Calculus : a complete course

Başlık:

Yazar:

Adams, R. A. (Robert Alexander), 1940-

ISBN:

9780201396072

9780201791310

Ek Yazar:

Adams, R. A. (Robert Alexander), 1940-

Edition:

5th ed.

Yayım Bilgisi:

Don Mills, Ont. : Addison-Wesley Longman, 2003.

Fiziksel Tanım:

xvi, 999, [101] pages : ill. ; 26 cm.

Konu Terimleri:

Calculus.

Kalkulus.

Mevcut:*

Library	Materyal Türü	Barkod	Yer Numarası	Durum
Searching... Pamukkale Merkez Kütüphanesi	Kitap	0101674	QA303 A28 2003	Searching... Unknown

This classic text has been praised for its high level of mathematical integrity including complete and precise statements of theorems, use of geometric reasoning in applied problems and the diverse range of applications across the sciences. The Fourth Edition features a new open design and has been reorganized to place emphasis on key topics and to deliver an efficient teaching and learning tool for introductory calculus. *Reorganized for efficiency's sake and to place a greater emphasis on key topics *New open design to promote ease of learning for the student *Early introduction of transcendental functions *Emphasis on geometry, especially in applied problems *Precise statements of theorems *Diverse range of applications from all the sciences including physics, chemistry, engineering and social sciences

Preface

To the Student

To the Instructor

Acknowledgments

What Is Calculus?

Preliminaries

P.1 Real Numbers and the Real Line

P.2 Cartesian Coordinates in the Plane

P.3 Graphs of Quadratic Equations

P.4 Functions and Their Graphs

P.5 Combining Functions to Make New Functions

P.6 Polynomials and Rational Functions

P.7 The Trigonometric Functions

1 Limits and Continuity

1.1 Examples of Velocity, Growth Rate, and Area

1.2 Limits of Functions

1.3 Limits at Infinity and Infinite Limits

1.4 Continuity

1.5 The Formal Definition of Limit

Chapter Review

2 Differentiation

2.1 Tangent Lines and Their Slopes

2.2 The Derivative

2.3 Differentiation Rules

2.4 The Chain Rule

2.5 Derivatives of Trigonometric Functions

2.6 The Mean-Value Theorem

2.7 Using Derivatives

2.8 Higher-Order Derivatives

2.9 Implicit Differentiation

2.10 Antiderivatives and Initial-Value Problems

2.11 Velocity and Acceleration

Chapter Review

3 Transcendental Functions

3.1 Inverse Functions

3.2 Exponential and Logarithmic Functions

3.3 The Natural Logarithm and Exponential

3.4 Growth and Decay

3.5 The Inverse Trigonometric Functions

3.6 Hyperbolic Functions

3.7 Second-Order Linear DEs with Constant Coefficients

Chapter Review

4 Some Applications of Derivatives

4.1 Related Rates

4.2 Extreme Values

4.3 Concavity and Inflections

4.4 Sketching the Graph of a Function

4.5 Extreme-Value Problems

4.6 Finding Roots of Equations

4.7 Linear Approximations

4.8 Taylor Polynomials

4.9 Indeterminate Forms

Chapter Review

5 Integration

5.1 Sums and Sigma Notation

5.2 Areas as Limits of Sums

5.3 The Definite Integral

5.4 Properties of the Definite Integral

5.5 The Fundamental Theorem of Calculus

5.6 The Method of Substitution

5.7 Areas of Plane Regions

Chapter Review

6 Techniques of Integration

6.1 Integration by Parts

6.2 Inverse Substitutions

6.3 Integrals of Rational Functions

6.4 Integration Using Computer Algebra or Tables

6.5 Improper Integrals

6.6 The Trapezoid and Midpoint Rules

6.7 Simpson's Rule

6.8 Other Aspects of Approximate Integration

Chapter Review

7 Applications of Integration

7.1 Volumes by Slicing-Solids of Revolution

7.2 More Volumes by Slicing

7.3 Arc Length and Surface Area

7.4 Mass, Moments, and Centres of Mass

7.5 Centroids

7.6 Other Physical Applications

7.7 Applications in Business, Finance, and Ecology

7.8 Probability

7.9 First-Order Differential Equations

Chapter Review

8 Conics, Parametric Curves, and Polar Curves

8.1 Conics

8.2 Parametric Curves

8.3 Smooth Parametric Curves and Their Slopes

8.4 Arc Lengths and Areas for Parametric Curves

8.5 Polar Coordinates and Polar Curves

8.6 Slopes, Areas, and Arc Lengths for Polar Curves

Chapter Review

9 Sequences, Series, and Power Series

9.1 Sequences and Convergence

9.2 Infinite Series

9.3 Convergence Tests for Positive Series

9.4 Absolute and Conditional Convergence

9.5 Power Series

9.6 Taylor and Maclaurin Series

9.7 Applications of Taylor and Maclaurin Series

9.8 The Binomial Theorem and Binomial Series

9.9 Fourier Series

Chapter Review

10 Vectors and Coordinate Geometry in 3-Space

10.1 Analytic Geometry in Three Dimensions

10.2 Vectors

10.3 The Cross Product in 3-Space

10.4 Planes and Lines

10.5 Quadric Surfaces

10.6 A Little Linear Algebra

10.7 Using Maple for Vector and Matrix Calculations

Chapter Review

11 Vector Functions and Curves

11.1 Vector Functions of One Variable

11.2 Some Applications of Vector Differentiation

11.3 Curves and Parametrizations

11.4 Curvature, Torsion, and the Frenet Frame

11.5 Curvature and Torsion for General Parametrizations

11.6 Kepler's Laws of Planetary Motion

Chapter Review

12 Partial Differentiation

12.1 Functions of Several Variables

12.2 Limits and Continuity

12.3 Partial Derivatives

12.4 Higher-Order Derivatives

12.5 The Chain Rule

12.6 Linear Approximations, Differentiability, and Differentials

12.7 Gradients and Directional Derivatives

12.8 Implicit Functions

12.9 Taylor Series and Approximations

Chapter Review

13 Applications of Partial Derivatives

13.1 Extreme Values

13.2 Extreme Values of Functions Defined on Restricted Domains

13.3 Lagrange Multipliers

13.4 The Method of Least Squares

13.5 Parametric Problems

13.6 Newton's Method

13.7 Calculations with Maple

Chapter Review

14 Multiple Integration

14.1 Double Integrals

14.2 Iteration of Double Integrals in Cartesian Coordinates

14.3 Improper Integrals and a Mean-Value Theorem

14.4 Double Integrals in Polar Coordinates

14.5 Triple Integrals

14.6 Change of Variables in Triple Integrals

14.7 Applications of Multiple Integrals

Chapter Review

15 Vector Fields

15.1 Vector and Scalar Fields

15.2 Conservative Fields

15.3 Line Integrals

15.4 Line Integrals of Vector Fields

15.5 Surfaces and Surface Integrals

15.6 Oriented Surfaces and Flux Integrals

Chapter Review

16 Vector Calculus

16.1 Gradient, Divergence, and Curl

16.2 Some Identities Involving Grad, Div, and Curl

16.3 Green's Theorem in the Plane

16.4 The Divergence Theorem in 3-Space

16.5 Stokes's Theorem

16.6 Some Physical Applications of Vector Calculus

16.7 Orthogonal Curvilinear Coordinates

Chapter Review

17 Ordinary Differential Equations

17.1 Classifying Differential Equations

17.2 Solving First-Order Equations

17.3 Existence, Uniqueness, and Numerical Methods

17.4 Differential Equations of Second Order

17.5 Linear Differential Equations with Constant Coefficients

17.6 Nonhomogeneous Linear Equations

17.7 Series Solutions of Differential Equations

Chapter Review

Appendix I Complex Numbers

Appendix II Complex Functions

Appendix III Continuous Functions

Appendix IV The Riemann

Appendix V Doing Calculus with Maple

Answers to Odd-Numbered Exercises

Index

Mevcut:*

Bound With These Titles

On Order

Özet

Özet

Table of Contents