Preface To the Student To the Instructor Before You Begin . 1 The Fast Track Introduction to Calculus 1.1 What Is Calculus? Calculus as a Way of Thinking What Does "Infinitesimal Change" Mean? 1.2 Limits: The Foundation of Calculus 1.3 The Three Difficult Problems That Led to the Invention of Calculus 2 Limits: How to Approach Indefinitely (and Thus Never Arrive) 2.1 One-Sided Limits: A Graphical Approach 2.2 Existence of One-Sided Limits 2.3 Two-Sided Limits 2.

4 Continuity at a Point 2.5 Continuity on an Interval 2.6 The Limit Laws 2.7 Calculating Limits--Algebraic Techniques 2.8 Limits Approaching Infinity 2.9 Limits Yielding Infinity 2.10 Parting Thoughts Chapter 2 Exercises 3 Derivatives: Change, Quantified 3.1 Solving the Instantaneous Speed Problem 3.

2 Solving the Tangent Line Problem--The Derivative at a Point 3.3 The Instantaneous Rate of Change Interpretation of the Derivative 3.4 Differentiability: When Derivatives Do (and Don't) Exist 3.5 The Derivative, a Graphical Approach 3.6 The Derivative, an Algebraic Approach Leibniz Notation 3.7 Differentiation Shortcuts: The Basic Rules 3.8 Differentiation Shortcuts: The Power Rule 3.9 Differentiation Shortcuts: The Product Rule 3.

10 Differentiation Shortcuts: The Chain Rule 3.11 Differentiation Shortcuts: The Quotient Rule 3.12 (Optional) Derivatives of Transcendental Functions 3.13 Higher-Order Derivatives 3.14 Parting Thoughts Chapter 3 Exercises 4 Applications of Differentiation 4.1 Related Rates 4.2 Linearization 4.3 The Increasing/Decreasing Test 4.

4 Optimization Theory: Local Extrema 4.5 Optimization Theory: Absolute Extrema 4.6 Applications of Optimization 4.7 What the Second Derivative Tells Us About the Function 4.8 Parting Thoughts Chapter 4 Exercises 5 Integration: Adding Up Change 5.1 Distance as Area 5.2 Leibniz's Notation for the Integral 5.3 The Fundamental Theorem of Calculus 5.

4 Antiderivatives and the Evaluation Theorem 5.5 Indefinite Integrals 5.6 Properties of Integrals 5.7 Net Signed Area 5.8 (Optional) Integrating Transcendental Functions 5.9 The Substitution Rule 5.10 Applications of Integration 5.11 Parting Thoughts Chapter 5 Exercises Epilogue Acknowledgments Appendix A: Review of Algebra and Geometry Appendix B: Review of Functions Appendix C: Additional Applied Examples Answers to Appendix and Chapter Exercises Bibliography Index of Applications Index of Subjects.