Calculus of a Single Variable Early Transcendental Functions

ISBN-10: 053873552X
ISBN-13: 9780538735520
Edition: 5th 2011
List price: $280.95 Buy it from $0.02 Rent it from $20.90
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Book details

List price: $280.95
Edition: 5th
Copyright year: 2011
Publisher: Brooks/Cole
Publication date: 1/1/2010
Binding: Hardcover
Pages: 944
Size: 8.50" wide x 10.50" long x 1.50" tall
Weight: 4.928
Language: English

Ron Larson received his PhD. in mathematics from the University of Colorado and has been a professor of mathematics at The Pennsylvania State University since 1970. He has pioneered the use of multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson has also conducted numerous seminars and in-service workshops for math teachers around the country about using computer technology as a teaching tool and motivational aid. His Interactive Calculus (a complete text on CD-ROM) received the 1996 Texty Award for the most innovative mathematics instructional material at the college level, and it was the first mainstream college textbook to be offered on the Internet.

Bruce Edwards has been a mathematics professor at the University of Florida since 1976. Dr. Edwards majored in mathematics at Stanford University, graduating in 1968. He then joined the Peace Corps and spent four years teaching math in Colombia, South America. He returned to the United States and Dartmouth in 1972, and he received his PhD. in mathematics in 1976. Dr. Edwards' research interests include the area of numerical analysis, with a particular interest in the so-called CORDIC algorithms used by computers and graphing calculators to compute function values. His hobbies include jogging, reading, chess, simulation baseball games, and travel.

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

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