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Calculus

ISBN-10: 013287640X

ISBN-13: 9780132876407

Edition: 1996

Authors: Robert Decker, Dale E. Varberg

List price: $47.00
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Book details

List price: $47.00
Copyright year: 1996
Publisher: Prentice Hall PTR
Publication date: 3/15/1996
Binding: Hardcover
Pages: 651
Size: 8.25" wide x 10.25" long x 1.00" tall
Weight: 2.530
Language: English

Preliminaries
Graphs and Equations
Functions
The Straight Line and Linear Functions
The Trigonometric Functions
Calculus: A First Look
Introduction to Limits Part I
Limits
Introduction to Limits Part II
The Derivative: Two Problems With One Theme
Exponential Functions
Logarithms and the Logarithmic Function
Chapter Review
Numerical and Graphical Techniques
Calculator and Computer Graphs
Calculator and Computer Graphs
Calculator and Computer Tables
Parameters
The Damped Harmonic Oscillator
Zooming and Local Linearity
Roots and Slopes: When and How Fast? Solving Equations
Linear Curve Fitting
Nonlinear Curve Fitting
Chapter Review
Derivatives
The Derivative as a Function
The Derivative as a Function
Rules for Finding Derivatives
Derivatives of Sines, Cosines, Logs and Exponentials
The Chain Rule
Higher-Order Derivatives
Implicit Differentiation and Related Rates
Differentials and Approximations
Chapter Review
Applications of the Derivative
Maxima and Minima
Increasing, Decreasing, and the Derivative
Monotonicity and Concavity
Local Maxima and Minima
Ideal Gases and Real Gases
More Max-Min Problems
Applications from Economics
Graphing with Parameters
The Mean Value Theorem
Chapter Review
The Integral
Antiderivatives (Indefinite Integrals)
Introduction to Differential Equations
The Draining Can
Area and Reimann Sums
Area and Distance
The Definite Integral and Numerical Integration
Area Functions
The Fundamental Theorem of Calculus
More Properties of the Definite Integral
Substitution
Chapter Review
Applications of the Integral
The Area of a Plane Region
Volumes of Solids: Slabs, Disks, Washers
Length of a Plane Curve
Arc Length
Work
Moments, Center of Mass
Chapter Review
Transcendental Functions and Differential Equations
Inverse Functions and Their Derivatives
A Different Approach to Logarithmic and Exponential Functions
Falling Objects
General Exponential and Logarithmic Functions
Exponential Growth and Decay
Numerical and Graphical Approaches to Differential Equations
Planning Your Retirement
The Trigonometric Functions and Their Inverses
The Hyperbolic Functions and Their Inverses
Chapter Review
Techniques of Integration
Substitution and Tables of Integrals
Integration by Parts
Integration by Parts
Some Trigonometric Integrals
Integration of Rational Functions
Population Models
Indeterminate Forms
Improper Integrals
Probability and Improper Integrals
Chapter Review
Infinite Series
Infinite Sequences and Dynamical Systems
Discrete Population Models
Infinite Series
Bouncing Balls and Infinite Series
Altering Series, Absolute Convergence
Taylor's Approximation to Functions
Taylor Series and Fourier Series
The Error in Taylor's Approximation
Newton's Method
General Power Series
The Gamma Function and Taylor Series
Approximations
Operations on Power Series
Chapter Review
Conics, Polar Coordinates and Parametric Curves
Conic Sections
Translation of Axes
The Polar Coordinate System and Graphs
Technology and Graphs of Polar Equations
Graphs in Polor Coordinates
Calculus in Polar Coordinates
Orbits of the Planets
Plane Curves: Parametric Representation
Chapter Review