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# Calculus of a Single Variable : Early Transcendental Functions

**by**Larson, Ron; Edwards, Bruce H.

5th

### 9780538735520

053873552X

Hardcover

1/1/2010

Brooks Cole

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## Summary

**The Single Variable portion of Calculus: Early Transcendental Functions, 5/e**, offers students innovative learning resources. Every edition from the first to the fifth of

**Calculus: Early Transcendental Functions, 5/e**has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas.

Larson writes a very clear, straight forward calculus book for students. The book has very good examples to help a student or teacher explain a topic. There are plenty of practice problems, with answers for the odd questions in the back. It provides examples and problems that also meet the **AP Calculus AB and BC curriculum**.

## Table of Contents

Preparation for Calculus | |

Graphs and Models | |

Linear Models and Rates of Change | |

Functions and Their Graphs | |

Fitting Models to Data | |

Inverse Functions | |

Exponential and Logarithmic Functions | |

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 | |

Differentiation | |

The Derivative and the Tangent Line Problem | |

Basic Differentiation Rules and Rates of Change | |

Product and Quotient Rules and Higher-Order Derivatives | |

The Chain Rule | |

Implicit Differentiation | |

Section Project: Optical Illusions | |

Derivatives of Inverse Functions | |

Related Rates | |

Newton's Method | |

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 | |

Differentials | |

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 | |

The Natural Logarithmic Function: Integration | |

Inverse Trigonometric Functions: Integration | |

Hyperbolic Functions | |

Section Project: St. Louis Arch | |

Differential Equations | |

Slope Fields and Euler's Method | |

Differential Equations: Growth and Decay | |

Differential Equations: Separation of Variables | |

The Logistic Equation | |

First-Order Linear Differential Equations | |

Section Project: Weight Loss | |

Predator-Prey Differential Equations | |

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 | |

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'H?pital's Rule | |

Improper Integrals | |

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 | |

Conics, Parametric Equations, and Polar Coordinates | |

Conics and Calculus | |

Plane Curves and Parametric Equations | |

Section Projects: 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 | |

Table of Contents provided by Publisher. All Rights Reserved. |