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Purchase Benefits
What is included with this book?
P. Preparation For Calculus | |
Graphs and Models | |
Linear Models and Rates of Change | |
Functions and Their Graphs | |
Fitting Models to Data Review Exercises P.S. Problem Solving | |
Limits And Their Properties | |
A Preview of Calculus | |
Finding Limits Graphically and Numerically | |
Evaluating Limits Analytically | |
Continuity and One-Sided Limits | |
Infinite Limits Section Project: Graphs and Limits of Trigonometric Functions Review Exercises P.S. Problem Solving | |
Differentiation | |
The Derivative and the Tangent Line Problem | |
Basic Differentiation Rules and Rates of Change | |
The Product and Quotient Rules and Higher-Order Derivatives | |
The Chain Rule | |
Implicit Differentiation Section Project: Optical Illusions | |
Related Rates Review Exercises P.S. Problem Solving | |
Applications Of Differentiation | |
Extrema on an Interval | |
Rolle's Theorem and the Mean Value Theorem | |
Increasing and Decreasing Functions and the First Derivative Test Section Project: Rainbows | |
Concavity and the Second Derivative TeSt. Limits at Infinity | |
A Summary of Curve Sketching | |
Optimization Problems Section Project: Connecticut River | |
Newton's Method | |
Differentials Review Exercises P.S. Problem Solving | |
Integration | |
Antiderivatives and Indefinite Integration | |
Area | |
Riemann Sums and Definite Integrals | |
The Fundamental Theorem of Calculus Section Project: Demonstrating the Fundamental Theorem | |
Integration by Substitution | |
Numerical Integration Review Exercises P.S. Problem Solving | |
Logarithmic, Exponential, And Other Transcendental Functions | |
The Natural Logarithmic Function: Differentiation | |
The Natural Logarithmic Function: Integration | |
Inverse Functions | |
Exponential Functions: Differentiation and Integration | |
Bases Other than e and Applications Section Project: Using Graphing Utilities to Estimate Slope | |
Inverse Trigonometric Functions: Differentiation | |
Inverse Trigonometric Functions: Integration | |
Hyperbolic Functions Section Project: St. Louis Arch Review Exercises P.S. Problem Solving | |
Differential Equations | |
Slope Fields and Euler's Method | |
Differential Equations: \Growth and Decay | |
Separation of Variables and the Logistic Equation | |
First-Order Linear Differential Equations Section Project: Weight Loss Review Exercises P.S. Problem Solving | |
Applications of Integration | |
Area of a Region Between Two Curves | |
Volume: The Disk Method | |
Volume: The Shell Method Section Project: Saturn | |
Arc Length and Surfaces of Revolution | |
Work Section Project: Tidal Energy | |
Moments, Centers of Mass, and Centroids | |
Fluid Pressure and Fluid Force Review Exercises P.S. Problem Solving | |
Integration Techniques, L'Hopital's Rule, and Improper Integrals | |
Basic Integration Rules | |
Integration by Parts | |
Trigonometric Integrals Section Project: Power Lines | |
Trigonometric Substitution | |
Partial Fractions | |
Integration by Tables and Other Integration Techniques | |
Indeterminate Forms and L'Hopital's Rule | |
Improper Integrals Review Exercises P.S. Problem Solving | |
Infinite Series | |
Sequences | |
Series and Convergence Section Project: Cantor's Disappearing Table | |
The Integral Test and p-Series Section Project: The Harmonic Series | |
Comparisons of Series Section Project: Solera Method | |
Alternating Series | |
The Ratio and Root Tests | |
Taylor Polynomials and Approximations | |
Power Series | |
Representation of Functions by Power Series | |
Taylor and Maclaurin Series Review Exercises P.S. Problem Solving | |
Conics, Parametric Equations, And Polar Coordinates | |
Conics and Calculus | |
Plane Curves and Parametric Equations Section Project: Cycloids | |
Parametric Equations and Calculus | |
Polar Coordinates and Polar Graphs Section Project: Anamorphic Art | |
Area and Arc Length in Polar Coordinates | |
Polar Equations of Conics and Kepler's Laws Review Exercises P.S. Problem Solving | |
Book Appendices | |
Proofs of Selected Theorems | |
Integration Tables | |
Online Appendices | |
Precalculus Review (please visit URL to come) | |
Real Numbers and the Real Number Line | |
The Cartesian Plane | |
Review of Trigonometric Functions | |
Rotation and the General Second-Degree Equation (please visit URL to come) | |
Complex Numbers (please visit URL to come) | |
Business and Economic Applications (please visit URL to come) | |
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