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ISBN13: 978-0201307993

ISBN10: 0201307995

Cover type:

Edition: 98

Copyright: 1998

Publisher: Addison-Wesley Longman, Inc.

Published: 1998

International: No

ISBN10: 0201307995

Cover type:

Edition: 98

Copyright: 1998

Publisher: Addison-Wesley Longman, Inc.

Published: 1998

International: No

A calculus text for engineering and science majors covering all the calculus core material, through vector integral calculus, plus some basic material in differential equations. Designed for either a one-year or a more leisurely paced three-semester sequence. Developed for the Engineering/ Physics focused course, this new text covers only material essential for these students. This lean text can be covered in two semesters, or in a traditional three-semester course. It doesn't "skimp" on mathematical techniques, as these are critical for further courses. Key features include early coverage of vectors, optional graphing calculator material, optional computer algebra systems projects, a modeling focus, and discussion of differential equations material throughout the text.

- Covers content necessary for Engineering/ Science majors in only two semesters (including vector integral calculus). Or, can be used in a more leisurely paced three-semester course.
- Early coverage of vectors provides the background necessary for the study of electricity, fluid dynamics, and magnetism.
- First order differential equations are covered in the first semester in conjunction with the Mean Value Theorem corollaries. Enables differential equations courses which follow calculus to begin at a higher level.
- Coverage meets ABET (American Board for Engineering and Technology) requirements.
- Graphing calculator use is optional.
- Includes optional Computer Algebra System and group modeling projects.
- Offers a strong mathematical modeling flavor.
- Does not compromise the mathematical coverage and rigor necessary for engineering and science majors.

Volume One

Chapter 1: Limits and Continuity

Limits and Rates of Change

Rules for Finding Limits

Continuity

Tangent Lines

Writing for Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 2: Derivatives

The Derivative as a Function

The Derivative as a Rate of Change

Products, Quotients, and Negative Powers

Derivatives of Trigonometric Functions

The Chain Rule

Implicit Differentiation and Rational Exponents; Related Rates

Writing for Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 3: Extreme Values and Differential Equations

Extreme Values of Functions

The Mean Value Theorem and Differential Equations

The Shape of a Graph

Graphical Solutions to Differential Equations

Exponential Functions and the Derivative of ex

Writing for Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 4: Initial Value Problems

Indefinite Integrals, Differential Equations, and Modeling

Integral Rules; Integration by Substitution

First Order Differential Equations

Vectors in the Plane

Modeling Projectile Motion

Questions to Guide Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 5: Definite Integrals

Estimating with Finite Sums

Riemann Sums and Definite Integrals

The Fundamental Theorem. The Natural Logarithm

Area

Substitution in Definite Integrals; Properties

The Mean Value Theorem and Proof of the Fundamental Theorem

Numerical Integration

Questions to Guide Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 6: Applications of Derivatives and Integrals

Optimization

Linearization and Differentials

Newton's Method

Volume

Springs, Pumping, and Lifting

Fluid Forces

Questions to Guide Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 7: Applications of Differential Equations

Growth and Decay; Linear First Order Differential Equations

Euler's Numerical Method

Models for Springs and Pendulums

Constant-Coefficient Homogeneous Second Order Linear Equations

Unforced Oscillatory Motion

Writing for Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 8: Inverse Trigonometric Functions

Inverse Functions and Their Derivatives

Inverse Trigonometric Functions

Derivatives of Inverse Trigonometric Functions; Integrals

Writing for Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 9: Techniques of Integration

Basic Integration Formulas

Integration by Parts-Running the Product Rule Backwards

Partial Fractions

Integration with a Computer Algebra System (CAS)

Numerical Integration: The Monte Carlo Method

Questions to Guide Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Volume Two

Chapter 10: Vectors in Space

Vectors in Space

Dot Products

Cross Products

Lines and Planes in Space

Space Curves

Arc Length and the Unit Tangent Vector T

The TNB Frame; Tangential and Normal Components of Acceleration

Writing for Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 11: Partial Derivatives

Functions, Limits, and Continuity

Partial Derivatives

The Chain Rule

Directional Derivatives, Gradient Vectors, and Tangent Planes

Linearization and Differentials

Partial Derivatives with Constrained Variables

Writing for Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 12: Multiple Integrals

Double Integrals

Areas, Moments, and Center of Mass

Double Integrals in Polar Form

Triple Integrals in Rectangular Coordinates

Masses and Moments in Three Dimensions

Triple Integrals in Cylindrical and Spherical Coordinates

Substitutions in Multiple Integrals

Writing for Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 13: Integration in Vector Fields

Line Integrals

Vector Fields, Work, Circulation, and Flux

Path Independence, Potential Functions, and Conservative Fields

Green's Theorem in the Plane

Surface Area and Surface Integrals

Parametrized Surfaces

Stokes's Theorem

The Divergence Theorem and a Unifed Theory

Writing for Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 14: Extreme Values and Extensions of the Limit Concept

Extreme Values and Saddle Points for Multivariable Functions

Lagrange Multipliers

Extensions of the Limit Concept

L'Hôpital's Rule

Improper Integrals

Writing for Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 15: Power Series

Power Series Representations of Functions

Taylor Series

Taylor's Theorem

Radius of Convergence

Convergence at Endpoints

Writing for Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

ISBN10: 0201307995

Cover type:

Edition: 98

Copyright: 1998

Publisher: Addison-Wesley Longman, Inc.

Published: 1998

International: No

A calculus text for engineering and science majors covering all the calculus core material, through vector integral calculus, plus some basic material in differential equations. Designed for either a one-year or a more leisurely paced three-semester sequence. Developed for the Engineering/ Physics focused course, this new text covers only material essential for these students. This lean text can be covered in two semesters, or in a traditional three-semester course. It doesn't "skimp" on mathematical techniques, as these are critical for further courses. Key features include early coverage of vectors, optional graphing calculator material, optional computer algebra systems projects, a modeling focus, and discussion of differential equations material throughout the text.

- Covers content necessary for Engineering/ Science majors in only two semesters (including vector integral calculus). Or, can be used in a more leisurely paced three-semester course.
- Early coverage of vectors provides the background necessary for the study of electricity, fluid dynamics, and magnetism.
- First order differential equations are covered in the first semester in conjunction with the Mean Value Theorem corollaries. Enables differential equations courses which follow calculus to begin at a higher level.
- Coverage meets ABET (American Board for Engineering and Technology) requirements.
- Graphing calculator use is optional.
- Includes optional Computer Algebra System and group modeling projects.
- Offers a strong mathematical modeling flavor.
- Does not compromise the mathematical coverage and rigor necessary for engineering and science majors.

Table of Contents

Volume One

Chapter 1: Limits and Continuity

Limits and Rates of Change

Rules for Finding Limits

Continuity

Tangent Lines

Writing for Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 2: Derivatives

The Derivative as a Function

The Derivative as a Rate of Change

Products, Quotients, and Negative Powers

Derivatives of Trigonometric Functions

The Chain Rule

Implicit Differentiation and Rational Exponents; Related Rates

Writing for Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 3: Extreme Values and Differential Equations

Extreme Values of Functions

The Mean Value Theorem and Differential Equations

The Shape of a Graph

Graphical Solutions to Differential Equations

Exponential Functions and the Derivative of ex

Writing for Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 4: Initial Value Problems

Indefinite Integrals, Differential Equations, and Modeling

Integral Rules; Integration by Substitution

First Order Differential Equations

Vectors in the Plane

Modeling Projectile Motion

Questions to Guide Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 5: Definite Integrals

Estimating with Finite Sums

Riemann Sums and Definite Integrals

The Fundamental Theorem. The Natural Logarithm

Area

Substitution in Definite Integrals; Properties

The Mean Value Theorem and Proof of the Fundamental Theorem

Numerical Integration

Questions to Guide Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 6: Applications of Derivatives and Integrals

Optimization

Linearization and Differentials

Newton's Method

Volume

Springs, Pumping, and Lifting

Fluid Forces

Questions to Guide Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 7: Applications of Differential Equations

Growth and Decay; Linear First Order Differential Equations

Euler's Numerical Method

Models for Springs and Pendulums

Constant-Coefficient Homogeneous Second Order Linear Equations

Unforced Oscillatory Motion

Writing for Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 8: Inverse Trigonometric Functions

Inverse Functions and Their Derivatives

Inverse Trigonometric Functions

Derivatives of Inverse Trigonometric Functions; Integrals

Writing for Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 9: Techniques of Integration

Basic Integration Formulas

Integration by Parts-Running the Product Rule Backwards

Partial Fractions

Integration with a Computer Algebra System (CAS)

Numerical Integration: The Monte Carlo Method

Questions to Guide Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Volume Two

Chapter 10: Vectors in Space

Vectors in Space

Dot Products

Cross Products

Lines and Planes in Space

Space Curves

Arc Length and the Unit Tangent Vector T

The TNB Frame; Tangential and Normal Components of Acceleration

Writing for Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 11: Partial Derivatives

Functions, Limits, and Continuity

Partial Derivatives

The Chain Rule

Directional Derivatives, Gradient Vectors, and Tangent Planes

Linearization and Differentials

Partial Derivatives with Constrained Variables

Writing for Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 12: Multiple Integrals

Double Integrals

Areas, Moments, and Center of Mass

Double Integrals in Polar Form

Triple Integrals in Rectangular Coordinates

Masses and Moments in Three Dimensions

Triple Integrals in Cylindrical and Spherical Coordinates

Substitutions in Multiple Integrals

Writing for Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 13: Integration in Vector Fields

Line Integrals

Vector Fields, Work, Circulation, and Flux

Path Independence, Potential Functions, and Conservative Fields

Green's Theorem in the Plane

Surface Area and Surface Integrals

Parametrized Surfaces

Stokes's Theorem

The Divergence Theorem and a Unifed Theory

Writing for Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 14: Extreme Values and Extensions of the Limit Concept

Extreme Values and Saddle Points for Multivariable Functions

Lagrange Multipliers

Extensions of the Limit Concept

L'Hôpital's Rule

Improper Integrals

Writing for Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

Chapter 15: Power Series

Power Series Representations of Functions

Taylor Series

Taylor's Theorem

Radius of Convergence

Convergence at Endpoints

Writing for Your Review

Practice Exercises

Additional Exercises-Theory, Examples, Applications

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