Calculus Early Transcendental Functions

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  • Edition: 5th
  • Format: Hardcover
  • Copyright: 2010-01-01
  • Publisher: Brooks Cole
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Designed for the three-semester engineering calculus course, CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, 5/e, continues to offer users innovative teaching and learning resources. The Larson team always has two main objectives for book revisions: to develop precise, readable materials for users that clearly define and demonstrate concepts and rules of calculus; and to design comprehensive teaching resources for users that employ proven pedagogical techniques and save time. The Larson/Edwards Calculus program offers a solution to address the needs of any calculus course and any level of calculus user. Every edition from the first to the fourth 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.

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
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
Antiderivatives and Indefinite Integration
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
Section Project: Tidal Energy
Moments, Centers of Mass, and Centroids
Fluid Pressure and Fluid Force
Integration Techniques, L'H?pital'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
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
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
Section Project: Distances in Space
Surfaces in Space
Cylindrical and Spherical Coordinates
Vector-Valued Functions
Vector-Valued Functions
Section Project: Witch of Agnesi
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
Section Project: Moire Fringes
Chain Rules for Functions of Several Variables
Directional Derivatives and Gradients
Tangent Planes and Normal Lines
Section Project: Wildflowers
Extrema of Functions of Two Variables
Applications of Extrema of Functions of Two Variables
Section Project: Building a Pipeline
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
Section Project: Center of Pressure on a Sail
Surface Area
Section Project: Capillary Action
Triple Integrals and Applications
Triple Integrals in Cylindrical and Spherical Coordinates
Section Project: Wrinkled and Bumpy Spheres
Change of Variables: Jacobians
Vector Analysis
Vector Fields
Line Integrals
Conservative Vector Fields and Independence of Path
Green's Theorem
Section Project: Hyperbolic and Trigonometric Functions
Parametric Surfaces
Surface Integrals
Section Project: Hyperboloid of One Sheet
Divergence Theorem
Stoke's Theorem
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