Satunino L. Salas is the author of various Wiley calculus textbooks. Garret Etgen is a professor of mathematics and the University of Houston.

• Chapter 1. Precalculus Review.11.1 What is Calculus? 11.2 Review of Elementary Mathematics.31.3 Review of Inequalities.111.4 Coordinate Plane; Analytic Geometry.171.5 Functions.241.6 The Elementary Functions.321.7 Combinations of Functions.411.8 A Note on Mathematical Proof; Mathematical Induction.47Chapter 2. Limits and Continuity.532.1 The Limit Process (An Intuitive Introduction).532.2 Definition of Limit.642.3 Some Limit Theorems.732.4 Continuity.822.5 The Pinching Theorem; Trigonometric Limits.912.6 Two Basic Theorems.97Project 2.6 The Bisection Method for Finding the Roots of f (x) = 0 102Chapter 3. The Derivative; The Process of Differentiation.1053.1 The Derivative.1053.2 Some Differentiation Formulas.1153.3 The d/dx Notation; Derivatives of Higher Order.1243.4 The Derivative as a Rate of Change.1303.5 The Chain Rule.1333.6 Differentiating the Trigonometric Functions.1423.7 Implicit Differentiation; Rational Powers.147Chapter 4. The Mean-Value Theorem; Applications of the First and Second Derivatives.1544.1 The Mean-Value Theorem.1544.2 Increasing and Decreasing Functions.1604.3 Local Extreme Values.1674.4 Endpoint Extreme Values; Absolute Extreme Values.1744.5 Some Max-Min Problems.182Project 4.5 Flight Paths of Birds 1904.6 Concavity and Points of Inflection.1904.7 Vertical and Horizontal Asymptotes; Vertical Tangents and Cusps.1954.8  Some Curve Sketching.2014.9 Velocity and Acceleration; Speed.209Project 4.9A Angular Velocity; Uniform Circular Motion 217Project 4.9B Energy of a Falling Body (Near the Surface of the Earth) 2174.10 Related Rates of Change Per Unit Time.2184.11 Differentials.223Project 4.11 Marginal Cost, Marginal Revenue, Marginal Profit 2284.12 Newton-Raphson Approximations.229Chapter 5. Integration.2345.1 An Area Problem; A Speed-Distance Problem.2345.2 The Definite Integral of a Continuous Function.2345.3 The Function f(x) = Integral from a to x of f(t) dt.2465.4The Fundamental Theorem of Integral Calculus.2545.5 Some Area Problems.260Project 5.5 Integrability; Integrating Discontinuous Functions 2665.6 Indefinite Integrals.2685.7 Working Back from the Chain Rule; the u-Substitution.2745.8 Additional Properties of the Definite Integral.2815.9 Mean-Value Theorems for Integrals; Average Value of a Function.285Chapter 6. Some Applications of the Integral.2926.1 More on Area.2926.2 Volume by Parallel Cross-Sections; Discs and Washers.2966.3 Volume by the Shell Method.3066.4 The Centroid of a Region; Pappus’s Theorem on Volumes.312Project 6.4 Centroid of a Solid of Revolution 3196.5 The Notion of Work.3196.6 Fluid Force.327Chapter 7. The Transcendental Functions.3337.1 One-to-One Functions; Inverse Functions.3337.2 The Logarithm Function, Part I.3427.3 The Logarithm Function, Part II.3477.4 The Exponential Function.356Project 7.4 Some Rational Bounds for the Number e 3647.5 Arbitrary Powers; Other Bases.3647.6 Exponential Growth and Decay.3707.7 The Inverse Trigonometric Functions.378Project 7.7 Refraction 3877.8 The Hyperbolic Sine and Cosine.3887.9 The Other Hyperbolic Functions.392Chapter 8. Techniques of Integration.3988.1 Integral Tables and Review.3988.2 Integration by Parts.402Project 8.2 Sine Waves y = sin nx and Cosine Waves y = cos nx 4108.3 Powers and Products of Trigonometric Functions.4118.4 Integrals Featuring Square Root of (a^2 – x^2), Square Root of (a^2 + x^2), and Square Root of (x^2 – a^2).4178.5 Rational Functions; Partial Functions.4228.6 Some Rationalizing Substitutions.4308.7 Numerical Integration.433Chapter 9. Some Differential Equations.4439.1 First-Order Linear Equations.4449.2 Integral Curves; Separable Equations.451Project 9.2 Orthogonal Trajectories 4589.3 The Equation y′′ + ay′+ by = 0.459Chapter 10. The Conic Sections; Polar Coordinates; Parametric Equations.46910.1 Geometry of Parabola, Ellipse, Hyperbola.46910.2 Polar Coordinates.47810.3 Graphing in Polar Coordinates.484Project 10.3 Parabola, Ellipse, Hyperbola in Polar Coordinates 49110.4 Area in Polar Coordinates.49210.5 Curves Given Parametrically.496Project 10.5 Parabolic Trajectories 50310.6 Tangents to Curves Given Parametrically.50310.7 Arc Length and Speed.50910.8 The Area of a Surface of Revolution; Pappus’s Theorem on Surface. Area 517Project 10.8 The Cycloid 525Chapter 11. Sequences; Indeterminate Forms; Improper Integrals.52811.1 The Least Upper Bound Axiom.52811.2 Sequences of Real Numbers.53211.3 The Limit of a Sequence.538Project 11.3 Sequences and the Newton-Raphson Method 54711.4 Some Important Limits.55011.5 The Indeterminate Forms (0/0).55411.6 The Indeterminate Form (∞/∞); Other Indeterminate Forms.56011.7 Improper Integrals.565Chapter 12. Infinite Series.57512.1 Sigma Notation 57512.2 Infinite Series 57712.3 The Integral Test; Basic Comparison, Limit Comparison 58512.4 The Root Test; the Ratio Test 59312.5 Absolute Convergence and Conditional Convergence; Alternating Series 59712.6 Taylor Polynomials in x; Taylor Series in x 60212.7 Taylor Polynomials and Taylor Series in x − a 61312.8 Power Series 61612.9 Differentiation and Integration of Power Series 623Project 12.9A The Binomial Series 633Project 12.9B Estimating π 634Appendix. A. Some Additional Topics. A-1A.1 Rotation of Axes; Eliminating the xy-Term A-1A.2 Determinants A-3Appendix B. Some Additional Proofs. A-8B.1 The Intermediate-Value Theorem A-8B.2 Boundedness; Extreme-Value Theorem A-9B.3 Inverses A-10B.4 The Integrability of Continuous Functions A-11B.5 The Integral as the Limit of Riemann Sums A-14Answers to Odd-Numbered Exercises A-15Index I-1Table of Integrals Inside Covers