cover -- copyright page -- title page -- Preface -- Contents -- Precalculus -- Numbers and Notation in History -- Numbers, Points, and the Algebra of Inequalities -- Intervals -- Sequences and their Limits -- Real Sequences -- Limits of Real Sequences -- Convergence to Unknown Limits -- Finding Limits -- Bounded Sets -- The Bisection Algorithm (Optional) -- Continuity -- Continuous Functions -- The Intermediate Value Theorem and Inverse Functions -- Extreme Values and Bounds for Functions -- Limits of Functions -- Discontinuities -- Exponentials and Logarithms -- Epsilons and Deltas (Optional) -- Differentiation -- Slope, Speed and Tangents -- Formal Differentiation I: The Algebra of Derivatives -- Formal Differentiation II: Exponentials and Logarithms -- Formal Differentiation III: Inverse Functions -- Formal Differentiation IV: The Chain Rule and Implicit Differentiation -- Related Rates -- Extrema Revisited -- Geometric Application of Limits and Derivatives -- Mean Value Theorems -- L'Hôpital's Rule and Indeterminate Forms -- Continuity and Derivatives (Optional) -- Integration -- Area and the Definition of the Integral -- General Theory of the Riemann Integral -- The Fundamental Theorem of Calculus -- Formal Integration I: Manipulation Formulas -- Formal Integration II: Trigonometric Functions -- Formal Integration III: Rational Functions and Partial Fractions -- Improper Integrals -- Geometric Applications of Riemann Sums -- Riemann's Characterization of Integrable Functions (Optional) -- Power Series -- Local Approximation of Functions by Polynomials -- Convergence of Series -- Unconditional Convergence -- Convergence of Power Series -- Handling Power Series -- Complex Numbers and Analytic Functions (Optional) -- The Rhetoric of Mathematics (Methods of Proof) -- Answers to Selected Problems -- Bibliography -- Index -- About the Author.