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Informationen zum Autor Mark Ryan 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 Calculus For Dummies and Geometry For Dummies. Klappentext The "must-know" formulas and equations Exactly what you need to know to conquer calculus Core calculus topics in quick, focused lessons The key concepts for crushing calculus This 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. Inside... Differentiation rules Integration techniques The fundamental theorem Optimization problems How to calculate volumes of unusual solids Tips for working with linear approximation Real-world examples Zusammenfassung "The must-know formulas and equations! exactly what you need to know to conquer calculus! core calculus topics in quick! focused lessons"--cover. Inhaltsverzeichnis Introduction 1 About This Book 1 Conventions Used in This Book 2 Foolish Assumptions 2 Icons Used in This Book 3 Where to Go from Here 3 Chapter 1: Calculus: No Big Deal 5 So What is Calculus Already? 5 Real-World Examples of Calculus 7 Differentiation 8 Integration 9 Why Calculus Works 11 Limits: Math microscopes 11 What happens when you zoom in 12 Chapter 2: Limits and Continuity 15 Taking it to the Limit 15 Three functions with one limit 15 One-sided limits 17 Limits and vertical asymptotes 18 Limits and horizontal asymptotes 18 Instantaneous speed 19 Limits and Continuity 21 The hole exception 22 Chapter 3: Evaluating Limits 25 Easy Limits 25 Limits to memorize 25 Plug-and-chug limits 26 "Real" Limit Problems 26 Factoring 27 Conjugate multiplication 27 Miscellaneous algebra 28 Limits at Infinity 29 Horizontal asymptotes 30 Solving limits at infinity 31 Chapter 4: Differentiation Orientation 33 The Derivative: It's Just Slope 34 The slope of a line 35 The derivative of a line 36 The Derivative: It's Just a Rate 36 Calculus on the playground 36 The rate-slope connection 38 The Derivative of a Curve 39 The Difference Quotient 40 Average and Instantaneous Rate 46 Three Cases Where the Derivative Does Not Exist 47 Chapter 5: Differentiation Rules 49 Basic Differentiation Rules 49 The constant rule 49 The power rule 49 The constant multiple rule 50 The sum and difference rules 51 Differentiating trig functions 52 Exponential and logarithmic functions 52 Derivative Rules for Experts 53 The product and quotient rules 53 The chain rule 54 Differentiating Implicitly 59 Chapter 6: Differentiation and the Shape of Curves 61 A Calculus Road Trip 61 Local Extrema 63 Finding the critical numbers 63 The First Derivative Test 65 The Second Derivative Test 66 Finding Absolute Extrema on a Closed Interval 69 Finding Absolute Extrema over a Function's Entire Domain 71 Concavity and Inflection Points 73 Graphs of Derivatives 75 The Mean Value Theorem 78 Chapter 7: Differentiation Problems 81 Optimization Proble...
