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Introduction 1 Part I: Pre ]Calculus Review 5 Chapter 1: Getting Down to Basics: Algebra and Geometry 7 Chapter 2: Funky Functions and Tricky Trig 25 Part II: Limits and Continuity 41 Chapter 3: A Graph Is Worth a Thousand Words: Limits and Continuity 43 Chapter 4: Nitty ]Gritty Limit Problems 53 Part III: Differentiation 79 Chapter 5: Getting the Big Picture: Differentiation Basics 81 Chapter 6: Rules, Rules, Rules: The Differentiation Handbook 91 Chapter 7: Analyzing Those Shapely Curves with the Derivative 119 Chapter 8: Using Differentiation to Solve Practical Problems 151 Chapter 9: Even More Practical Applications of Differentiation 179 Part IV: Integration and Infinite Series 197 Chapter 10: Getting into Integration 199 Chapter 11: Integration: Reverse Differentiation 219 Chapter 12: Integration Rules for Calculus Connoisseurs 235 Chapter 13: Who Needs Freud? Using the Integral to Solve Your Problems 261 Chapter 14: Infinite (Sort of) Integrals 281 Chapter 15: Infinite Series: Welcome to the Outer Limits 291 Part V: The Part of Tens 313 Chapter 16: Ten Things about Limits, Continuity, and Infinite Series 315 Chapter 17: Ten Things You Better Remember about Differentiation 319 Index 323
Mark Ryan has taught pre-algebra through calculus for more than 25 years. In 1997, he founded The Math Center in Winnetka, Illinois, where he teaches classes and tutors students in all levels of mathematics.