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| P. Preliminaries | |
| Lines | |
| Functions and Graphs | |
| Exponential Functions | |
| Inverse Functions and Logarithms | |
| Trigonometric Functions and Their Inverses | |
| Parametric Equations | |
| Modeling Change | |
| Limits and Continuity | |
| Rates of Change and Limits | |
| Finding Limits and One-Sided Limits | |
| Limits Involving Infinity | |
| Continuity | |
| Tangent Lines | |
| Derivatives | |
| The Derivative as a Function | |
| The Derivative as a Rate of Change | |
| Derivatives of Products, Quotients, and Negative Powers | |
| Derivatives of Trigonometric Functions | |
| The Chain Rule | |
| Implicit Differentiation | |
| Related Rates | |
| Derivatives of Inverse Trigonometric Functions | |
| Derivatives of Exponential and Logarithmic Functions | |
| Applications of Derivatives | |
| Extreme Values of Functions | |
| The Mean Value Theorem and Differential Equations | |
| The Shape of a Graph | |
| Graphical Solutions of Autonomous Differential Equations | |
| Modeling and Optimization | |
| Linearization and Differentials | |
| Newton's Method | |
| Integration | |
| Indefinite Integrals, Differential Equations, and Modeling | |
| Integral Rules | |
| Integration by Substitution | |
| Estimating with Finite Sums | |
| Riemann Sums and Definite Integrals | |
| The Mean Value and Fundamental Theorems | |
| Substitution in Definite Integrals | |
| Numerical Integration | |
| Applications of Integrals | |
| Volumes by Slicing and Rotation About an Axis | |
| Modeling Volume Using Cylindrical Shells | |
| Lengths of Plane Curves | |
| First Order Separable Differential Equations | |
| Springs, Pumping and Lifting | |
| Fluid Forces | |
| Moments and Centers of Mass | |
| Transcendental Functions and Differential Equations | |
| Logarithms | |
| Exponential Functions | |
| Linear First-Order Differential Equations | |
| Euler's Method | |
| Population Models | |
| Hyperbolic Functions | |
| Integration Techniques, L'Hôpital's Rule, and Improper Integrals | |
| Basic Integration Formulas | |
| Integration by Parts | |
| Partial Fractions | |
| Trigonometric Substitutions | |
| Integral Tables, Computer Algebra Systems, and Monte Carlo Integration | |
| L'Hôpital's Rule | |
| Improper Integrals | |
| Infinite Series | |
| Limits of Sequences of Numbers | |
| Subsequences, Bounded Sequences, and Picard's Method | |
| Infinite Series | |
| Series of Nonnegative Terms | |
| Alternating Series, Absolute and Conditional Convergence | |
| Power Series | |
| Taylor and Maclaurin Series | |
| Applications of Power Series | |
| Fourier Series | |
| Fourier Cosine and Sine Series | |
| Vectors in the Plane and Polar Functions | |
| Vectors in the Plane | |
| Dot Products | |
| Vector-Valued Functions | |
| Modeling Projectile Motion | |
| Polar Coordinates and Graphs | |
| Calculus of Polar Curves | |
| Vectors and Motion in Space | |
| Cartesian (Rectangular) Coordinates and Vectors in Space | |
| Dot and Cross Products | |
| Lines and Planes in Space | |
| Cylinders and Quadric Surfaces | |
| Vector-Valued Functions and Space Curves | |
| Arc Length and the Unit Tangent Vector T | |
| The TNB Frame | |
| Tangential and Normal Components of Acceleration | |
| Planetary Motion and Satellites | |
| Multivariable Functions and Their Derivatives | |
| Functions of Several Variables | |
| Limits and Continuity in Higher Dimensions | |
| Partial Derivatives | |
| The Chain Rule | |
| Directional Derivatives, Gradient Vectors, and Tangent Planes | |
| Linearization and Differentials | |
| Extreme Values and Saddle Points | |
| Lagrange Multipliers | |
| Partial Derivatives with Constrained Variables | |
| Taylor's Formula for Two Variables | |
| Multiple Integrals | |
| Double Integrals | |
| Areas, Moments, and Centers of Mass | |
| Double Integrals in Polar Form | |
| Triple Integrals in Rectangular Coordinates | |
| Masses and Moments in Three Dimensions | |
| Triple Integrals in Cylindrical and Spherical Coordinates | |
| Substitutions in Multiple Integrals | |
| Integration in Vector Fields | |
| Line Integrals | |
| Vector Fields, Work, Circulation, and Flux | |
| Path Independence, Potential Functions, and Conservative Fields | |
| Green's Theorem in the Plane | |
| Surface Area and Surface Integrals | |
| Parametrized Surfaces | |
| Stokes' Theorem | |
| Divergence Theorem and a Unified Theory | |
| Appendices | |
| Mathematical Induction | |
| Proofs of Limit Theorems in Section | |
| Proof of the Chain Rule | |
| Complex Numbers | |
| Simpson's One-Third Rule | |
| Cauchy's Mean Mean Value Theorem and the Stronger Form of L'Hôpital's Rule | |
| Limits That Arise Frequently | |
| Proof of Taylor's Theorem | |
| The Distributive Law for Vector Cross Products | |
| Determinants and Cramer's Rule | |
| The Mixed Derivative Theorem and the Increment Theorem | |
| The Area of a Parallelogram's Projection on a Plane | |
| Table of Contents provided by Publisher. All Rights Reserved. |
