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Calculus with Analytic Geometry

ISBN-10: 0070577277
ISBN-13: 9780070577275
Edition: 2nd 1996 (Revised)
List price: $108.67
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Description: Written by acclaimed author and mathematician George Simmons, this revision is designed for the calculus course offered in two and four year colleges and universities. It takes an intuitive approach to calculus and focuses on the application of  More...

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Book details

List price: $108.67
Edition: 2nd
Copyright year: 1996
Publisher: McGraw-Hill Higher Education
Publication date: 6/1/1996
Binding: Paperback
Pages: 496
Size: 8.25" wide x 10.75" long x 0.75" tall
Weight: 2.090
Language: English

Written by acclaimed author and mathematician George Simmons, this revision is designed for the calculus course offered in two and four year colleges and universities. It takes an intuitive approach to calculus and focuses on the application of methods to real-world problems. Throughout the text, calculus is treated as a problem solving science of immense capability.

Numbers, Functions, and Graphs
Introduction
The Real Line and Coordinate Plane: Pythagoras
Slopes and Equations of Straight Lines
Circles and Parabolas: Descartes and Fermat
The Concept of a Function
Graphs of Functions
Introductory Trigonometry
The Functions Sin O and Cos O
The Derivative of a Function
What is Calculus ?
The Problems of Tangents
How to Calculate the Slope of the Tangent
The Definition of the Derivative
Velocity and Rates of Change: Newton and Leibriz
The Concept of a Limit: Two Trigonometric Limits
Continuous Functions: The Mean Value Theorem and Other Theorem
The Computation of Derivatives
Derivatives of Polynomials
The Product and Quotient Rules
Composite Functions and the Chain Rule
Some Trigonometric Derivatives
Implicit Functions and Fractional Exponents
Derivatives of Higher Order
Applications of Derivatives
Increasing and Decreasing Functions: Maxima and Minima
Concavity and Points of Inflection
Applied Maximum and Minimum Problems
More Maximum-Minimum Problems
Related Rates
Newtons Method for Solving Equations
Applications to Economics: Marginal Analysis
Indefinite Integrals and Differential Equations
Introduction
Differentials and Tangent Line Approximations
Indefinite Integrals: Integration by Substitution
Differential Equations: Separation of Variables
Motion Under Gravity: Escape Velocity and Black Holes
Definite Integrals
Introduction
The Problem of Areas
The Sigma Notation and Certain Special Sums
The Area Under a Curve: Definite Integrals
The Computation of Areas as Limits
The Fundamental Theorem of Calculus
Properties of Definite Integrals
Applications of Integration
Introduction: The Intuitive Meaning of Integration
The Area between Two Curves
Volumes: The Disk Method
Volumes: The Method of Cylindrical Shells
Arc Length
The Area of a Surface of Revolution
Work and Energy
Hydrostatic Force PART II
Exponential and Logarithm Functions
Introduction
Review of Exponents and Logarithms
The Number e and the Function y = e x
The Natural Logarithm Function y = ln x
Applications Population Growth and Radioactive Decay
More Applications
Trigonometric Functions
Review of Trigonometry
The Derivatives of the Sine and Cosine
The Integrals of the Sine and Cosine
The Derivatives of the Other Four Functions
The Inverse Trigonometric Functions
Simple Harmonic Motion
Hyperbolic Functions
Methods of Integration
Introduction
The Method of Substitution
Certain Trigonometric Integrals
Trigonometric Substitutions
Completing the Square
The Method of Partial Fractions
Integration by Parts
A Mixed Bag
Numerical Integration
Further Applications of Integration
The Center of Mass of a Discrete System
Centroids
The Theorems of Pappus
Moment of Inertia
Indeterminate Forms and Improper Integrals
Introduction. The Mean Value Theorem Revisited
The Interminate Form 0/0. L'Hospital's Rule
Other Interminate Forms
Improper Integrals
The Normal Distribution
Infinite Series of Constants
What is an Infinite Series ?
Convergent Sequences
Convergent and Divergent Series
General Properties of Convergent Series
Series on Non-negative Terms: Comparison Test

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