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Calculus

by
Edition:
7th
ISBN13:

9780538497817

ISBN10:
0538497815
Format:
Hardcover
Pub. Date:
1/1/2011
Publisher(s):
Cengage Learning
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Summary

Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS, Seventh Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course!

Table of Contents

Diagnostic Tests
A Preview of Calculus
Functions And Limits
Four Ways to Represent a Function
Mathematical Models: A Catalog of Essential Functions
New Functions from Old Functions
The Tangent and Velocity Problems
The Limit of a Function
Calculating Limits Using the Limit Laws
The Precise Definition of a Limit
Continuity
Review
Principles of Problem Solving
Derivatives
Derivatives and Rates of Change
Writing Project: Writing Project: Early Methods for Finding Tangents
The Derivative as a Function
Differentiation Formulas
Applied Project: Building a Better Roller Coaster
Derivatives of Trigonometric Functions
The Chain Rule
Applied Project: Where Should a Pilot Start Descent?
Implicit Differentiation
Laboratory Project: Families of Implicit Curves
Rates of Change in the Natural and Social Sciences
Related Rates
Linear Approximations and Differentials
Laboratory Project: Taylor Polynomials
Review
Problems Plus
Applications Of Differentiation
Maximum and Minimum Values
Applied Project: The Calculus of Rainbows
The Mean Value Theorem
How Derivatives Affect the Shape of a Graph
Limits at Infinity
Horizontal Asymptotes
Summary of Curve Sketching
Graphing with Calculus and Calculators
Optimization Problems
Applied Project: The Shape of a Can
Newton's Method
Antiderivatives
Review
Problems Plus
Integrals
Areas and Distances
The Definite Integral
Discovery Project: Area Functions
The Fundamental Theorem of Calculus
Indefinite Integrals and the Net Change Theorem
Writing Project: Newton, Leibniz, and the Invention of Calculus
The Substitution Rule
Review
Problems Plus
Applications Of Integration
Areas Between Curves
Applied Project: The Gini Index
Volume
Volumes by Cylindrical Shells
Work
Average Value of a Function
Review
Problems Plus
Inverse Functions: Exponential, Logarithmic, And Inverse Trigonometric Functions
Inverse Functions
Instructors may cover either Sections 6.2-6.4 or Sections 6.2*-6.4*
See the Preface
Exponential Functions and Their Derivatives
Logarithmic Functions
Derivatives of Logarithmic Functions
The Natural Logarithmic Function
The Natural Exponential Function
General Logarithmic and Exponential Functions
Exponential Growth and Decay
Inverse Trigonometric Functions
Applied Project: Where to Sit at the Movies
Hyperbolic Functions
Indeterminate Forms and l'Hospital's Rule
Writing Project: The Origins of l'Hospital's Rule
Review
Problems Plus
Techniques Of Integration
Integration by Parts
Trigonometric Integrals
Trigonometric Substitution
Integration of Rational Functions by Partial Fractions
Strategy for Integration
Applied Project: Calculus and Baseball
Integration Using Tables and Computer Algebra Systems
Discovery Project: Patterns in Integrals
Approximate Integration
Improper Integrals
Review
Problems Plus
Further Applications Of Integration
Arc Length
Discovery Project: Arc Length ConteSt. Area of a Surface of Revolution
Discovery Project: Rotating on a Slant
Applications to Physics and Engineering
Discovery Project: Complementary Coffee Cups
Applications to Economics and Biology
Probability
Review
Problems Plus
Differential Equations
Modeling with Differential Equations
Direction Fields and Euler's Method
Separable Equations
Applied Project: How Fast Does a Tank Drain?
Applied Project: Which is Faster, Going Up or Coming Down?
Models for Population Growth
Linear Equations
Predator-Prey Systems
Review
Problems Plus
Parametric Equations And Polar Coordinates
Curves Defined by Parametric Equations
Laboratory Project: Families of Hypocycloids
Calculus with Parametric Curves
Laboratory Project: B?zier Curves
Polar Coordinates
Laboratory Project: Families of Polar Curves
Areas and Lengths in Polar Coordinates
Conic Sections
Conic Sections in Polar Coordinates
Review
Problems Plus
Infinite Sequences And Series
Sequences
Laboratory Project: Logistic Sequences
Series
The Integral Test and Estimates of Sums
The Comparison Tests
Alternating Series
Absolute Convergence and the Ratio and Root Tests
Strategy for Testing Series
Power Series
Representations of Functions as Power Series
Taylor and Maclaurin Series
Laboratory Project: An Elusive Limit
Writing Project: How Newton Discovered the Binomial Series
Applications of Taylor Polynomials
Applied Project: Radiation from the Stars
Review
Problems Plus
Vectors And The Geometry Of Space
Three-Dimensional Coordinate Systems
Vectors
The Dot Product
The Cross Product
Discovery Project: The Geometry of a Tetrahedron
Equations of Lines and Planes
Cylinders and Quadric Surfaces
Review
Problems Plus
Vector Functions
Vector Functions and Space Curves
Derivatives and Integrals of Vector Functions
Arc Length and Curvature
Motion in Space: Velocity and Acceleration
Applied Project: Kepler's Laws
Review
Problems Plus
Partial Derivatives
Functions of Several Variables
Limits and Continuity
Partial Derivatives
Tangent Planes and Linear Approximation
The Chain Rule
Directional Derivatives and the Gradient Vector
Maximum and Minimum Values
Applied Project: Designing a Dumpster
Discovery Project: Quadratic Approximations and Critical Points
Lagrange Multipliers
Applied Project: Rocket Science
Applied Project: Hydro-Turbine Optimization
Review
Problems Plus
Multiple Integrals
Double Integrals over Rectangles
Iterated Integrals
Double Integrals over General Regions
Double Integrals in Polar Coordinates
Applications of Double Integrals
Triple Integrals
Discovery Project: Volumes of Hyperspheres
Triple Integrals in Cylindrical Coordinates
Discovery Project: The Intersection of Three Cylinders
Triple Integrals in Spherical Coordinates
Applied Project: Roller Derby
Change of Variables in Multiple Integrals
Review
Problems Plus
Vector Calculu
Line Integrals
The Fundamental Theorem for Line Integrals
Green's Theorem
Curl and Divergence
Parametric Surfaces and Their Areas
Surface Integrals
Stokes' Theorem
Writing Project: Three Men and Two Theorems
The Divergence Theorem
Summary
Review
Problems Plus
Second-Order Differential Equations
Second-Order Linear Equations
Nonhomogeneous Linear Equations
Applications of Second-Order Differential Equations
Series Solutions
Review
Problems Plus
Appendixes
Intervals, Inequalities, and Absolute Values
Coordinate Geometry and Lines
Graphs of Second-Degree Equations
Trigonometry
Sigma Notation
Proofs of Theorems
Graphing Calculators and Computers
Complex Numbers
Answers to Odd-Numbered Exercises
Table of Contents provided by Publisher. All Rights Reserved.


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