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(NOTE: Every chapter ends with Questions to Guide Your Review, Practice Exercises, and Additional Exercises.) | |
P. Preliminaries | |
Real Numbers and the Real Line | |
Coordinates, Lines, and Increments | |
Functions | |
Shifting Graphs | |
Trigonometric Functions | |
Limits and Continuity | |
Rates of Change and Limits | |
Rules for Finding Limits | |
Target Values and Formal Definitions of Limits | |
Extensions of the Limit Concept | |
Continuity | |
Tangent Lines | |
Derivatives | |
The Derivative of a Function | |
Differentiation Rules | |
Rates of Change | |
Derivatives of Trigonometric Functions | |
The Chain Rule | |
Implicit Differentiation and Rational Exponents | |
Related Rates of Change | |
Applications of Derivatives | |
Extreme Values of Functions | |
The Mean Value Theorem | |
The First Derivative Test for Local Extreme Values | |
Graphing with y e and y deg | |
Limits as x aelig; a, Asymptotes, and Dominant Terms | |
Optimization Linearization and Differentials | |
Newton's Method | |
Integration | |
Indefinite Integrals | |
Differential Equations, Initial Value Problems, and Mathematical Modeling | |
Integration by Substitution-Running the Chain Rule Backward | |
Estimating with Finite Sums | |
Riemann Sums and Definite Integrals | |
Properties, Area, and the Mean Value Theorem | |
Substitution in Definite Integrals | |
Numerical Integration | |
Applications of Integrals | |
Areas Between Curves | |
Finding Volumes by Slicing | |
Volumes of Solids of Revolution-Disks and Washers | |
Cylindrical Shells Lengths of Plan Curves | |
Areas of Surfaces of Revolution | |
Moments and Centers of Mass | |
Work | |
Fluid Pressures and Forces | |
The Basic Pattern and Other Modeling Applications | |
Transcendental Functions | |
Inverse Functions and Their Derivatives | |
Natural Logarithms | |
The Exponential Function | |
ax and logax | |
Growth and Decay | |
L'Hocirc;pital's Rule | |
Relative Rates of Growth | |
Inverse Trigonomic Functions | |
Derivatives of Inverse Trigonometric Functions; Integrals | |
Hyperbolic Functions | |
First Order Differential Equations | |
Euler's Numerical Method; Slope Fields | |
Techniques of Integration | |
Basic Integration Formulas | |
Integration by Parts | |
Partial Fractions | |
Trigonometric Substitutions | |
Integral Tables and CAS | |
Improper Integrals | |
Infinite Series | |
Limits of Sequences of Numbers | |
Theorems for Calculating Limits of Sequences | |
Infinite Series | |
The Integral Test for Series of Nonnegative Terms | |
Comparison Tests for Series of Nonnegative Terms | |
The Ratio and Root Tests for Series of Nonnegative Terms | |
Alternating Series, Absolute and Conditional Convergence | |
Power Series | |
Taylor and Maclaurin Series | |
Convergence of Taylor Series; Error Estimates | |
Applications of Power Series | |
Conic Sections, Parametrized Curves, and Polar Coordinates | |
Conic Sections and Quadratic Equations | |
Classifying Conic Sections by Eccentricity | |
Quadratic Equations and Rotations | |
Parametrizations of Plan Curves | |
Calculus with Parametrized Curves | |
Polar Coordinates | |
Graphing in Polar Coordinates | |
Polar Equations for Conic Sections | |
Integration in Polar Coordinates | |
Vectors and Analytic Geometry in Space | |
Vectors in the Plane | |
Cartesian (Rectangular) Coordinates and Vectors in Space | |
Dot Products | |
Cross Products | |
Lines and Planes in Space | |
Cylinders and Quadric Surfaces | |
Cylindrical and Spherical Coordinates | |
Vector-Valued Functions and Motion in Space | |
Vector-Valued Functions and Space Curves | |
Modeling Projectile Motion | |
Arc Length and the Unit Tangent Vector T | |
Curvature, Torison, and the TNB Frame | |
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