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Calculus Early Vectors

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ISBN-10: 0534493483

ISBN-13: 9780534493486

Edition: 1999

Authors: James Stewart, Arthur Belmonte, Albert Boggess, Dante DeBlassie

List price: $269.95
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Once again keeping a keen ear to the needs of the evolving calculus community, Stewart created this text at the suggestion and with the collaboration of professors in the mathematics department at Texas A&M University. With an early introduction to vectors and vector functions, the approach is ideal for engineering students who use vectors early in their curriculum. Stewart begins by introducing vectors in Chapter 1, along with their basic operations, such as addition, scalar multiplication, and dot product. The definition of vector functions and parametric curves is given at the end of Chapter 1 using a two-dimensional trajectory of a projectile as motivation. Limits, derivatives, and…    
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Book details

List price: $269.95
Copyright year: 1999
Publisher: Brooks/Cole
Publication date: 5/9/2003
Binding: Hardcover
Pages: 1120
Size: 8.50" wide x 10.00" long x 2.00" tall
Weight: 5.082
Language: English

Review and Preview
Functions and Their Graphs
Types of Functions
Shifting and Scaling
Graphing Calculators and Computers
Principles of Problem Solving
A Preview of Calculus
Introduction to Vectors and Vector Functions
Vectors
The Dot Product
Vector Functions
Review
Limits and Rates of Change
The Tangent and Velocity Problems
The Limit of a Function
Calculating Limits Using the Limit Law
The Precise Definition of a Limit
Continuity
Limits at Infinity
Horizontal Asymptotes
Tangents, Velocities, and Other Rates of Change
Review
Derivatives
Derivatives
Differentiation Formulas
Rates of Change in the Natural and Social Sciences
Derivatives of Trigonometric Functions
The Chain Rule
Implicit Differentiation
Derivatives of Vector Functions
Higher Derivatives
Slopes and Tangents of Parametric Curves
Related Rates
Differentials; Linear and Quadratic Approximations
Newton's Method
Review
Problems Plus
Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions
Exponential Functions and Their Derivatives
Inverse Functions
Logarithmic Functions
Derivatives of Logarithmic Functions
Exponential Growth and Decay
Inverse Trigonometric Functions
Hyperbolic Functions
Indeterminate Forms and L'Hospital's Rule
Review
Applications Plus
Applications of Differentiation
What does f Say about f?
Maximum and Minimum Values
Derivatives and the Shapes of Curves
Graphing with Calculus and Calculators
Applied Maximum and Minimum Problems
Applications to Economics
Antiderivatives
Review
Problems Plus
Integrals
Sigma Notation
Area
The Definite Integral
The Fundamental Theorem of Calculus
The Substitution Rule
The Logarithm Defined as an Integral
Review
Applications Plus
Applications of Integration
Areas between Curves
Volume
Volumes by Cylindrical Shells
Work
Average Value of a Function
Review
Problems Plus
Techniques of Integration
Integration by Parts
Trigonometric Integrals
Trigonometric Substitution
Integration of Rational Functions by Partial Fractions
Rationalizing Substitutions
Strategy for Integration
Using Tables of Integrals and Computer Algebra Systems
Approximate Integration
Improper Integrals
Review
Applications Plus
Further Applications of Integration
Differential Equations
First-Order Linear Equations
Arc Length
Area of Surface of Revolution
Moments and Centers of Mass
Hydrostatic Pressure and Force
Applications to Economics and Biology
Review
Problems Plus
Infinite Sequences and Series
Sequences
Series
The Integral Test and Comparison Tests
Other Convergence Tests
Power Series
Representation of Functions as Power Series
Taylor and Maclaurin Series
The Binomial Series
Writing Project: How Newton Discovered the Binomial Series
Applications of Taylor Polynomials
Review
Applications Plus
Three-Dimensional Analytic Geometry and Vectors
Three-Dimensional Coordinate Systems
Vectors and the Dot Product in Three Dimension
The Cross Product
Equations of Lines and Planes
Quadric Surfaces
Vector Functions and Space Curves
Arc Length and Curvature
Motion in Space
Review
Applications Plus
Partial Derivatives
Functions of Several Variables
Limits and Continuity
Partial Derivatives
Tangent Planes and Differentials
The Chain Rule
Directional Derivatives and the Gradient Vector
Maximum and Minimum Values
Lagrange Multipliers
Review
Problems Plus
Multiple Integrals
Double Integrals over Rectangles
Iterated Integrals
Double Integrals over General Regions
Polar Coordinates
Applications of Double Integrals
Surface Area
Triple Integrals
Cylindrical and Spherical Coordinates
Triple Integrals in Cylindrical and Spherical Coordinates
Change of Variables in Multiple Integrals
Review
Applications Plus
Vector Calculus
Vector Fields
Line Integrals
The Fundamental Theorem for Line Integrals
Green's Theorem
Curl and Divergence
Parametric Surfaces and their Areas
Surface Integrals
Stoke's Theorem
The Divergence Theorem
Summary
Review
Problems Plus
Second-Order Differential Equations
Second-Order Linear Equations
Nonhomogeneous Linear Equations
Applications of Second-Order Differential Equations
Using Series to Solve Differential Equations
Review
Problems Plus
Numbers, Inequalities, and Absolute Values
Coordinate Geometry and Lines
Graphs of Second-Degree Equations
Trigonometry
Mathematical Induction
Proofs of Theorems
Lies My Calculator and Computer Told Me
Complex Numbers
Conic Sections
Conic Sections in Polar Coordinates
Answers to Odd-Numbered Exercises
Index