Calculus: A Complete Introduction: Teach Yourself

Author: Hugh Neill

Publisher: Hachette UK

ISBN: 1473678455

Category: Mathematics

Page: 368

View: 8890

Calculus: A Complete Introduction is the most comprehensive yet easy-to-use introduction to using calculus. Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge. The book covers all areas of calculus, including functions, gradients, rates of change, differentiation, exponential and logarithmic functions and integration. Everything you will need to know is here in one book. Each chapter includes not only an explanation of the knowledge and skills you need, but also worked examples and test questions.

Calculus

A Complete Introduction: Teach Yourself

Author: Hugh Neill

Publisher: Teach Yourself

ISBN: 9781473678446

Category: Mathematics

Page: 388

View: 4808

Calculus: A Complete Introduction is the most comprehensive yet easy-to-use introduction to using calculus. Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge. The book covers all areas of calculus, including functions, gradients, rates of change, differentiation, exponential and logarithmic functions and integration. Everything you will need to know is here in one book. Each chapter includes not only an explanation of the knowledge and skills you need, but also worked examples and test questions.

Calculus

A Complete Course

Author: Robert A. Adams,Robert Alexander Adams

Publisher: Don Mills, Ont. : Addison-Wesley Longman

ISBN: 9780201396072

Category: Mathematics

Page: 1027

View: 9635


Trigonometrie für Dummies

Author: Mary Jane Sterling

Publisher: John Wiley & Sons

ISBN: 3527638563

Category: Mathematics

Page: 377

View: 7360

Trigonometrie besch?ftigt sich mit Winkeln und Dreiecken. Das h?rt sich ja ganz einfach an, aber jeder, der sich schon mit Trigonometrie besch?ftigen durfte, wei? wie verdammt kniffelig sie sein kann. ?Trigonometrie f?r Dummies? f?hrt die Leser in diese sonderbare Welt ein und versucht dabei auch zu zeigen wo, wann und warum es sinnvoll ist, sich mit diesem Thema zu besch?ftigen. Am Ende sind dann Sinus, Cosinus, Tangens und Cotangens keine Fremden mehr sondern gute alte Bekannte.

Fractional Calculus with Applications in Mechanics

Vibrations and Diffusion Processes

Author: Teodor M. Atanackovic,Stevan Pilipovic,Bogoljub Stankovic,Dusan Zorica

Publisher: John Wiley & Sons

ISBN: 1118577469

Category: Mathematics

Page: 336

View: 9527

This book contains mathematical preliminaries in which basicdefinitions of fractional derivatives and spaces are presented. Thecentral part of the book contains various applications in classicalmechanics including fields such as: viscoelasticity, heatconduction, wave propagation and variational Hamilton–typeprinciples. Mathematical rigor will be observed in theapplications. The authors provide some problems formulated in theclassical setting and some in the distributional setting. Thesolutions to these problems are presented in analytical form andthese solutions are then analyzed numerically. Theorems on theexistence of solutions will be presented for all examplesdiscussed. In using various constitutive equations the restrictionsfollowing from the second law of thermodynamics will beimplemented. Finally, the physical implications of obtainedsolutions will be discussed in detail.

Eine kleine Geschichte der Unendlichkeit

Author: Brian Clegg

Publisher: Rowohlt Verlag GmbH

ISBN: 364404371X

Category: Fiction

Page: 352

View: 6951

Philosophen und Mathematiker hat das Nachsinnen über das Wesen des Unendlichen buchstäblich den Verstand geraubt – und dennoch ist es ein Konzept, das immer wieder unser Leben bestimmt. In diesem mit Anekdoten und Geschichten gespickten Buch nimmt uns Brian Clegg mit auf eine Reise durch das Grenzland zwischen dem extrem Großen und dem Ultimativen, von Archimedes, der die Zahl der Sandkörner bestimmte, die das Universum füllen würden, bis zu den neuesten Theorien über die physikalische Realität des Unendlichen.

Wahrscheinlichkeitstheorie und Stochastische Prozesse

Author: Michael Mürmann

Publisher: Springer-Verlag

ISBN: 364238160X

Category: Mathematics

Page: 428

View: 2795

Dieses Lehrbuch beschäftigt sich mit den zentralen Gebieten einer maßtheoretisch orientierten Wahrscheinlichkeitstheorie im Umfang einer zweisemestrigen Vorlesung. Nach den Grundlagen werden Grenzwertsätze und schwache Konvergenz behandelt. Es folgt die Darstellung und Betrachtung der stochastischen Abhängigkeit durch die bedingte Erwartung, die mit der Radon-Nikodym-Ableitung realisiert wird. Sie wird angewandt auf die Theorie der stochastischen Prozesse, die nach der allgemeinen Konstruktion aus der Untersuchung von Martingalen und Markov-Prozessen besteht. Neu in einem Lehrbuch über allgemeine Wahrscheinlichkeitstheorie ist eine Einführung in die stochastische Analysis von Semimartingalen auf der Grundlage einer geeigneten Stetigkeitsbedingung mit Anwendungen auf die Theorie der Finanzmärkte. Das Buch enthält zahlreiche Übungen, teilweise mit Lösungen. Neben der Theorie vertiefen Anmerkungen, besonders zu mathematischen Modellen für Phänomene der Realität, das Verständnis.​

Meilensteine der Mathematik

Author: Ian Stewart

Publisher: Spektrum Akademischer Verlag

ISBN: 9783827423009

Category: Science

Page: 288

View: 8350

Wer hat die Null erfunden? Wie können imaginäre Zahlen helfen, dass reale Wolkenkratzer nicht umfallen? Wo treffen sich parallele Linien? Und wann haben Sie heute zuletzt abstrakte Algebra genutzt? (Doch, Sie haben.) Wie die Mathematik die moderne Welt erschaffen hat – eine illustrierte Geschichte der Mathematik für ein breites Publikum, von den Ursprüngen im Zweistromland bis zur Gegenwart Ian Stewarts spannende Geschichte der Mathematik führt uns von der frühen Hochkultur der Babylonier bis zu den letzten ungelösten Rätseln dieser Disziplin. In typisch Stewart'scher Manier, also unterhaltsam und zugleich fundiert, schildert und erklärt er die großen Meilensteine der Mathematik – von den ersten Zahlensystemen bis zur Chaostheorie – und geht der Frage nach, welche Auswirkungen sie auf die Gesellschaft hatten und wie sie den Alltag auf alle Zeit veränderten. Er bringt uns dabei auch die Geistesgrößen der Mathematik näher, von den Naturforschern und Denkern Babyloniens, Griechenlands und Ägyptens über Newton und Descartes bis zu Fermat, Babbage und Gödel. Ohne den Leser mit komplizierten Formeln zu erschrecken, macht er die Schlüsselkonzepte der Mathematik verständlich. Als anregender historischer Streifzug für den interessierten Laien steckt Meilensteine der Mathematik voller faszinierender Details und kurioser Anekdoten. Hundert Abbildungen und Diagramme beleuchten und erhellen ein Gebiet, das von vielen Menschen gefürchtet wird, das aber unsere heutige Welt entscheidend geprägt hat.

Calculus of Variations and Optimal Control Theory

A Concise Introduction

Author: Daniel Liberzon

Publisher: Princeton University Press

ISBN: 0691151873

Category: Mathematics

Page: 235

View: 3432

This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control

Calculus and Analysis

A Combined Approach

Author: Horst R. Beyer

Publisher: John Wiley & Sons

ISBN: 0470617950

Category: Mathematics

Page: 671

View: 2742

A NEW APPROACH TO CALCULUS THAT BETTER ENABLES STUDENTS TO PROGRESS TO MORE ADVANCED COURSES AND APPLICATIONS Calculus and Analysis: A Combined Approach bridges the gap between mathematical thinking skills and advanced calculus topics by providing an introduction to the key theory for understanding and working with applications in engineering and the sciences. Through a modern approach that utilizes fully calculated problems, the book addresses the importance of calculus and analysis in the applied sciences, with a focus on differential equations. Differing from the common classical approach to the topic, this book presents a modern perspective on calculus that follows motivations from Otto Toeplitz's famous genetic model. The result is an introduction that leads to great simplifications and provides a focused treatment commonly found in the applied sciences, particularly differential equations. The author begins with a short introduction to elementary mathematical logic. Next, the book explores the concept of sets and maps, providing readers with a strong foundation for understanding and solving modern mathematical problems. Ensuring a complete presentation, topics are uniformly presented in chapters that consist of three parts: Introductory Motivations presents historical mathematical problems or problems arising from applications that led to the development of mathematical solutions Theory provides rigorous development of the essential parts of the machinery of analysis; proofs are intentionally detailed, but simplified as much as possible to aid reader comprehension Examples and Problems promotes problem-solving skills through application-based exercises that emphasize theoretical mechanics, general relativity, and quantum mechanics Calculus and Analysis: A Combined Approach is an excellent book for courses on calculus and mathematical analysis at the upper-undergraduate and graduate levels. It is also a valuable resource for engineers, physicists, mathematicians, and anyone working in the applied sciences who would like to master their understanding of basic tools in modern calculus and analysis.

Introduction to Stochastic Calculus with Applications

Author: Fima C. Klebaner

Publisher: Imperial College Press

ISBN: 1860945554

Category: Mathematics

Page: 416

View: 7770

This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.

Stochastic Calculus

A Practical Introduction

Author: Richard Durrett

Publisher: CRC Press

ISBN: 9780849380716

Category: Mathematics

Page: 341

View: 807

This compact yet thorough text zeros in on the parts of the theory that are particularly relevant to applications . It begins with a description of Brownian motion and the associated stochastic calculus, including their relationship to partial differential equations. It solves stochastic differential equations by a variety of methods and studies in detail the one-dimensional case. The book concludes with a treatment of semigroups and generators, applying the theory of Harris chains to diffusions, and presenting a quick course in weak convergence of Markov chains to diffusions. The presentation is unparalleled in its clarity and simplicity. Whether your students are interested in probability, analysis, differential geometry or applications in operations research, physics, finance, or the many other areas to which the subject applies, you'll find that this text brings together the material you need to effectively and efficiently impart the practical background they need.

Introduction to Calculus and Analysis Volume II/2

Chapters 5 - 8

Author: Richard Courant,Fritz John

Publisher: Springer Science & Business Media

ISBN: 9783540665700

Category: Mathematics

Page: 412

View: 3143

From the reviews: "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students." --Acta Scientiarum Mathematicarum, 1991

Introduction to Stochastic Processes, Second Edition

Author: Gregory F. Lawler

Publisher: CRC Press

ISBN: 9781584886518

Category: Mathematics

Page: 248

View: 5915

Emphasizing fundamental mathematical ideas rather than proofs, Introduction to Stochastic Processes, Second Edition provides quick access to important foundations of probability theory applicable to problems in many fields. Assuming that you have a reasonable level of computer literacy, the ability to write simple programs, and the access to software for linear algebra computations, the author approaches the problems and theorems with a focus on stochastic processes evolving with time, rather than a particular emphasis on measure theory. For those lacking in exposure to linear differential and difference equations, the author begins with a brief introduction to these concepts. He proceeds to discuss Markov chains, optimal stopping, martingales, and Brownian motion. The book concludes with a chapter on stochastic integration. The author supplies many basic, general examples and provides exercises at the end of each chapter. New to the Second Edition: Expanded chapter on stochastic integration that introduces modern mathematical finance Introduction of Girsanov transformation and the Feynman-Kac formula Expanded discussion of Itô's formula and the Black-Scholes formula for pricing options New topics such as Doob's maximal inequality and a discussion on self similarity in the chapter on Brownian motion Applicable to the fields of mathematics, statistics, and engineering as well as computer science, economics, business, biological science, psychology, and engineering, this concise introduction is an excellent resource both for students and professionals.

1089 oder das Wunder der Zahlen

eine Reise in die Welt der Mathematik

Author: David J. Acheson

Publisher: N.A

ISBN: 9783866470200

Category:

Page: 189

View: 7894

Das Buch beginnt mit einem alten Zaubertrick - Man nehme eine 3-stellige Zahl, etwa 782, kehre sie um, ziehe die kleinere von der größeren ab und addiere dazu die Umkehrung. Also - 782 - 287 = 495, dann 495 + 594. Und schon ist man mitten in der Wunderwelt der Mathematik, denn das Ergebnis ist immer - 1089. Mit solchen und vielen weiteren Beispielen aus Alltag, Geschichte und Wissenschaft gelingt es David Acheson, die faszinierende Welt der Mathematik zu erschließen - ein geistreicher Überblick, eine für jeden verständliche Einführung.

Advanced Calculus

An Introduction to Modern Analysis

Author: Voxman

Publisher: CRC Press

ISBN: 9780824769499

Category: Mathematics

Page: 696

View: 681

Introduction to linear algebra and ordinary differential equations; Limits and metric spaces; Continuity, compactness and connectedness; The derivative: theory and elementary applications; A first look at integration; Differentiation of functions of several variables; An introduction to fourier analysis; An introduction to modern integration theory; An introduction to complex integration.

Introduction to the Calculus of Variations and Control with Modern Applications

Author: John A. Burns

Publisher: CRC Press

ISBN: 146657139X

Category: Mathematics

Page: 562

View: 926

Introduction to the Calculus of Variations and Control with Modern Applications provides the fundamental background required to develop rigorous necessary conditions that are the starting points for theoretical and numerical approaches to modern variational calculus and control problems. The book also presents some classical sufficient conditions and discusses the importance of distinguishing between the necessary and sufficient conditions. In the first part of the text, the author develops the calculus of variations and provides complete proofs of the main results. He explains how the ideas behind the proofs are essential to the development of modern optimization and control theory. Focusing on optimal control problems, the second part shows how optimal control is a natural extension of the classical calculus of variations to more complex problems. By emphasizing the basic ideas and their mathematical development, this book gives you the foundation to use these mathematical tools to then tackle new problems. The text moves from simple to more complex problems, allowing you to see how the fundamental theory can be modified to address more difficult and advanced challenges. This approach helps you understand how to deal with future problems and applications in a realistic work environment.

Introduction To The Calculus of Variations And Its Applications, Second Edition

Author: Frederic Wan

Publisher: CRC Press

ISBN: 9780412051418

Category: Mathematics

Page: 640

View: 9254

This comprehensive text provides all information necessary for an introductory course on the calculus of variations and optimal control theory. Following a thorough discussion of the basic problem, including sufficient conditions for optimality, the theory and techniques are extended to problems with a free end point, a free boundary, auxiliary and inequality constraints, leading to a study of optimal control theory.