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(Practice Exercises, Additional Exercises, and Questions to Guide Your Review appear at the end of each chapter.)? | |
Preliminaries | |
Real Numbers and the Real Line | |
Lines, Circles, and Parabolas | |
Functions and Their Graphs | |
Identifying Functions; Mathematical Models | |
Combining Functions; Shifting and Scaling Graphs | |
Trigonometric Functions | |
Graphing with Calculators and Computers | |
Limits and Derivative? | |
Rates of Change and Limits | |
Calculating Limits Using the Limit Laws | |
Precise Definition of a Limit | |
One-Sided Limits and Limits at Infinity | |
Infinite Limits and Vertical Asymptotes | |
Continuity | |
Tangents and Derivatives | |
Differentiatio? | |
The Derivative as a Function | |
Differentiation Rules | |
The Derivative as a Rate of Change | |
Derivatives of Trigonometric Functions | |
The Chain Rule and Parametric Equations | |
Implicit Differentiation | |
Related Rates | |
Linearization and Differentials | |
Applications of Derivative? | |
Extreme Values of Functions | |
The Mean Value Theorem | |
Monotonic Functions and the First Derivative Test | |
Concavity and Curve Sketching | |
Applied Optimization Problems | |
Indeterminate Forms and L'Hopital's Rule | |
Newton's Method | |
Antiderivatives | |
Integratio? | |
Estimating with Finite Sums | |
Sigma Notation and Limits of Finite Sums | |
The Definite Integral | |
The Fundamental Theorem of Calculus | |
Indefinite Integrals and the Substitution Rule | |
Substitution and Area Between Curves | |
Applications of Definite Integral? | |
Volumes by Slicing and Rotation About an Axis | |
Volumes by Cylindrical Shells | |
Lengths of Plane Curves | |
Moments and Centers of Mass | |
Areas of Surfaces of Revolution and The Theorems of Pappus Work | |
Fluid Pressures and Forces | |
Transcendental Function? | |
Inverse Functions and their Derivatives | |
Natural Logarithms | |
The Exponential Function | |
ax and loga x | |
Exponential Growth and Decay | |
Relative Rates of Growth | |
Inverse Trigonometric Functions | |
Hyperbolic Functions | |
Techniques of Integratio? | |
Basic Integration Formulas | |
Integration by Parts | |
Integration of Rational Functions by Partial Fractions | |
Trigonometric Integrals | |
Trigonometric Substitutions | |
Integral Tables and Computer Algebra Systems | |
Numerical Integration | |
Improper Integrals | |
Further Applications of Integratio? | |
Slope Fields and Separable Differential Equations | |
First-Order Linear Differential Equations | |
Euler's Method | |
Graphical Solutions of Autonomous Equations | |
Applications of First-Order Differential Equations | |
Conic Sections and Polar Coordinate? | |
Conic Sections and Quadratic Equation? | |
Classifying Conic Sections by Eccentricity | |
Quadratic Equations and Rotations | |
Conics and Parametric Equations; The Cycloid | |
Polar Coordinate? | |
Graphing in Polar Coordinates | |
Area and Lengths in Polar Coordinates | |
Conic Sections in Polar Coordinates | |
Infinite Sequences and Serie? | |
Sequences | |
Infinite Series | |
The Integral Test | |
Compari | |
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