Essential Calculus : Early Transcendental Functions

by Larson

• ISBN13: 9780618879182
• ISBN10: 0618879188
• Edition: 1st
• Format: Hardcover
• Copyright: 2007-01-10
• Publisher: Brooks Cole

Summary

Essential Calculus: Early Transcendental Functions responds to the growing demand for a more streamlined and faster paced text at a lower price for students. This text continues the Larson tradition by offering instructors proven pedagogical techniques and accessible content and innovative learning resources for student success.

Table of Contents

Limits and Their Properties

Linear Models and Rates of Change

Functions and Their Graphs

Inverse Functions

Exponential and Logarithmic Functions

Finding Limits Graphically and Numerically

Evaluating Limits Analytically

Continuity and One-Sided Limits

Infinite Limits

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

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

Concavity and the Second Derivative Test

Limits at Infinity

Optimization Problems

Differentials

Integration

Antiderivatives and Indefinite Integration

Area

Riemann Sums and Definite Integrals

The Fundamental Theorem of Calculus

Integration by Substitution

Numerical Integration

The Natural Logarithmic Function: Integration

Inverse Trigonometric Functions: Integration

Hyperbolic Functions

Applications of Integration

Area of a Region Between Two Curves

Volume: The Disk Method

Volume: The Shell Method

Arc Length and Surfaces of Revolution

Applications in Physics and Engineering

Differential Equations: Growth and Decay

Integration Techniques, L'H?pital's Rule, and Improper Integrals

Integration by Parts

Trigonometric Integrals

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

The Integral and Comparison Tests

Other Convergence Tests

Taylor Polynomials and Approximations

Power Series

Representation of Functions by Power Series

Taylor and Maclaurin Series

Conics, Parametric Equations, and Polar Coordinates

Plane Curves and Parametric Equations

Parametric Equations and Calculus

Polar Coordinates and Polar Graphs

Area and Arc Length in Polar Coordinates

Polar Equations and Conics and Kepler's Laws

Vectors and the Geometry of Space

Vectors in the Plane

Space Coordinates and Vectors in Space

The Dot Product of Two Vectors

The Cross Product of Two Vectors in Space

Lines and Planes in Space

Surfaces in Space

Cylindrical and Spherical Coordinates

Vector-Valued Functions

Vector-Valued Functions

Differentiation and Integration of Vector-Valued Functions

Velocity and Acceleration

Tangent Vectors and Normal Vectors

Arc Length and Curvature

Functions of Several Variables

Introduction to Functions of Several Variables

Limits and Continuity

Partial Derivatives

Differentials and the Chain Rule

Directional Derivatives and Gradients

Tangent Planes and Normal Lines

Extrema of Functions of Two Variables

Lagrange Multipliers

Multiple Integration

Iterated Integrals and Area in the Plane

Double Integrals and Volume

Change of Variables: Polar Coordinates

Center of Mass and Moments of Inertia

Surface Area

Triple Integrals and Applications

Triple Integrals in Cylindrical and Spherical Coordinates

Change of Variables: Jacobians

Vector Analysis

Vector Fields

Line Integrals

Conservative Vector Fields and Independence of Path

Green's Theorem

Parametric Surfaces

Surface Integrals

Divergence Theorem

Stokes's Theorem

Proofs of Selected Theorems

Integration Tables

Business and Economic Applications

Answers to Odd-Numbered

Exercises

Index

Additional Appendices

Precalculus Review

Real Numbers and the Real Number Line

The Cartesian Plane

Review of Trigonometric Functions

Rotation and General Second-Degree Equation

Complex Numbers

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