Patrick Jones has a master’s degree in mathematics from the University of Louisville and has taught at the University of Louisville, Vanderbilt University, and Austin Community College. Jones now primarily spends his time expanding his YouTube video library as PatrickJMT and has amassed more than 280,000 subscribers.

Introduction 1

Part I: The Questions 5

Chapter 1: Algebra Review 7

Chapter 2: Trigonometry Review 17

Chapter 3: Limits and Rates of Change 29

Chapter 4: Derivative Basics 43

Chapter 5: The Product, Quotient, and Chain Rules 49

Chapter 6: Exponential and Logarithmic Functions and Tangent Lines 55

Chapter 7: Implicit Differentiation 59

Chapter 8: Applications of Derivatives 63

Chapter 9: Areas and Riemann Sums 75

Chapter 10: The Fundamental Theorem of Calculus and the Net Change Theorem 79

Chapter 11: Applications of Integration 87

Chapter 12: Inverse Trigonometric Functions, Hyperbolic Functions, and L'Hopital's Rule 99

Chapter 13: U-Substitution and Integration by Parts 107

Chapter 14: Trigonometric Integrals, Trigonometric Substitution, and Partial Fractions 113

Chapter 15: Improper Integrals and More Approximating Techniques 121

Part II: The Answers 125

Chapter 16: Answers and Explanations 127

Index 595

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