Kelley - The Complete Idiot's Guide to Calculus - (Alpha 2nd ed 2006), matma

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//-->CalculusSecond Editionby W. Michael KelleyA member of Penguin Group (USA) Inc.For Nick, Erin, and Sara, the happiest kids I know. I only hope that 10 years from nowyou’ll still think Dad is funny and smile when he comes home from work.ALPHA BOOKSPublished by the Penguin GroupPenguin Group (USA) Inc., 375 Hudson Street, New York, New York 10014, USAPenguin Group (Canada), 90 Eglinton Avenue East, Suite 700, Toronto, Ontario M4P 2Y3, Canada (a division ofPearson Penguin Canada Inc.)Penguin Books Ltd., 80 Strand, London WC2R 0RL, EnglandPenguin Ireland, 25 St. Stephen's Green, Dublin 2, Ireland (a division of Penguin Books Ltd.)Penguin Group (Australia), 250 Camberwell Road, Camberwell, Victoria 3124, Australia (a division of PearsonAustralia Group Pty. Ltd.)Penguin Books India Pvt. Ltd., 11 Community Centre, Panchsheel Park, New Delhi—110 017, IndiaPenguin Group (NZ), 67 Apollo Drive, Rosedale, North Shore, Auckland 1311, New Zealand (a division of PearsonNew Zealand Ltd.)Penguin Books (South Africa) (Pty.) Ltd., 24 Sturdee Avenue, Rosebank, Johannesburg 2196, South AfricaPenguin Books Ltd., Registered Offices: 80 Strand, London WC2R 0RL, EnglandCopyright © 2006 by W. Michael KelleyAll rights reserved. No part of this book shall be reproduced, stored in a retrieval system, or transmitted by anymeans, electronic, mechanical, photocopying, recording, or otherwise, without written permission from the pub-lisher. No patent liability is assumed with respect to the use of the information contained herein. Although everyprecaution has been taken in the preparation of this book, the publisher and author assume no responsibility forerrors or omissions. Neither is any liability assumed for damages resulting from the use of information containedherein. For information, address Alpha Books, 800 East 96th Street, Indianapolis, IN 46240.THE COMPLETE IDIOT’S GUIDE TO and Design are registered trademarks of Penguin Group (USA) Inc.International Standard Book Number:1-4362-1548-XLibrary of Congress Catalog Card Number: 2006920724Note:This publication contains the opinions and ideas of its author. It is intended to provide helpful and informa-tive material on the subject matter covered. It is sold with the understanding that the author and publisher are notengaged in rendering professional services in the book. If the reader requires personal assistance or advice, a compe-tent professional should be consulted.The author and publisher specifically disclaim any responsibility for any liability, loss, or risk, personal or otherwise,which is incurred as a consequence, directly or indirectly, of the use and application of any of the contents of thisbook.Publisher:Marie Butler-KnightEditorial Director/Acquisitions Editor:Mike SandersManaging Editor:Billy FieldsDevelopment Editor:Ginny BessSenior Production Editor:Janette LynnCopy Editor:Ross PattyCartoonist:Chris EliopoulosBook Designers:Trina Wurst/Kurt OwensIndexer:Brad HerrimanLayout:Rebecca HarmonProofreader:John EtchisonContents at a GlancePart 1:The Roots of Calculus1 What Is Calculus, Anyway?Everyone’s heard of calculus, but most people wouldn’t recognize it ifit bit them on the arm.132 Polish Up Your Algebra SkillsShake out the cobwebs and clear out the comical moths that fly outof your algebra book when it’s opened.133 Equations, Relations, and Functions, Oh My!Before you’re off to see the calculus wizard, you’ll have to meet hishenchmen.254 Trigonometry: Last Stop Before CalculusTime to nail down exactly what is meant by cosine, once and for all,and why it has nothing to do with loans.37Part 2:Laying the Foundation for Calculus5 Take It to the LimitLearn how to gauge a function’s intentions—are they always honorable?53556577896 Evaluating Limits NumericallyTheory, shmeory. How do I do my limit homework? It’s due in an hour!7 ContinuityEnsuring a smooth ride for the rest of the course.8 The Difference QuotientTime to meet the most famous limit of them all face to face. Try todo something with your hair!Part 3:The Derivative9 Laying Down the Law for DerivativesAll the major rules and laws of derivatives in one delicioussmorgasbord!9910110 Common Differentiation TasksThe chores you’d do day in and day out if your evil stepmother werea mathematician.11311 Using Derivatives to GraphHow to put a little wiggle in your graph, or why the Puritans werenot big fans of calculus.12312 Derivatives and MotionIntroducing position, velocity, acceleration, and Peanut the cat!13514313 Common Derivative ApplicationsThe rootin’-tootin’ orneriest hombres of the derivative world.Part 4:The Integral14 Approximating AreaIf you can find the area of a rectangle, then you’re in business.15515716715 AntiderivativesOnce you get good at driving forward, it’s time to put it in reverseand see how things go.16 Applications of the Fundamental TheoremYou can do so much with something simple like definite integralsthat you’ll feel like a mathematical Martha Stewart.17717 Integration Tips for FractionsYou’ll have to integrate fractions out the wazoo, so you might aswell come to terms with them now.18718 Advanced Integration MethodsAdvance from integration apprentice to master craftsman.19720719 Applications of IntegrationWho knew that spinning graphs in three dimensions could be sodang fun?Part 5:Differential Equations, Sequences, Series, and Salutations20 Differential EquationsJust like ordinary equations, but with a creamy filling.21922123121 Visualizing Differential EquationsWhat could be more fun than drawing a ton of teeny-weenylittle line segments?22 Sequences and SeriesIf having an infinitely long list of numbers isn’t excitingenough, try adding them together!24323 Infinite Series Convergence TestsAre you actually going somewhere with that long-windedlist of yours?25124 Special SeriesSeries that think they’re functions. (I think I saw this ondaytime TV.)26325 Final ExamHow absorbent is your brain? Have you mastered calculus?Get ready to put yourself to the test.275AppendixesA Solutions to “You’ve Got Problems”B GlossaryIndex291319329ContentsPart 1: The Roots of Calculus1 What Is Calculus, Anyway?13What’s the Purpose of Calculus? ........................................................4Finding the Slopes of Curves ............................................................4Calculating the Area of Bizarre Shapes ............................................4Justifying Old Formulas ....................................................................4Calculate Complicatedx-Intercepts....................................................5Visualizing Graphs ..........................................................................5Finding the Average Value of a Function ..........................................5Calculating Optimal Values ..............................................................6Who’s Responsible for This? ............................................................6Ancient Influences ............................................................................7Newton vs. Leibniz ..........................................................................9Will I Ever Learn This? ..................................................................112 Polish Up Your Algebra Skills13Walk the Line: Linear Equations ....................................................14Common Forms of Linear Equations ..............................................14Calculating Slope ............................................................................16You’ve Got the Power: Exponential Rules ......................................17Breaking Up Is Hard to Do: Factoring Polynomials ......................19Greatest Common Factors ..............................................................20Special Factoring Patterns ..............................................................20Solving Quadratic Equations ............................................................21Method One: Factoring ..................................................................21Method Two: Completing the Square ..............................................22Method Three: The Quadratic Formula ..........................................233 Equations, Relations, and Functions, Oh My!25What Makes a Function Tick? ........................................................26Functional Symmetry ......................................................................28Graphs to Know by Heart ................................................................30Constructing an Inverse Function ..................................................31Parametric Equations ......................................................................33What’s a Parameter? ......................................................................33Converting to Rectangular Form ....................................................334 Trigonometry: Last Stop Before Calculus37Getting Repetitive: Periodic Functions ..........................................38Introducing the Trigonometric Functions ......................................39Sine (Written as y = sin x) ..............................................................39Cosine (Written as y = cos x) ............................................................39Tangent (Written as y = tan x) ........................................................40 [ Pobierz całość w formacie PDF ]
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