Calculus: Early Transcendental Functions Chapter 0: Preliminaries 0.1, "The Real Numbers and the Cartesian Plane" 0.2, "Lines and Functions" 0.3, "Graphing Calculators and Computer Algebra Systems" 0.4, "Trigonometric Functions" 0.5, "Transformations of Functions" Chapter 1: Limits and Continuity 1.1, "A Brief Preview of Calculus: Tangent Lines and the Length of a Curve 1.2, "The Concept of Limit" 1.3, "Computation of Limits" 1.4, "Continuity and Its Consequences" 1.5, "Limits Involving Infinity; Asymptotes" 1.6, "Formal Definition of the Limit" 1.7, "Limits and LossofSignificance Errors" Chapter 2: Differentiation 2.1, "Tangent Lines and Velocity" 2.2, "The Derivative" 2.3, "Computation of Derivatives: The Power Rule" 2.4, "The Product and Quotient Rules" 2.5, "The Chain Rule" 2.6, "Derivatives of Trigonometric Functions" 2.7, "Implicit Differentiation" 2.8, "The Mean Value Theorem" Chapter 3: Applications of the Derivative 3.1, "Linear Approximations and Newton's Method" 3.2, "Maximum and Minimum Values" 3.3, "Increasing and Decreasing Functions" 3.4, "Concavity and the Second Derivative Test" 3.5, "Overview of Curve Sketching" 3.6, "Optimization" 3.7, "Related Rates" 3.8, "Rates of Change in Economics and the Sciences" Chapter 4: Integration 4.1, "Antiderivatives" 4.2, "Sums and Sigma Notation" 4.3, "Area" 4.4, "The Definite Integral" 4.5, "The Fundamental Theorem of Calculus" 4.6, "Integration by Substitution" 4.7, "Numerical Integration" Chapter 5: Applications of the Definite Integral 5.1, "Area Between Curves" 5.2, "Volume: Slicing, Disks and Washers" 5.3, "Volumes by Cylindrical Shells" 5.4, "Arc Length and Surface Area" 5.5, "Projectile Motion" 5.6, "Applications of Integration to Physics and Engineering" Chapter 6: Exponentials, Logarithms and Other Transcendental Functions 6.1, "The Natural Logarithm" 6.2, "Inverse Functions" 6.3, "The Exponential Function" 6.4, "The Inverse Trigonometric Functions" 6.5, "The Calculus of the Inverse Trigonometric Functions" 6.6, "The Hyperbolic Functions" Chapter 7: Integration Techniques 7.1, "Review of Formulas and Techniques" 7.2, "Integration by Parts" 7.3, "Trigonometric Techniques of Integration" 7.4, "Integration of Rational Functions Using Partial Fractions" 7.5, "Integration Tables and Computer Algebra Systems" 7.6, "Improper Integrals" 57.7, "Probability" Chapter 8: FirstOrder Differential Equations 8.1, "Modeling with Differential Equations" 8.2, "Separable Differential Equations" 8.3, "Direction Fields and Euler's Method" 8.4, "Systems of FirstOrder Differential Equations" Chapter 9: Infinite Series 9.1, "Sequences of Real Numbers" 9.2, "Infinite Series" 9.3, "The Integral and Comparison Tests" 9.4, "Alternating Series" 9.5, "Absolute Convergence and the Ratio Test" 9.6, "Power Series" 9.7, "Taylor Series" 9.8, "Applications of Taylor Series" 9.9, "Fourier Series" Chapter 10: Parametric Equations and Polar Coordinates 10.1, "Plane curves and Parametric Equations" 10.2, "Calculus and Parametric Equations" 10.3, "Arc Length and Surface Area in Parametric Equations" 10.4, "Polar Coordinates" 10.5, "Calculus and Polar Coordinates" 10.6, "Conic Sections" 10.7, "Conic Sections in Polar Coordinates" Chapter 11: Vectors and the Geometry of Space 11.1, "Vectors in the Plane" 11.2, "Vectors in Space" 11.3, "The Dot Product" 11.4, "The Cross Product" 11.5, "Lines and Planes in Space" 11.6, "Surfaces in Space" Chapter 12: VectorValued Functions 12.1, "VectorValued Functions" 12.2, "The Calculus of VectorValued Functions" 12.3, "Motion in Space" 12.4, "Curvature" 12.5, "Tangent and Normal Vectors" 12.6, "Parametric Surfaces" Chapter 13: Functions of Several Variables and Partial Differentiation 13.1, "Functions of Several Variables" 13.2, "Limits and Continuity" 13.3, "Partial Derivatives" 13.4, "T

