《袖珍数学手册》（英文版第四版）Pocket Book of Integrals and Mathematical Formulas

Pocket book of Integrals and Mathematical formulas 4th Edition L=∫.√+(4/d)d (MG) (R+H) Ronald J Tallarida Chapman Hall/CRC

Pocket book of Integrals and Mathematical formulas 4th edition

Pocket Book of Integrals and Mathematical Formulas 4th Edition

Pocket Book of Integrals and Mathematical Formulas 4th Edition Ronald J. Tallarida Temple University Philadelphia, Pennsylvania, U.S.A

Pocket book of Integrals and Mathematical formulas 4th edition Ronald J. Tallarida Temple Universit CRC Press A CHAPMAN HALL BOoK

Pocket Book of Integrals and Mathematical Formulas 4th Edition Ronald J. Tallarida Temple University Philadelphia, Pennsylvania, U.S.A

parkway NV Boca Raton, FL D2008 by Taylor Francis Group, LLC Chapman Hall/CRC is an imprint of Taylor Francis Group, an Informa business alted States of America on acid-free pap International Standard Book Number-13 978-1-4200-6304-2(Softcover) obtalned from aut shillito the copyright holders ofa er U.S. Copyright Law, no part of this book may be reprinted, reproduced, cluding photocopying, microtulmin recording, or in any in ermission to photocopy or use material electronically from this work Pcenter, Inc (CCC) od Drive, Damers, MA 01923, 978-750-8400. CCC is a not-forprof photocopy license by the CCC. system of payment has Library of Congress Cataloging-in-Publication Data integrals and mathematical formulas/author. Includes bibliographical references and index. Mathematics.Tables. I. Title 2007045335 the C httpe//www.crcpress.com

Chapman & Hall/CRC Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487‑2742 © 2008 by Taylor & Francis Group, LLC Chapman & Hall/CRC is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid‑free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number‑13: 978‑1‑4200‑6304‑2 (Softcover) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The Authors and Publishers have attempted to trace the copyright holders of all material reproduced in this publi‑ cation and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www. copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978‑750‑8400. CCC is a not‑for‑profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging‑in‑Publication Data Tallarida, Ronald J. Pocket book of integrals and mathematical formulas / author, Ronald J. Tallarida. ‑‑ 4th ed. p. cm. Includes bibliographical references and index. ISBN 978‑1‑4200‑6304‑2 (alk. paper) 1. Integrals‑‑Tables. 2. Mathematics‑‑Tables. I. Title. QA310.T35 2008 510.2’12‑‑dc22 2007045335 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

Preface to the fourth edition As in the previous works, this new edition preserves the ontent, size, and convenience of this portable reference source for students and workers who use mathematic while introducing much new material. New in this fourth edition is an expanded chapter on series that now includes many fascinating properties of the natural numbers that follow from number theory, a field that has attracted much new interest since the recent proof of Fermat's last theorem. While the proofs of many of these theorems are deep, and in some cases still lacking, all the number theory topics included here are easy to describe and form bridge between arithmetic and higher mathematic fourth edition also includes new applications such as the eostationary satellite orbit, drug kinetics(as an applica tion of differential equations), and an expanded statistics section that now discusses the normal approximation of the binomial distribution as well as a treatment of non- linear regression. The widespread use of computers now makes the latter topic amenable to all students, and thus ll users of the pocket Book of integrals can benefit from the concise summary of this topic. The chapter on financial mathematics, introduced in the third edition, has proved successful and is retained without change in this edition hereas the Table of Integrals has been reformatted for easier usage. This change in format also allowed the inclu- sion of all the new topics without the necessity of increas- appeal as a true, handy pocket book that students and pro- fessionals will find useful in their mathematical pursuits R.. T Philadelphia

Preface to the Fourth Edition As in the previous works, this new edition preserves the content, size, and convenience of this portable reference source for students and workers who use mathematics, while introducing much new material. New in this fourth edition is an expanded chapter­ on series that now includes many fascinating properties of the natural numbers that follow from number theory, a field that has attracted much new interest since the recent proof of Fermat’s last theorem. While the proofs of many of these theorems are deep, and in some cases still lacking, all the number theory topics included here are easy to describe and form a bridge between arithmetic and higher mathematics. The fourth edition also includes new applications such as the geostationary satellite orbit, drug kinetics (as an applica￾tion of differential equations), and an expanded statistics section that now discusses the normal approximation of the binomial distribution as well as a treatment of non￾linear regression. The widespread use of computers now makes the latter topic amenable to all students, and thus all users of the Pocket Book of Integrals can benefit from the concise summary of this topic. The chapter on financial mathematics, introduced in the third edition, has proved successful and is retained without change in this edition, whereas the Table of Integrals has been reformatted for easier usage. This change in format also allowed the inclu￾sion of all the new topics without the necessity of increas￾ing the physical size of the book, thereby keeping its wide appeal as a true, handy pocket book that students and pro￾fessionals will find useful in their mathematical pursuits. R. J. T. Philadelphia Chapman & Hall/CRC Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487‑2742 © 2008 by Taylor & Francis Group, LLC Chapman & Hall/CRC is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid‑free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number‑13: 978‑1‑4200‑6304‑2 (Softcover) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The Authors and Publishers have attempted to trace the copyright holders of all material reproduced in this publi‑ cation and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www. copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978‑750‑8400. CCC is a not‑for‑profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging‑in‑Publication Data Tallarida, Ronald J. Pocket book of integrals and mathematical formulas / author, Ronald J. Tallarida. ‑‑ 4th ed. p. cm. Includes bibliographical references and index. ISBN 978‑1‑4200‑6304‑2 (alk. paper) 1. Integrals‑‑Tables. 2. Mathematics‑‑Tables. I. Title. QA310.T35 2008 510.2’12‑‑dc22 2007045335 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

Preface to the Third Edition This new edition has been enlarged to contain all the mate- rial in the second edition, an expanded chapter on statistics includes sample size estimations for means and portions, and a totally new chapter on financial math- ematics In adding this new chapter we have also included a number of tables that aid in performing the calculations on annuities, true interest, amortization schedules, compound interest, systematic withdrawals from interest accounts, etc. The treatment and style of this material reflect the rest of the book, i.e, clear explanations of concepts, relevant formulas, and worked examples. The new financial material includes analyses not readily found in other sources, such as the effect f lump sum payments on amortization schedules and a novel in-out formula"that calculates current regular deposits to avings in order to allow the start of systematic withdrawals of a specified amount at a later date. While many engineer mathematicians, and scientists have found much use for this handy pocket book, this new edition extends its usage to them and to the many business persons and individuals who make financial calculations Philadelphia

Preface to the Third Edition This new edition has been enlarged to contain all the mate￾rial in the second edition, an expanded chapter on statistics that now includes sample size estimations for means and proportions, and a totally new chapter on financial math￾ematics. In adding this new chapter we have also included a number of tables that aid in performing the calculations on annuities, true interest, amortization schedules, compound interest, systematic withdrawals from interest accounts, etc. The treatment and style of this material reflect the rest of the book, i.e., clear explanations of concepts, relevant formulas, and worked examples. The new financial material includes analyses not readily found in other sources, such as the effect of lump sum payments on amortization schedules and a novel “in-out formula” that calculates current regular deposits to savings in order to allow the start of systematic withdrawals of a specified amount at a later date. While many engineers, mathematicians, and scientists have found much use for this handy pocket book, this new edition extends its usage to them and to the many business persons and individuals who make financial calculations. R. J. T. Philadelphia

Preface to the Second edition This second edition has been enlarged by the addition of sev- eral new topics while preserving its convenient pocket size. New in this edition are the following topics: Z-transforms, orthogonal polynomials, Bessel functions, probability an a summary of the most common probability distributions(binomial, Poisson, normal, t, Chi square, and F), the error function, and several topics in multivariable calculus that include surface area and volume, the ideal gas laws, and a table of centroids of common plane shapes. A list of physical constants has also been added to this edition. I am grateful for many valuable suggestions from users of the first edition, especially Lt. Col. W.E. Skeith and his olleagues at the U.S. Air Force Academy R.. T Philadelphia, 1992

Preface to the Second Edition This second edition has been enlarged by the addition of sev￾eral new topics while preserving its convenient pocket size. New in this edition are the following topics: z-transforms, orthogonal polynomials, Bessel functions, probability and Bayes’ rule, a summary of the most common probability distributions (­binomial, Poisson, normal, t, Chi square, and F), the error function, and several topics in multivariable calculus that include surface area and volume, the ideal gas laws, and a table of centroids of common plane shapes. A list of physical constants has also been added to this edition. I am grateful for many valuable suggestions from users of the first edition, especially Lt. Col. W. E. Skeith and his colleagues at the U.S. Air Force Academy. R. J. T. Philadelphia, 1992

Preface to the first edition The material of this book has been compiled so that it may serve the needs of students and teachers as well as profes- sional workers who use mathematics. The contents and siz make it especially convenient and portable. The widespread availability and low price of scientific calculators have greatly reduced the need for many numerical tables(e.g, logarithms, trigonometric functions, powers, etc. )that make most handbooks bulky. However, most calculators do not give integrals, derivatives, series, and other mathematical formulas and figures that are often needed. Accordingly, this book contains that information in addition to a comprehen- sive table of integrals. a section on statistics and the accom- panying tables, also not readily provided by calculators, have also been included The size of the book is comparable to that of many calcula- tors, and it is really very much a companion to the calcula- tor and the computer as a source of information for writing ones own programs. To facilitate such use, the author and the publisher have worked together to make the format tractive and clear. Yet, an important requirement in a book of this kind is accuracy. Toward that end we have checked each item against at least two independent sources. Students and professionals alike will find this book a valu- ble supplement to standard textbooks, a source for review. and a handy reference for many years Ronald tallarida

Preface to the First Edition The material of this book has been compiled so that it may serve the needs of students and teachers as well as profes￾sional workers who use mathematics. The contents and size make it especially convenient and portable. The widespread availability and low price of scientific calculators have greatly reduced the need for many numerical tables (e.g., logarithms, trigonometric functions, powers, etc.) that make most handbooks bulky. However, most calculators do not give integrals, derivatives, series, and other mathematical formulas and figures that are often needed. Accordingly, this book contains that information in addition to a comprehen￾sive table of integrals. A section­ on statistics and the accom￾panying tables, also not readily provided by calculators, have also been included. The size of the book is comparable to that of many calcula￾tors, and it is really very much a companion to the calcula￾tor and the computer as a source of information for writing one’s own programs. To facilitate such use, the author and the publisher have worked together to make the format attractive and clear. Yet, an important requirement in a book of this kind is accuracy. Toward that end we have checked each item against at least two independent sources. Students and professionals alike will find this book a valu￾able supplement to standard textbooks, a source for review, and a handy reference for many years. Ronald J. Tallarida Philadelphia

About the author Ronald Tallarida holds B.S. and M.S. degrees in physics/ mathematics and a Ph. D. in pharmacology. His primary appointment is professor of pharmacology at Temple Univer sity School of Medicine, Philadelphia. For over 30 years he o served as an adjunct professor of biomedical engineer ing at Drexel University in Philadelphia where he received the lindback Award for Distinguished Teaching of math- matics. As an author and researcher, he has published over 250 works that include seven books, has been the recipient of research grants from NIH, and has served as a consultant to both industry and government agencies. His main research interests are in the areas of mathematical modeling of bio- logical systems, feedback control, and the action of drugs nd drug combination

About the Author Ronald J. Tallarida holds B.S. and M.S. degrees in physics/ mathematics and a Ph.D. in pharmacology. His primary appointment is professor of pharmacology at Temple Univer￾sity School of Medicine­, Philadelphia. For over 30 years he also served as an adjunct professor­ of biomedical engineer￾ing at Drexel University in Philadelphia where he received the Lindback Award for Distinguished Teaching of Math￾ematics. As an author and researcher, he has published over 250 works that include seven books, has been the recipient of research grants from NIH, and has served as a consultant to both industry and government agencies. His main research interests are in the areas of mathematical modeling of bio￾logical systems, feedback control, and the action of drugs and drug combinations