Limits, Limits Everywhere PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Limits, Limits Everywhere PDF full book. Access full book title Limits, Limits Everywhere by David Applebaum. Download full books in PDF and EPUB format.
Author: David Applebaum
Publisher: OUP Oxford
ISBN: 0191627879
Category : Mathematics
Languages : en
Pages : 337
Get Book Here
Book Description
A quantity can be made smaller and smaller without it ever vanishing. This fact has profound consequences for science, technology, and even the way we think about numbers. In this book, we will explore this idea by moving at an easy pace through an account of elementary real analysis and, in particular, will focus on numbers, sequences, and series. Almost all textbooks on introductory analysis assume some background in calculus. This book doesn't and, instead, the emphasis is on the application of analysis to number theory. The book is split into two parts. Part 1 follows a standard university course on analysis and each chapter closes with a set of exercises. Here, numbers, inequalities, convergence of sequences, and infinite series are all covered. Part 2 contains a selection of more unusual topics that aren't usually found in books of this type. It includes proofs of the irrationality of e and π, continued fractions, an introduction to the Riemann zeta function, Cantor's theory of the infinite, and Dedekind cuts. There is also a survey of what analysis can do for the calculus and a brief history of the subject. A lot of material found in a standard university course on "real analysis" is covered and most of the mathematics is written in standard theorem-proof style. However, more details are given than is usually the case to help readers who find this style daunting. Both set theory and proof by induction are avoided in the interests of making the book accessible to a wider readership, but both of these topics are the subjects of appendices for those who are interested in them. And unlike most university texts at this level, topics that have featured in popular science books, such as the Riemann hypothesis, are introduced here. As a result, this book occupies a unique position between a popular mathematics book and a first year college or university text, and offers a relaxed introduction to a fascinating and important branch of mathematics.
Author: David Applebaum
Publisher: OUP Oxford
ISBN: 0191627879
Category : Mathematics
Languages : en
Pages : 337
Get Book Here
Book Description
A quantity can be made smaller and smaller without it ever vanishing. This fact has profound consequences for science, technology, and even the way we think about numbers. In this book, we will explore this idea by moving at an easy pace through an account of elementary real analysis and, in particular, will focus on numbers, sequences, and series. Almost all textbooks on introductory analysis assume some background in calculus. This book doesn't and, instead, the emphasis is on the application of analysis to number theory. The book is split into two parts. Part 1 follows a standard university course on analysis and each chapter closes with a set of exercises. Here, numbers, inequalities, convergence of sequences, and infinite series are all covered. Part 2 contains a selection of more unusual topics that aren't usually found in books of this type. It includes proofs of the irrationality of e and π, continued fractions, an introduction to the Riemann zeta function, Cantor's theory of the infinite, and Dedekind cuts. There is also a survey of what analysis can do for the calculus and a brief history of the subject. A lot of material found in a standard university course on "real analysis" is covered and most of the mathematics is written in standard theorem-proof style. However, more details are given than is usually the case to help readers who find this style daunting. Both set theory and proof by induction are avoided in the interests of making the book accessible to a wider readership, but both of these topics are the subjects of appendices for those who are interested in them. And unlike most university texts at this level, topics that have featured in popular science books, such as the Riemann hypothesis, are introduced here. As a result, this book occupies a unique position between a popular mathematics book and a first year college or university text, and offers a relaxed introduction to a fascinating and important branch of mathematics.
Author: David Applebaum
Publisher: Oxford University Press
ISBN: 0199640084
Category : Mathematics
Languages : en
Pages : 217
Get Book Here
Book Description
An account of elementary real analysis positioned between a popular mathematics book and a first year college or university text. This book doesn't assume knowledge of calculus and, instead, the emphasis is on the application of analysis to number theory.
Author: Sarah Adams
Publisher:
ISBN:
Category : Best friends
Languages : en
Pages : 280
Get Book Here
Book Description
I have found rock bottom. It's here, moving in with my older brother because I'm too broke to afford to live on my own. It's okay though, because we've always been close and I think I'm going to have fun living with him again.That is until I meet Cooper...Turns out, my brother has very strong opinions on the idea of me dating his best friend and is dead set against it. According to him, Cooper is everything I should stay away from: flirtatious, adventurous, non-committal, and freaking hot. (I added that last part because I feel like you need the whole picture.) My brother is right-I should stay away from Cooper James and his pretty blue eyes. He's the opposite of what I need right now.Nah-who am I kidding? I'm going for it.The Off Limits Rule is a closed door romance, perfect for readers who love lots of sizzle but no explicit content.
Author: David M. Bressoud
Publisher: Princeton University Press
ISBN: 0691218781
Category : Mathematics
Languages : en
Pages : 242
Get Book Here
Book Description
Calculus Reordered takes readers on a remarkable journey through hundreds of years to tell the story of how calculus grew to what we know today. David Bressoud explains why calculus is credited to Isaac Newton and Gottfried Leibniz in the seventeenth century, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus presents a sounder way for students to learn this fascinating area of mathematics. Delving into calculus's birth in the Hellenistic Eastern Mediterranean--especially Syracuse in Sicily and Alexandria in Egypt--as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus's evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends instead that the historical order--which follows first integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities--makes more sense in the classroom environment. Exploring the motivations behind calculus's discovery, Calculus Reordered highlights how this essential tool of mathematics came to be.
Author: Bernard R. Gelbaum
Publisher: Courier Corporation
ISBN: 0486134911
Category : Mathematics
Languages : en
Pages : 226
Get Book Here
Book Description
These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition.
Author: Michael Hauskeller
Publisher: Bloomsbury Publishing
ISBN: 1350073652
Category : Philosophy
Languages : en
Pages : 257
Get Book Here
Book Description
What is the point of living? If we are all going to die anyway, if nothing will remain of whatever we achieve in this life, why should we bother trying to achieve anything in the first place? Can we be mortal and still live a meaningful life? Questions such as these have been asked for a long time, but nobody has found a conclusive answer yet. The connection between death and meaning, however, has taken centre stage in the philosophical and literary work of some of the world's greatest writers: Fyodor Dostoyevsky, Leo Tolstoy, Soren Kierkegaard, Arthur Schopenhauer, Herman Melville, Friedrich Nietzsche, William James, Ludwig Wittgenstein, Marcel Proust, and Albert Camus. This book explores their ideas, weaving a rich tapestry of concepts, voices and images, helping the reader to understand the concerns at the heart of those writers' work and uncovering common themes and stark contrasts in their understanding of what kind of world we live in and what really matters in life.
Author: Mabel P. Malter
Publisher:
ISBN:
Category : Thought and thinking
Languages : en
Pages : 470
Get Book Here
Book Description
Author: Corey M. Dunn
Publisher: CRC Press
ISBN: 149873202X
Category : Mathematics
Languages : en
Pages : 419
Get Book Here
Book Description
Introduction to Analysis is an ideal text for a one semester course on analysis. The book covers standard material on the real numbers, sequences, continuity, differentiation, and series, and includes an introduction to proof. The author has endeavored to write this book entirely from the student’s perspective: there is enough rigor to challenge even the best students in the class, but also enough explanation and detail to meet the needs of a struggling student. From the Author to the student: "I vividly recall sitting in an Analysis class and asking myself, ‘What is all of this for?’ or ‘I don’t have any idea what’s going on.’ This book is designed to help the student who finds themselves asking the same sorts of questions, but will also challenge the brightest students." Chapter 1 is a basic introduction to logic and proofs. Informal summaries of the idea of proof provided before each result, and before a solution to a practice problem. Every chapter begins with a short summary, followed by a brief abstract of each section. Each section ends with a concise and referenced summary of the material which is designed to give the student a "big picture" idea of each section. There is a brief and non-technical summary of the goals of a proof or solution for each of the results and practice problems in this book, which are clearly marked as "Idea of proof," or as "Methodology", followed by a clearly marked formal proof or solution. Many references to previous definitions and results. A "Troubleshooting Guide" appears at the end of each chapter that answers common questions.
Author: Karen Marie Moning
Publisher: Dell
ISBN: 0399593659
Category : Fiction
Languages : en
Pages : 578
Get Book Here
Book Description
NEW YORK TIMES BESTSELLER • MacKayla Lane and Jericho Barrons return in the epic conclusion to the pulse-pounding Fever series, where a world thrown into chaos grows more treacherous at every turn. As Mac, Barrons, Ryodan, and Jada struggle to restore control, enemies become allies, right and wrong cease to exist, and the lines between life and death, lust and love, disappear completely. Black holes loom menacingly over Dublin, threatening to destroy the earth, yet the greatest danger is the one MacKayla Lane has unleashed from within: The Sinsar Dubh—a sentient book of unthinkable evil—has possessed her body and will stop at nothing in its insatiable quest for power. The fate of Man and Fae rests on destroying the book and recovering the long-lost Song of Making, the sole magic that can repair the fragile fabric of the earth. But to achieve these aims, sidhe-seers, the Nine, Seelie, and Unseelie must form unlikely alliances and make heart-wrenching choices. For Barrons and Jada, this means finding the Seelie queen, who alone can wield the mysterious song, negotiating with a lethal Unseelie prince hell-bent on ruling the Fae courts, and figuring out how to destroy the Sinsar Dubh while keeping Mac alive. This time, there’s no gain without sacrifice, no pursuit without risk, no victory without irrevocable loss. In the battle for Mac’s soul, every decision exacts a tremendous price. Karen Marie Moning’s explosive Fever series continues DARKFEVER • BLOODFEVER • FAEFEVER • DREAMFEVER • SHADOWFEVER • ICED • BURNED • FEVERBORN • FEVERSONG • HIGH VOLTAGE • KINGDOM OF SHADOW AND LIGHT
Author: Aisling McCluskey
Publisher: Oxford University Press
ISBN: 0198817568
Category : Mathematics
Languages : en
Pages : 398
Get Book Here
Book Description
Analysis underpins calculus, much as calculus underpins virtually all mathematical sciences. A sound understanding of analysis' results and techniques is therefore valuable for a wide range of disciplines both within mathematics itself and beyond its traditional boundaries. This text seeks to develop such an understanding for undergraduate students on mathematics and mathematically related programmes. Keenly aware of contemporary students' diversity of motivation, background knowledge and time pressures, it consistently strives to blend beneficial aspects of the workbook, the formal teaching text, and the informal and intuitive tutorial discussion. The authors devote ample space and time for development of confidence in handling the fundamental ideas of the topic. They also focus on learning through doing, presenting a comprehensive range of examples and exercises, some worked through in full detail, some supported by sketch solutions and hints, some left open to the reader's initiative. Without undervaluing the absolute necessity of secure logical argument, they legitimise the use of informal, heuristic, even imprecise initial explorations of problems aimed at deciding how to tackle them. In this respect they authors create an atmosphere like that of an apprenticeship, in which the trainee analyst can look over the shoulder of the experienced practitioner.
