Stewart Calculus
1 Functions and Limits 1.1 Four Ways to Represent a Function 1.2 Mathematical Models: A Catalog of Essential Functions 1.3 New Functions from Old Functions 1.4 The Tangent and Velocity Problems 1.5 The Limit of a Function 1.6 Calculating Limits Using the Limit Laws 1.7 The Precise Definition of a Limit 1.8 Continuity 2 Derivatives 2.1 Derivatives and Rates of Change 2.2 The Derivative as a Function 2.3 Differentiation Formulas 2.4 Derivatives of Trigonometric Functions 2.5 The Chain Rule 2.6 Implicit Differentiation 2.7 Rates of Change in the Natural and Social Sciences 2.8 Related Rates 2.9 Linear Approximations and Differentials 3 Applications of Differentiation 3.1 Maximum and Minimum Values 3.2 The Mean Value Theorem 3.3 How Derivatives Affect the Shape of a Graph 3.4 Limits at Infinity; Horizontal Asymptotes 3.5 Summary of Curve Sketching 3.6 Graphing with Calculus and Calculators 3.7 Optimization Problems 3.8 Newton's Method 3.9 Antiderivatives 4 Integrals 4.1 Areas and Distances 4.2 The Definite Integral 4.3 The Fundamental Theorem of Calculus 4.4 Indefinite Integrals and the Net Change Theorem 4.5 The Substitution Rule 5 Applications of Integration 5.1 Areas Between Curves 5.2 Volumes 5.3 Volumes by Cylindrical Shells 5.4 Work 5.5 Average Value of a Function 6 Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions 6.1 Inverse Functions 6.2 Exponential Functions and Their Derivatives 6.2* The Natural Logarithmic Function 6.3 Logarithmic Functions 6.3* The Natural Exponential Function 6.4 Derivatives of Logarithmic Functions 6.4* General Logarithmic and Exponential Functions 6.5 Exponential Growth and Decay 6.6 Inverse Trigonometric Functions 6.7 Hyperbolic Functions 6.8 Indeterminate Forms and l'Hospital's Rule 7 Techniques of Integration 7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonometric Substitution 7.4 Integration of Rational Functions by Partial Fractions 7.5 Strategy for Integration 7.6 Integration Using Tables and Computer Algebra Systems 7.7 Approximate Integration 7.8 Improper Integrals 8 Further Applications of Integration 8.1 Arc Length 8.2 Area of a Surface of Revolution 8.3 Applications to Physics and Engineering 8.4 Applications to Economics and Biology 8.5 Probability 9 Differential Equations 9.1 Modeling with Differential Equations 9.2 Direction Fields and Euler's Method 9.3 Separable Equations 9.4 Models for Population Growth 9.5 Linear Equations 9.6 Predator-Prey Systems 10 Parametric Equations and Polar Coordinates 10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves 10.3 Polar Coordinates 10.4 Areas and Lengths in Polar Coordinates 10.5 Conic Sections 10.6 Conic Sections in Polar Coordinates (SV AP*) 10 Curves in Parametric, Vector, and Polar Form (SV AP*) 10.1 Curves Defined by Parametric Equations (SV AP*) 10.2 Calculus with Parametric Curves (SV AP*) 10.3 Vectors in Two Dimensions (SV AP*) 10.4 Vector Functions and Their Derivatives (SV AP*) 10.5 Curvilinear Motion: Velocity and Acceleration (SV AP*) 10.6 Polar Coordinates (SV AP*) 10.7 Areas and Lengths in Polar Coordinates (SV AP*) 10.8 Conic Sections (SV AP*) 10.9 Conic Sections in Polar Coordinates 11 Infinite Sequences and Series 11.1 Sequences 11.2 Series 11.3 The Integral Test and Estimates of Sums 11.4 The Comparison Tests 11.5 Alternating Series 11.6 Absolute Convergence and the Ratio and Root Tests 11.8 Power Series 11.9 Representations of Functions as Power Series 11.10 Taylor and Maclaurin Series 11.11 Applications of Taylor Polynomials 12 Vectors and the Geometry of Space 12.1 Three-Dimensional Coordinate Systems 12.2 Vectors 12.3 The Dot Product 12.4 The Cross Product 12.5 Equations of Lines and Planes 12.6 Cylinders and Quadric Surfaces 13 Vector Functions 13.1 Vector Functions and Space Curves 13.2 Derivatives and Integrals of Vector Functions 13.3 Arc Length and Curvature 13.4 Motion in Space: Velocity and Acceleration 14 Partial Derivatives 14.1 Functions of Several Variables 14.2 Limits and Continuity 14.3 Partial Derivatives 14.4 Tangent Planes and Linear Approximations 14.5 The Chain Rule 14.6 Directional Derivatives and the Gradient Vector 14.7 Maximum and Minimum Values 14.8 Lagrange Multipliers 15 Multiple Integrals 15.1 Double Integrals over Rectangles 15.2 Iterated Integrals 15.3 Double Integrals over General Regions 15.4 Double Integrals in Polar Coordinates 15.5 Applications of Double Integrals 15.6 Surface Area 15.7 Triple Integrals 15.8 Triple Integrals in Cylindrical Coordinates 15.9 Triple Integrals in Spherical Coordinates 15.10 Change of Variables in Multiple Integrals 16 Vector Calculus 16.1 Vector Fields 16.2 Line Integrals 16.3 The Fundamental Theorem for Line Integrals 16.4 Green's Theorem 16.5 Curl and Divergence 16.6 Parametric Surfaces and Their Areas 16.7 Surface Integrals 16.8 Stokes' Theorem 16.9 The Divergence Theorem 17 Second-Order Differential Equations 17.1 Second-Order Linear Equations 17.2 Nonhomogeneous Linear Equations 17.3 Applications of Second-Order Differential Equations 17.4 Series Solutions Appendixes Appendix G : Graphing Calculators and Computers