Single Variable Calculus Early Transcendentals, Volume 1

by Stewart, James

• ISBN13: 9780534496784
• ISBN10: 0534496784
• Edition: 5th
• Format: Hardcover
• Copyright: 2004-06-21
• Publisher: Brooks Cole

Summary

Stewart's CALCULUS: EARLY TRANSCENDENTALS, Fifth Edition, Volume One has the mathematical precision, accuracy, clarity of exposition and outstanding examples and problem sets that have characterized the first four editions. In this Fifth Edition, Stewart retains the focus on problem solving and the pedagogical system that has worked so well for students in a wide variety of colleges and universities throughout the world. He has made refinements to the exposition and examples to ensure that students have the best materials available. Further support for students and instructors is now available through a vast array of supplementary material. This new one-term version of the text provides more options for choosing a text to fit the course needs, along with the flexibility to select the resources that you want with the text.

Table of Contents

Preface	ix
To the Student	xviii
A Preview of Calculus	2	(8)
Functions and Models	10	(76)
Four Ways to Represent a Function	11	(14)
Mathematical Models: A Catalog of Essential Functions	25	(13)
New Functions from Old Functions	38	(10)
Graphing Calculators and Computers	48	(7)
Exponential Functions	55	(8)
Inverse Functions and Logarithms	63	(23)
Review	77	(3)
Principles of Problem Solving	80	(6)
Limits and Derivatives	86	(96)
The Tangent and Velocity Problems	87	(5)
The Limit of a Function	92	(12)
Calculating Limits Using the Limit Laws	104	(10)
The Precise Definition of a Limit	114	(10)
Continuity	124	(11)
Limits at Infinity; Horizontal Asymptotes	135	(14)
Tangents, Velocities, and Other Rates of Change	149	(9)
Derivatives	158	(7)
Writing Project: Early Methods for Finding Tangents	164	(1)
The Derivative as a Function	165	(17)
Review	176	(4)
Problems Plus	180	(2)
Differentiation Rules	182	(96)
Derivatives of Polynomials and Exponential Functions	183	(9)
The Product and Quotient Rules	192	(7)
Rates of Change in the Natural and Social Sciences	199	(12)
Derivatives of Trigonometric Functions	211	(6)
The Chain Rule	217	(10)
Implicit Differentiation	227	(9)
Higher Derivatives	236	(8)
Applied Project: Where Should a Pilot Start Descent?	243	(1)
Applied Project: Building a Better Roller Coaster	243	(1)
Derivatives of Logarithmic Functions	244	(6)
Hyperbolic Functions	250	(6)
Related Rates	256	(6)
Linear Approximations and Differentials	262	(16)
Laboratory Project Taylor Polynomials	269	(1)
Review	270	(4)
Problems Plus	274	(4)
Applications of Differentiation	278	(90)
Maximum and Minimum Values	279	(11)
Applied Project The Calculus of Rainbows	288	(2)
The Mean Value Theorem	290	(6)
How Derivatives Affect the Shape of a Graph	296	(11)
Indeterminate Forms and L'Hospital's Rule	307	(9)
Writing Project The Origins of L'Hospitals Rule	315	(1)
Summary of Curve Sketching	316	(8)
Graphing with Calculus and Calculators	324	(7)
Optimization Problems	331	(11)
Applied Project The Shape of a Can	341	(1)
Applications to Business and Economics	342	(5)
Newton's Method	347	(6)
Antiderivatives	353	(15)
Review	361	(4)
Problems Plus	365	(3)
Integrals	368	(68)
Areas and Distances	369	(11)
The Definite Integral	380	(14)
Discovery Project Area Functions	393	(1)
The Fundamental Theorem of Calculus	394	(11)
Indefinite Integrals and the Net Change Theorem	405	(9)
Writing Project Newton, Leibniz, and the Invention of Calculus	413	(1)
The Substitution Rule	414	(8)
The Logarithm Defined as an Integral	422	(14)
Review	430	(4)
Problems Plus	434	(2)
Applications of Integration	436
Areas between Curves	437	(7)
Volumes	444	(11)
Volumes by Cylindrical Shells	455	(5)
Work	460	(4)
Average Value of a Function	464
Applied Project Where to Sit at the Movies	468	(1)
Review	468	(2)
Problems Plus	470
Appendixes	1	(86)
A. Numbers, Inequalities, and Absolute Values	2	(8)
B. Coordinate Geometry and Lines	10	(6)
C. Graphs of Second-Degree Equations	16	(8)
D. Trigonometry	24	(10)
E. Sigma Notation	34	(5)
F. Proofs of Theorems	39	(7)
G. Complex Numbers	46	(9)
H. Answers to Odd-Numbered Exercises	55	(32)
Index	87