9780618879182

Essential Calculus : Early Transcendental Functions

by
  • ISBN13:

    9780618879182

  • ISBN10:

    0618879188

  • Edition: 1st
  • Format: Nonspecific Binding
  • Copyright: 2007-01-10
  • Publisher: Brooks Cole

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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
Table of Contents provided by Publisher. All Rights Reserved.

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