceptual Insight, Graphical Insight, Assumptions Matter, Reminder, and Historical Perspective.4. A rich collection of examples and exercises of graduated difficulty that teach basic skills as well as problem-solving techniques, reinforce conceptual understanding, and motivate calculus through interesting applications. Each section also contains exercises that develop additional insights and challenge students to further develop their skills. Achieve for Calculus redefines homework by offering guidance for every student and support for every instructor. Homework is designed to teach by correcting students' misconceptions through targeted feedback, meaningful hints, and full solutions, helping teach students conceptual understanding and critical thinking in real-world contexts.

The goal of the book is to summarize those methods for evaluating Feynman integrals that have been developed over a span of more than fifty years. The book characterizes the most powerful methods and illustrates them with numerous examples starting from very simple ones and progressing to nontrivial examples. The book demonstrates how to choose adequate methods and combine evaluation methods in a non-trivial way. The most powerful methods are characterized and then illustrated through numerous examples. This is an updated textbook version of the previous book (Evaluating Feynman integrals, STMP 211) of the author.

Get ahead in pre-calculus Pre-calculus courses have become increasingly popular with 35 percent of students in the U.S. taking the course in middle or high school. Often, completion of such a course is a prerequisite for calculus and other upper level mathematics courses. Pre-Calculus For Dummies is an invaluable resource for students enrolled in pre-calculus courses. By presenting the essential topics in a clear and concise manner, the book helps students improve their understanding of pre-calculus and become prepared for upper level math courses. Provides fundamental information in an approachable manner Includes fresh example problems Practical explanations mirror today's teaching methods Offers relevant cultural references Whether used as a classroom aid or as a refresher in preparation for an introductory calculus course, this book is one you'll want to have on hand to perform your very best.