Single Variable Calculus With Vector Functions for Ap Calculus

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  • Edition: 1st
  • Format: Paperback
  • Copyright: 2006-03-14
  • Publisher: Brooks Cole
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Stewart's SINGLE VARIABLE CALCULUS WITH VECTOR FUNCTIONS has the mathematical precision, accuracy, clarity of exposition and outstanding examples and problem sets that characterized all of James Stewart?s texts. In this new text, Stewart focuses on problem solving, using the pedagogical system that has worked so well for students in a wide variety of academic settings throughout the world.

Table of Contents

Functions And Models
Four Ways to Represent a Function
Mathematical Models: A Catalog of Essential Functions
New Functions from Old Functions
Graphing Calculators and Computers
Exponential Functions
Inverse Functions and Logarithms
Principles of Problem Solving
Limits And Derivatives
The Tangent and Velocity Problems
The Limit of a Function
Calculating Limits Using the Limit Laws
The Precise Definition of a Limit
Limits at Infinity
Horizontal Asymptotes
Tangents, Velocities, and Other Rates of Change
Writing Project: Early Methods for Finding Tangents
The Derivative as a Function
Problems Plus
Differentiation Rules
Derivatives of Polynomials and Exponential Functions
The Product and Quotient Rules
Rates of Change in the Natural and Social Sciences
Derivatives of Trigonometric Functions
The Chain Rule
Implicit Differentiation
Higher Derivatives, Applied Project: Where Should a Pilot Start Descent? , Applied Project: Building a Better Roller Coaster
Derivatives of Logarithmic Functions
Hyperbolic Functions
Related Rates
Linear Approximations and Differentials, Laboratory Project: Taylor Polynomials
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
Indeterminate Forms and L?Hospital?s Rule, Writing Project: The Origins of L?Hospital?s Rule
Summary of Curve Sketching
Graphing with Calculus and Calculators
Optimization Problems, Applied Project: The Shape of a Can
Applications to Business and Economics
Newton?s Method
Problems Plus
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
The Logarithm Defined as an Integral
Problems Plus
Applications Of Integration
Areas between Curves
Volumes by Cylindrical Shells
Average Value of a Function
Applied Project: Where to Sit at the Movie
Problems Plus
Techniques Of Integration
Integration by Parts
Trigonometric Integrals
Trigonometric Substitution
Integration of Rational Functions by Partial Fractions
Strategy for Integration
Integration Using Tables and Computer Algebra Systems, Discovery Project: Patterns in Integrals
Approximate Integration
Improper Integrals
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
Applications to Economics and Biology
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? Exponential Growth and Decay, Applied Project: Calculus and Baseball
The Logistic Equation
Linear Equations
Predator-Prey Systems
Problems Plus
Curves In Parametric, Vector, And Polar Form
Curves Defined by Parametric Equations, Laboratory Project: Running Circles around Circles
Calculus with Parametric Curves, Laboratory Project: Bezier Curves
Vectors in Two Dimensions
Vector Functions and Their Derivatives
Curvilinear Motions: Velocity and Acceleration
Polar Coordinates
Areas and Lengths in Polar Coordinates
Conic Sections
Conic Sections in Polar Coordinates
Problems Plus
Infinite Sequences And Series
Sequences, Laboratory Project: Logistic Sequences
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
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