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Calculus: Early Transcendentals

by

Calculus: Early Transcendentals Cover

 

Synopses & Reviews

Publisher Comments:

Organized to support an "early transcendentals" approach to the course, this version of Rogawski's highly anticipated text presents calculus with solid mathematical precision but with an everyday sensibility that puts the main concepts in clear terms.  It is rigorous without being inaccessible and clear without being too informal--it has the perfect balance for instructors and their students. 
 
Also available in a late transcendentals version (0-7167-6911-5).

About the Author

About Jon Rogawski

Jon Rogawski received his undergraduate degree (and simultaneously a master's degree in mathematics) at Yale, and a Ph.D. in mathematics from Princeton University, where he studied under Robert Langlands. Prior to joining the Department of Mathematics at UCLA, where he is currently Full Professor, he held teaching positions at Yale and the University of Chicago, and research positions at the Institute for Advanced Study and University of Bonn.

 

Jon's areas of interest are number theory, automorphic forms, and harmonic analysis on semisimple groups. He has published numerous research articles in leading mathematical journals, including a research monograph entitled "Automorphic Representations of Unitary Groups in Three Variables" (Princeton University Press). He is the recipient of a Sloan Fellowship and an editor of The Pacific Journal of Mathematics.

 

Jon and his wife Julie, a physician in family practice, have four children. They run a busy household and, whenever possible, enjoy family vacations in the mountains of California. Jon is a passionate classical music lover and plays the violin and classical guitar.

Table of Contents

Chapter 1 PRECALCULUS REVIEW
1.1 Real Numbers, Functions, Equations, and Graphs

1.2 Linear and Quadratic Functions

1.3 The Basic Classes of Functions

1.4 Trigonometric Functions

1.5 Inverse Functions

1.6 Exponential and Logarithmic Functions

1.7 Technology: Calculators and Computers

 
Chapter 2 LIMITS

2.1 Limits, Rates of Change, and Tangent Lines

2.2 Limits: A Numerical and Graphical Approach

2.3 Basic Limit Laws

2.4 Limits and Continuity

2.5 Evaluating Limits Algebraically

2.6 Trigonometric Limits

2.7 Intermediate Value Theorem

2.8 The Formal Definition of a Limit

Chapter 3 DIFFERENTIATION

3.1 Definition of the Derivative

3.2 The Derivative as a Function

3.3 Product and Quotient Rules

3.4 Rates of Change

3.5 Higher Derivatives

3.6 Derivatives of Trigonometric Functions

3.7 The Chain Rule

3.8 Implicit Differentiation

3.9 Derivatives of Inverse Functions

3.10 Derivatives of Logarithmic Functions

3.11 Related Rates

Chapter 4 APPLICATIONS OF THE DERIVATIVE

4.1 Linear Approximation and Applications

4.2 Extreme Values

4.3 The Mean Value Theorem and Monotonicity

4.4 The Shape of a Graph

4.5 Graph Sketching and Asymptotes

4.6 Applied Optimization

4.7 L'Hoˆpital's Rule

4.8 Newton's Method

4.9 Antiderivatives

Chapter 5 THE INTEGRAL

5.1 Approximating and Computing Area

5.2 The Definite Integral

5.3 The Fundamental Theorem of Calculus, Part I

5.4 The Fundamental Theorem of Calculus, Part II

5.5 Net or Total Change as the Integral of a Rate

5.6 Substitution Method

5.7 Integrals of Exponential and Logarithmic Functions

5.8 Exponential Growth and Decay

Chapter 6 APPLICATIONS OF THE INTEGRAL

6.1 Area Between Two Curves

6.2 Setting Up Integrals: Volumes, Density, Average Value

6.3 Volumes of Revolution

6.4 The Method of Cylindrical Shells

6.5 Work and Energy

Chapter 7 TECHNIQUES OF INTEGRATION

7.1 Numerical Integration

7.2 Integration by Parts

7.3 Trigonometric Integrals

7.4 Trigonometric Substitution

7.5 Integrals of Hyperbolic and Inverse Hyperbolic

Functions

7.6 The Method of Partial Fractions

7.7 Improper Integrals

 
Chapter 8 FURTHER APPLICATIONSOF THE INTEGRAL AND TAYLOR POLYNOMIALS

8.1 Arc Length and Surface Area

8.2 Fluid Pressure and Force

8.3 Center of Mass

8.4 Taylor Polynomials

Chapter 9 INTRODUCTION TO DIFFERENTIAL EQUATIONS

9.1 Separable Equations

9.2 Models Involving y'= k(y-b)

9.3 Graphical and Numerical Methods

9.4 The Logistic Equation

9.5 First-order Linear Equations

Chapter 10 INFINITE SERIES

10.1 Sequences

10.2 Summing an Infinite Series

10.3 Convergence of Series with Positive Terms

10.4 Absolute and Conditional Convergence

10.5 The Ratio and Root Tests

10.6 Power Series

10.7 Taylor Series

 
Chapter 11 PARAMETRIC EQUATIONS, mPOLAR COORDINATES, AND CONIC SECTIONS

11.1 Parametric Equations

11.2 Arc Length and Speed

11.3 Polar Coordinates

11.4 Area and Arc Length in Polar Coordinates

11.5 Conic Sections

Chapter 12 VECTOR GEOMETRY

12.1 Vectors in the Plane

12.2 Vectors in Three Dimensions

12.3 Dot Product and the Angle Between Two Vectors

12.4 The Cross Product

12.5 Planes in Three-Space

12.6 Survey of Quadric Surfaces

12.7 Cylindrical and Spherical Coordinates

 
Chapter 13 CALCULUS OF VECTOR-VALUED FUNCTIONS

13.1 Vector-Valued Functions

13.2 Calculus of Vector-Valued Functions

13.3 Arc Length and Speed

13.4 Curvature

13.5 Motion in Three-Space

13.6 Planetary Motion According to Kepler and Newton

 
Chapter 14 DIFFERENTIATION IN SEVERAL VARIABLES

14.1 Functions in Two or More Variables

14.2 Limits and Continuity in Several Variables

14.3 Partial Derivatives

14.4 Linear Approximation,Differentiability, and Tangent Planes

14.5 The Gradient and Directional Derivatives

14.6 The Chain Rule

14.7 Optimization in Several Variables

14.8 Lagrange Multipliers: Optimizing with a Constraint

Chapter 15 MULTIPLE INTEGRATION

15.1 Integrals in Several Variables

15.2 Double Integrals over More General Regions

15.3 Triple Integrals

15.4 Integration in Polar, Cylindrical, and Spherical Coordinates

15.5 Change of Variables

Chapter 16 LINE AND SURFACE INTEGRALS

16.1 Vector Fields

16.2 Line Integrals

16.3 Conservative Vector Fields

16.4 Parametrized Surfaces and Surface Integrals

16.5 Integrals of Vector Fields

 
Chapter 17 FUNDAMENTAL THEOREMS OF VECTOR ANALYSIS

17.1 Green's Theorem

17.2 Stokes' Theorem

17.3 Divergence Theorem

APPENDICES

A. The Language of Mathematics

B. Properties of Real Numbers

C. Mathematical Induction and the Binomial Theorem

D. Additional Proofs of Theorems

ANSWERS TO ODD-NUMBERED EXERCISES

Product Details

ISBN:
9781429210737
Author:
Rogawski, Jon
Publisher:
W.H. Freeman & Company
Author:
Cram101 Textbook Reviews
Subject:
Calculus
Subject:
Mathematics-Calculus
Subject:
Education-General
Copyright:
Edition Description:
Trade Cloth
Publication Date:
20070631
Binding:
HARDCOVER
Grade Level:
College/higher education:
Language:
English
Illustrations:
Y
Pages:
1050
Dimensions:
10.00 x 8.50 in

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