Calculus: Early Transcendental FunctionsChapter 0: Preliminaries0.1, Polynomials and Rational Functions0.2, Graphing Calculators and Computer Algebra Systems0.3, Inverse Functions0.4, Trigonometric and Inverse Trigonometric Functions0.5, Exponential and Logarithmic Functions0.6, Transformations of FunctionsChapter 1: Limits and Continuity1.1, A Brief Preview of Calculus: Tangent Lines and the Length of a Curve1.2, The Concept of Limit1.3, Computation of Limits1.4, Continuity and Its Consequences1.5, Limits Involving Infinity; Asymptotes1.6, Formal Definition of the Limit1.7, Limits and Loss-of-Significance ErrorsChapter 2: Differentiation2.1, Tangent Lines and Velocity2.2, The Derivative2.3, Computation of Derivatives: The Power Rule2.4, The Product and Quotient Rules2.5, The Chain Rule2.6, Derivatives of Trigonometric Functions2.7, Derivatives of Exponential and Logarithmic Functions2.8, Implicit Differentiation and Inverse Trigonometric Functions2.9, The Hyperbolic Functions2.10, The Mean Value TheoremChapter 3: Applications of the Derivative3.1, Linear Approximations and Newton's Method3.2, Indeterminate Forms and L'Hopital's Rule 3.3, Maximum and Minimum Values3.4, Increasing and Decreasing Functions3.5, Concavity and the Second Derivative Test3.6, Overview of Curve Sketching3.7, Optimization3.8, Related Rates3.9, Rates of Change in Economics and the SciencesChapter 4: Integration4.1, Antiderivatives4.2, Sums and Sigma Notation4.3, Area4.4, The Definite Integral4.5, The Fundamental Theorem of Calculus4.6, Integration by Substitution4.7, Numerical Integration4.8, The Natural Logarithm as an IntegralChapter 5: Applications of the Definite Integral5.1, Area Between Curves5.2, Volume: Slicing, Disks and Washers5.3, Volumes by Cylindrical Shells5.4, Arc Length and Surface Area5.5, Projectile Motion5.6, Applications of Integration to Physics and Engineering5.7, ProbabilityChapter 6: Integration Techniques6.1, Review of Formulas and Techniques6.2, Integration by Parts6.3, Trigonometric Techniques of Integration6.4, Integration of Rational Functions Using Partial Fractions6.5, Integration Tables and Computer Algebra Systems6.6, Improper IntegralsChapter 7: First-Order Differential Equations7.1, Modeling with Differential Equations7.2, Separable Differential Equations7.3, Direction Fields and Euler's Method7.4, Systems of First-Order Differential EquationsChapter 8: Infinite Series8.1, Sequences of Real Numbers8.2, Infinite Series8.3, The Integral and Comparison Tests8.4, Alternating Series8.5, Absolute Convergence and the Ratio Test8.6, Power Series8.7, Taylor Series8.8, Applications of Taylor Series8.9, Fourier SeriesChapter 9: Parametric Equations and Polar Coordinates9.1, Plane Curves and Parametric Equations9.2, Calculus and Parametric Equations9.3, Arc Length and Surface Area in Parametric Equations9.4, Polar Coordinates9.5, Calculus and Polar Coordinates9.6, Conic Sections9.7, Conic Sections in Polar CoordinatesChapter 10: Vectors and the Geometry of Space10.1, Vectors in the Plane10.2, Vectors in Space10.3, The Dot Product10.4, The Cross Product10.5, Lines and Planes in Space10.6, Surfaces in SpaceChapter 11: Vector-Valued Functions11.1, Vector-Valued Functions11.2, The Calculus of Vector-Valued Functions11.3, Motion in Space11.4, Curvature11.5, Tangent and Normal Vectors11.6, Parametric SurfacesChapter 12: Functions of Several Variables and Partial Differentiation12.1, Functions of Several Variables12.2, Limits and Continuity12.3, Partial Derivatives12.4, Tangent Planes and Linear Approximations12.5, The Chain Rule12.6, The Gradient and Directional Derivatives12.7, Extrema of Functions of Several Variables12.8, Constrained Optimization and and Lagrange MultipliersChapter 13: Multiple Integrals13.1, Double Integrals13.2, Area, Volume and Center of Mass13.3, Double Integrals in Polar Coordinates13.4, Surface Area13.5, Triple Integrals13.6, Cylindrical Coordinates13.7, Spherical Coordinates13.8, Change of Variables in Multiple IntegralsChapter 14: Vector Calculus14.1, Vector Fields14.2, Line Integrals14.3, Independence of Path and Conservative Vector Fields14.4, Green's Theorem 14.5, Curl and Divergence14.6, Surface Integrals14.7, The Divergence Theorem14.8, Stokes' Theorem14.9, Applications of Vector CalculusChapter 15: Second Order Differential Equations15.1, Second-Order Equations With Constant Coefficients15.2, Nonhomogeneous Equations: Undetermined Coefficients15.3, Applications of Second-Order Equations15.4, Power Series Solutions of Differential EquationsAppendix A: Proofs of Selected TheoremsAppendix B: Answers to Odd-Numbered Exercises
