Calculus Single and Multivariable

by Blank, Brian E.; Krantz, Steven G.

• ISBN13: 9780470453605
• ISBN10: 0470453605
• eBook ISBN(s): 9780470911860, 9781118207659
• Edition: 2nd
• Format: Hardcover
• Copyright: 2011-10-18
• Publisher: Wiley
• More Book Details

Summary

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.

Table of Contents

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

Table of Contents provided by Publisher. All Rights Reserved.