ü Readable rigor: The writing of this text is cogent, clear, and compelling; while carefully maintaining mathematical precision.ü Depth of Exercises: Exercise sets have real depth and are organised into three parts; skills exercises (Problems for Practice), more challenging and thought-provoking exercises (Further Theory and Practice), and technology exercises (Calculator/Computer Sciences)ü Pedagogical Features: These include: Insight, A Look Back, A Look Forward, Quick Quiz, Preview, Key/Basic Steps, Summary of Key Topics, Genesis and Developmentü Advanced Students Are Engaged Early: Students who were exposed to calculus in high school are challenged and engaged early; for instance, by early exposure to sequences (in Chapter 2, "Limits")ü Technology: Technology is an essential part of modern life. It is used throughout the book in a natural and comfortable manner. Students see how scientists and engineers think about mathematical questions.

Brian Erf Blank is an associate professor of mathematics at Washington University in St. Louis. He received his Ph.D. in 1980 at Cornell University, with Anthony Knapp as advisor. His 20th century work involved harmonic analysis.

Steven George Krantz is an American scholar, mathematician, and writer. He has authored more than 235 research papers and more than 125 books. Additionally, Krantz has edited journals such as the Notices of the American Mathematical Society and The Journal of Geometric Analysis.

Basics
Preview
Number Systems
Planar Coordinates and Graphing in the Plane
Lines and Their Slopes
Functions and Their Graphs
Combining Functions
Trigonometry
Summary of Key Topics
Review Exercises for Chapter 1
Genesis and Development
Limits
Preview
The Concept of Limit
Limit Theorems
Continuity
Infinite Limits and Asymptotes
Limits of Sequences
Exponential and Logarithmic Functions
Summary of Key Topics
Review Exercises
Genesis and Development
The Derivative
Preview
Rates of Change and Tangent Lines
The Derivative
Rules for Differentiation
Differentiation of Some Basic Functions
The Chain Rule
Derivatives of Inverse Functions
Higher Derivatives
Implicit Differentiation
Differentials and Approximation of Functions
Other Transcendental Functions
Summary of Key Topics
Review Exercises
Genesis and Development
Applications of the Derivative
Preview
Related Rates
The Mean Value Theorem
Maxima and Minima of Functions
Applied Maximum-Minimum Problems
Concavity
Graphing Functions
L'Hopital's Rule
The Newton-Raphson Method
Antidifferentiation and Applications
Summary of Key Topics
Review Exercises
Genesis and Development
The Integral
Preview
Introduction to Integration-The Area Problem
The Riemann Integral
Properties of the Integral
The Fundamental Theorem of Calculus
A Calculus Approach to the Logarithm and Exponential Functions
Integration by Substitution
More on the Calculation of Area
Numerical Techniques of Integration
Summary of Key Topics
Review Exercises
Genesis and Development
Techniques of Integration
Preview
Integration by Parts
Powers and Products of Trigonometric Functions
Trigonometric Substitution
Partial Fractions-Linear Factors
Partial Fractions-Irreducible Quadratic Factors
Improper Integrals-Unbounded Integrands
Improper Integrals-Unbounded Intervals
Summary of Key Topics
Review Exercises
Genesis and Development
Applications of the Integral
Preview
Volumes
Arc Length and Surface Area
The Average Value of a Function
Center of Mass
Work
First Order Differential Equations-Separable Equations
First Order Differential Equations-Linear Equations
Summary of Key Topics
Review Exercises
Genesis and Development
Infinite Series
Preview
Series
The Divergence Test and The Integral Test
The Comparison Tests
Alternating Series
The Ratio and Root Tests
Introduction to Power Series
Representing Functions by Power Series
Taylor Series
Summary of Key Topics
Review Exercises
Genesis and Development
Vectors
Preview
Vectors in the Plane
Vectors in Three-Dimensional Space
The Dot Product and Applications
The Cross Product and Triple Product
Lines and Planes in Space
Summary of Key Topics in Chapter 9
Review Exercises for Chapter 9
Genesis and Development
Curves in Space
Preview
Vector-Valued Functions-Limits, Derivatives, and Continuity
Velocity and Acceleration
Tangent Vectors and Arc Length
Curvature
Applications of Vector-Valued Functions to Motion
Summary of Key Topics in Chapter 10
Review Exercises for Chapter 10
Genesis and Development
Functions of Several Variables
Preview
Functions of Several Variables
Cylinders and Quadric Surfaces
Limits and Continuity
Partial Derivatives
Differentiability and The Chain Rule
Gradients and Directional Derivatives
Tangent Planes
Maximum-Minimum Problems
Lagrange Multipliers
Summary of Key Topics in Chapter 11
Review Exercises for Chapter 11
Genesis and Development
Multiple Integrals
Preview
Double Integrals over Rectangular Regions
Integration over More General Regions
Calculation of Volumes of Solids
Polar Coordinates
Integrating in Polar Coordinates
Triple Integrals
Physical Applications
Other Coordinate Systems
Summary of Key Topics in Chapter 12
Review Exercises for Chapter 12
Genesis and Development
Vector Calculus
Preview
Vector Fields
Line Integrals
Conservative Vector Fields and Path Independence
Divergence, Gradient, and Curl
Green's Theorem
Surface Integrals
Stokes's Theorem
The Divergence Theorem
Summary of Key Topics in Chapter 13
Review Exercises for Chapter 13
Genesis and Development
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Calculus Single and Multivariable

9780470453605

0470453605

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