{"product_id":"calculus-essentials-for-dummies-isbn-9781119591207","title":"Calculus Essentials For Dummies","description":"\u003cp\u003e\u003ci\u003eCalculus Essentials For Dummies\u003c\/i\u003e (9781119591207) was previously published as \u003ci\u003eCalculus Essentials For Dummies \u003c\/i\u003e(9780470618356). While this version features a new \u003ci\u003eDummies\u003c\/i\u003e cover and design, the content is the same as the prior release and should not be considered a new or updated product.\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eMany colleges and universities require students to take at least one math course, and Calculus I is often the chosen option. \u003ci\u003eCalculus Essentials For Dummies\u003c\/i\u003e provides explanations of key concepts for students who may have taken calculus in high school and want to review the most important concepts as they gear up for a faster-paced college course. Free of review and ramp-up material, \u003ci\u003eCalculus Essentials For Dummies\u003c\/i\u003e sticks to the point with content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical two-semester high school calculus class or a college level Calculus I course, from limits and differentiation to integration and infinite series. This guide is also a perfect reference for parents who need to review critical calculus concepts as they help high school students with homework assignments, as well as for adult learners headed back into the classroom who just need a refresher of the core concepts.\u003c\/p\u003e \u003cp\u003e\u003ci\u003e\u003cb\u003eThe Essentials For Dummies\u003c\/b\u003e\u003c\/i\u003e\u003cb\u003e Series\u003c\/b\u003e\u003cbr\u003e Dummies is proud to present our new series, \u003ci\u003eThe Essentials For Dummies\u003c\/i\u003e. Now students who are prepping for exams, preparing to study new material, or who just need a refresher can have a concise, easy-to-understand review guide that covers an entire course by concentrating solely on the most important concepts. From algebra and chemistry to grammar and Spanish, our expert authors focus on the skills students most need to succeed in a subject.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIntroduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAbout This Book 1\u003c\/p\u003e \u003cp\u003eConventions Used in This Book 2\u003c\/p\u003e \u003cp\u003eFoolish Assumptions 2\u003c\/p\u003e \u003cp\u003eIcons Used in This Book 3\u003c\/p\u003e \u003cp\u003eWhere to Go from Here 3\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1: Calculus: No Big Deal\u003c\/b\u003e\u003cb\u003e 5\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSo What is Calculus Already? 5\u003c\/p\u003e \u003cp\u003eReal-World Examples of Calculus 7\u003c\/p\u003e \u003cp\u003eDifferentiation 8\u003c\/p\u003e \u003cp\u003eIntegration 9\u003c\/p\u003e \u003cp\u003eWhy Calculus Works 11\u003c\/p\u003e \u003cp\u003eLimits: Math microscopes 11\u003c\/p\u003e \u003cp\u003eWhat happens when you zoom in 12\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2: Limits and Continuity\u003c\/b\u003e\u003cb\u003e 15\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eTaking it to the Limit 15\u003c\/p\u003e \u003cp\u003eThree functions with one limit 15\u003c\/p\u003e \u003cp\u003eOne-sided limits 17\u003c\/p\u003e \u003cp\u003eLimits and vertical asymptotes 18\u003c\/p\u003e \u003cp\u003eLimits and horizontal asymptotes 18\u003c\/p\u003e \u003cp\u003eInstantaneous speed 19\u003c\/p\u003e \u003cp\u003eLimits and Continuity 21\u003c\/p\u003e \u003cp\u003eThe hole exception 22\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3: Evaluating Limits\u003c\/b\u003e\u003cb\u003e 25\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eEasy Limits 25\u003c\/p\u003e \u003cp\u003eLimits to memorize 25\u003c\/p\u003e \u003cp\u003ePlug-and-chug limits 26\u003c\/p\u003e \u003cp\u003e“Real” Limit Problems 26\u003c\/p\u003e \u003cp\u003eFactoring 27\u003c\/p\u003e \u003cp\u003eConjugate multiplication 27\u003c\/p\u003e \u003cp\u003eMiscellaneous algebra 28\u003c\/p\u003e \u003cp\u003eLimits at Infinity 29\u003c\/p\u003e \u003cp\u003eHorizontal asymptotes 30\u003c\/p\u003e \u003cp\u003eSolving limits at infinity 31\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4: Differentiation Orientation\u003c\/b\u003e\u003cb\u003e 33\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe Derivative: It’s Just Slope 34\u003c\/p\u003e \u003cp\u003eThe slope of a line 35\u003c\/p\u003e \u003cp\u003eThe derivative of a line 36\u003c\/p\u003e \u003cp\u003eThe Derivative: It’s Just a Rate 36\u003c\/p\u003e \u003cp\u003eCalculus on the playground 36\u003c\/p\u003e \u003cp\u003eThe rate-slope connection 38\u003c\/p\u003e \u003cp\u003eThe Derivative of a Curve 39\u003c\/p\u003e \u003cp\u003eThe Difference Quotient 40\u003c\/p\u003e \u003cp\u003eAverage and Instantaneous Rate 46\u003c\/p\u003e \u003cp\u003eThree Cases Where the Derivative Does Not Exist 47\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5: Differentiation Rules\u003c\/b\u003e\u003cb\u003e 49\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eBasic Differentiation Rules 49\u003c\/p\u003e \u003cp\u003eThe constant rule 49\u003c\/p\u003e \u003cp\u003eThe power rule 49\u003c\/p\u003e \u003cp\u003eThe constant multiple rule 50\u003c\/p\u003e \u003cp\u003eThe sum and difference rules 51\u003c\/p\u003e \u003cp\u003eDifferentiating trig functions 52\u003c\/p\u003e \u003cp\u003eExponential and logarithmic functions 52\u003c\/p\u003e \u003cp\u003eDerivative Rules for Experts 53\u003c\/p\u003e \u003cp\u003eThe product and quotient rules 53\u003c\/p\u003e \u003cp\u003eThe chain rule 54\u003c\/p\u003e \u003cp\u003eDifferentiating Implicitly 59\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6: Differentiation and the Shape of Curves\u003c\/b\u003e\u003cb\u003e 61\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA Calculus Road Trip 61\u003c\/p\u003e \u003cp\u003eLocal Extrema 63\u003c\/p\u003e \u003cp\u003eFinding the critical numbers 63\u003c\/p\u003e \u003cp\u003eThe First Derivative Test 65\u003c\/p\u003e \u003cp\u003eThe Second Derivative Test 66\u003c\/p\u003e \u003cp\u003eFinding Absolute Extrema on a Closed Interval 69\u003c\/p\u003e \u003cp\u003eFinding Absolute Extrema over a Function’s Entire Domain 71\u003c\/p\u003e \u003cp\u003eConcavity and Inflection Points 73\u003c\/p\u003e \u003cp\u003eGraphs of Derivatives 75\u003c\/p\u003e \u003cp\u003eThe Mean Value Theorem 78\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 7: Differentiation Problems\u003c\/b\u003e\u003cb\u003e 81\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eOptimization Problems 81\u003c\/p\u003e \u003cp\u003eThe maximum area of a corral 81\u003c\/p\u003e \u003cp\u003ePosition, Velocity, and Acceleration 83\u003c\/p\u003e \u003cp\u003eVelocity versus speed 84\u003c\/p\u003e \u003cp\u003eMaximum and minimum height 86\u003c\/p\u003e \u003cp\u003eVelocity and displacement 87\u003c\/p\u003e \u003cp\u003eSpeed and distance travelled 88\u003c\/p\u003e \u003cp\u003eAcceleration 89\u003c\/p\u003e \u003cp\u003eTying it all together 90\u003c\/p\u003e \u003cp\u003eRelated Rates 91\u003c\/p\u003e \u003cp\u003eA calculus crossroads 91\u003c\/p\u003e \u003cp\u003eFilling up a trough 94\u003c\/p\u003e \u003cp\u003eLinear Approximation 97\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 8: Introduction to Integration \u003c\/b\u003e\u003cb\u003e101\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntegration: Just Fancy Addition 101\u003c\/p\u003e \u003cp\u003eFinding the Area under a Curve 103\u003c\/p\u003e \u003cp\u003eDealing with negative area 105\u003c\/p\u003e \u003cp\u003eApproximating Area 105\u003c\/p\u003e \u003cp\u003eApproximating area with left sums 105\u003c\/p\u003e \u003cp\u003eApproximating area with right sums 108\u003c\/p\u003e \u003cp\u003eApproximating area with midpoint sums 110\u003c\/p\u003e \u003cp\u003eSummation Notation 112\u003c\/p\u003e \u003cp\u003eSumming up the basics 112\u003c\/p\u003e \u003cp\u003eWriting Riemann sums with sigma notation 113\u003c\/p\u003e \u003cp\u003eFinding Exact Area with the Definite Integral 116\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 9: Integration: Backwards Differentiation \u003c\/b\u003e\u003cb\u003e119\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAntidifferentiation: Reverse Differentiation 119\u003c\/p\u003e \u003cp\u003eThe Annoying Area Function 121\u003c\/p\u003e \u003cp\u003eThe Fundamental Theorem 124\u003c\/p\u003e \u003cp\u003eFundamental Theorem: Take Two 126\u003c\/p\u003e \u003cp\u003eAntiderivatives: Basic Techniques 128\u003c\/p\u003e \u003cp\u003eReverse rules 128\u003c\/p\u003e \u003cp\u003eGuess and check 130\u003c\/p\u003e \u003cp\u003eSubstitution 132\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 10: Integration for Experts \u003c\/b\u003e\u003cb\u003e137\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntegration by Parts 137\u003c\/p\u003e \u003cp\u003ePicking your u 139\u003c\/p\u003e \u003cp\u003eTricky Trig Integrals 141\u003c\/p\u003e \u003cp\u003eSines and cosines 141\u003c\/p\u003e \u003cp\u003eSecants and tangents 144\u003c\/p\u003e \u003cp\u003eCosecants and cotangents 147\u003c\/p\u003e \u003cp\u003eTrigonometric Substitution 147\u003c\/p\u003e \u003cp\u003eCase 1: Tangents 148\u003c\/p\u003e \u003cp\u003eCase 2: Sines 150\u003c\/p\u003e \u003cp\u003eCase 3: Secants 151\u003c\/p\u003e \u003cp\u003ePartial Fractions 152\u003c\/p\u003e \u003cp\u003eCase 1: The denominator contains only linear factors 152\u003c\/p\u003e \u003cp\u003eCase 2: The denominator contains unfactorable quadratic factors 153\u003c\/p\u003e \u003cp\u003eCase 3: The denominator contains repeated factors 155\u003c\/p\u003e \u003cp\u003eEquating coefficients 155\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 11: Using the Integral to Solve Problems\u003c\/b\u003e\u003cb\u003e 157\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe Mean Value Theorem for Integrals and Average Value 158\u003c\/p\u003e \u003cp\u003eThe Area between Two Curves 160\u003c\/p\u003e \u003cp\u003eVolumes of Weird Solids 162\u003c\/p\u003e \u003cp\u003eThe meat-slicer method 162\u003c\/p\u003e \u003cp\u003eThe disk method 163\u003c\/p\u003e \u003cp\u003eThe washer method 165\u003c\/p\u003e \u003cp\u003eThe matryoshka doll method 166\u003c\/p\u003e \u003cp\u003eArc Length 168\u003c\/p\u003e \u003cp\u003eImproper Integrals 171\u003c\/p\u003e \u003cp\u003eImproper integrals with vertical asymptotes 171\u003c\/p\u003e \u003cp\u003eImproper integrals with infinite limits of integration 173\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 12: Eight Things to Remember \u003c\/b\u003e\u003cb\u003e175\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003ea\u003csup\u003e2\u003c\/sup\u003e- b\u003csup\u003e2\u003c\/sup\u003e = \u003c\/i\u003e(\u003ci\u003ea - b\u003c\/i\u003e)(\u003ci\u003ea + b\u003c\/i\u003e) 175\u003c\/p\u003e \u003cp\u003e\u003ci\u003e0\/5 = 0 \u003c\/i\u003eBut \u003ci\u003e5\/0 \u003c\/i\u003eis Undefined 175\u003c\/p\u003e \u003cp\u003eSohCahToa 175\u003c\/p\u003e \u003cp\u003eTrig Values to Know 176\u003c\/p\u003e \u003cp\u003e\u003ci\u003esin\u003csup\u003e2\u003c\/sup\u003e\u003c\/i\u003e\u003ci\u003eϴ + cos\u003csup\u003e2\u003c\/sup\u003eϴ = 1 \u003c\/i\u003e176\u003c\/p\u003e \u003cp\u003eThe Product Rule 176\u003c\/p\u003e \u003cp\u003eThe Quotient Rule 176\u003c\/p\u003e \u003cp\u003eYour Sunglasses 176\u003c\/p\u003e \u003cp\u003eIndex 177\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eMark Ryan\u003c\/b\u003e is the owner of The Math Center in Chicago, Illinois, where he teaches students in all levels of mathematics, from pre-algebra to calculus. He is the author of \u003ci\u003eCalculus For Dummies\u003c\/i\u003e and \u003ci\u003e Geometry For Dummies.\u003c\/i\u003e   \u003c\/p\u003e\u003cul\u003e \u003cli\u003eThe \"must-know\" formulas and equations\u003c\/li\u003e \u003cli\u003eExactly what you need to know to conquer calculus\u003c\/li\u003e \u003cli\u003eCore calculus topics in quick, focused lessons\u003c\/li\u003e\t \u003c\/ul\u003e \u003cp\u003e\u003cb\u003eThe key concepts for crushing calculus\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003eThis practical, friendly guide provides clear explanations of the core concepts you need to take your calculus skills to the next level. Understand how differentiation works, from finding the slope of a curve to finding the minimum and maximum values of a function. Discover how integration and area approximation are used to solve calculus problems. Get the lowdown on limits and continuity. And more! This book is perfect for cramming, homework help, or review. \u003c\/p\u003e\u003cp\u003e\u003cb\u003eInside...\u003c\/b\u003e \u003c\/p\u003e\u003cul\u003e \u003cli\u003eDifferentiation rules\u003c\/li\u003e \u003cli\u003eIntegration techniques\u003c\/li\u003e \u003cli\u003eThe fundamental theorem\u003c\/li\u003e \u003cli\u003eOptimization problems\u003c\/li\u003e \u003cli\u003eHow to calculate volumes of unusual solids\u003c\/li\u003e \u003cli\u003eTips for working with linear approximation\u003c\/li\u003e \u003cli\u003eReal-world examples\u003c\/li\u003e \u003c\/ul\u003e","brand":"For Dummies","offers":[{"title":"Default Title","offer_id":47988876869861,"sku":"NP9781119591207","price":12.99,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119591207.jpg?v=1761781879","url":"https:\/\/k12savings.com\/es\/products\/calculus-essentials-for-dummies-isbn-9781119591207","provider":"K12savings","version":"1.0","type":"link"}