Tabla de contenidos provista por Syndetics

• 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 Solving Equations
• 0.5 Trigonometric Functions
• 0.6 Exponential and Logarithmic Functions
• 0.7 Transformations of Functions
• 0.8 Preview of Calculus
• 1 Limits and Continuity
• 1.1 The Concept of Limit
• 1.2 Computation of Limits
• 1.3 Continuity and its Consequences
• 1.4 Limits Involving Infinity
• 1.5 Formal Definition of the Limit
• 1.6 Limits and Loss-of-Significance Errors
• 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 Derivatives of Trigonometric Functions
• 2.6 Derivatives of Exponential and Logarithmic Functions
• 2.7 The Chain Rule
• 2.8 Implicit Differentiation and Related Rates
• 2.9 The Mean Value Theorem
• 3 Applications of Differentiation
• 3.1 Linear Approximations adn L'Hopital's Rule
• 3.2 Newton's Method
• 3.3 Maximum and Minimum Values
• 3.4 Increasing and Decreasing Functions
• 3.5 Concavity
• 3.6 Overview of Curve Sketching
• 3.7 Optimization
• 3.8 Rates of Change in Applications
• 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
• 5 Applications of the Definite Integral
• 5.1 Area Between Curves
• 5.2 Volume
• 5.3 Volumes by Cylindrical Shells
• 5.4 Arc Length and Surface Area
• 5.5 Projectile Motion
• 5.6 Work, Moments, and Hydrostatic Force
• 5.7 Probability
• 6 Exponentials, Logarithms, and Other Transcendental Functions
• 6.1 The Natural Logarithm Revisited
• 6.2 Inverse Functions
• 6.3 The Exponential Function Revisited
• 6.4 Growth and Decay Problems
• 6.5 Separable Differential Equations
• 6.6 Euler's Method
• 6.7 The Inverse Trigonometric Functions
• 6.8 The Calculus of the Inverse Trigonometric Functions
• 6.9 The Hyperbolic Functions
• 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 Indeterminate Forms and L'Hopital's Rule
• 7.7 Improper Integrals
• 8 Infinite Series
• 8.1 Sequences of Real Numbers
• 8.2 Infinite Series
• 8.3 The Integral Test and Comparison Tests
• 8.4 Alternating Series
• 8.5 Absolute Convergence and the Ratio Test
• 8.6 Power Series
• 8.7 Taylor Series
• 8.8 Fourier Series
• 9 Parametric Equations and Polar Coordinates
• 9.1 Plane Curves and Parametric Equations
• 9.2 Calculus and Parametric Equations
• 9.3 Arc Length and Surface Area in Parametric Equations
• 9.4 Polar Coordinates
• 9.5 Calculus and Polar Coordinates
• 9.6 Conic Sections
• 9.7 Conic Sections in Polar Coordinates
• 10 Vectors and the Geometry of Space
• 10.1 Vectors in the Plane
• 10.2 Vectors in Space
• 10.3 The Dot Product
• 10.4 The Cross Product
• 10.5 Lines and Planes in Space
• 10.6 Surfaces in Space
• 11 Vector-Valued Functions
• 11.1 Vector-Valued Functions
• 11.2 The Calculus of Vector-Valued Functions
• 11.3 Motion in Space
• 11.4 Curvature
• 11.5 Tangent and Normal Vectors
• 12 Functions of Several Variables and Differentiation
• 12.1 Functions of Several Variables
• 12.2 Limits and Continuity
• 12.3 Partial Derivatives
• 12.4 Tangent Planes and Linear Approximations
• 12.5 The Chain Rule
• 12.6 The Gradient and Directional Derivatives
• 12.7 Extrema of Functions of Several Variables
• 12.8 Constrained Optimization and Lagrange Multipliers
• 13 Multiple Integrals
• 13.1 Double Integrals
• 13.2 Area, Volume and Center of Mass
• 13.3 Double Integrals in Polar Coordinates
• 13.4 Surface Area
• 13.5 Triple Integrals
• 13.6 Cylindrical Coordinates