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Single Variable Essential Calculus : Early Transcendentals,9780495109570

Single Variable Essential Calculus : Early Transcendentals

by
Edition:
1st
ISBN13:

9780495109570

ISBN10:
0495109576
Format:
Hardcover
Pub. Date:
3/1/2006
Publisher(s):
Brooks Cole
List Price: $202.66

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Summary

This book is a response to those instructors who feel that calculus textbooks are too big. In writing the book James Stewart asked himself:What is essential for a three-semester calculus course for scientists and engineers? Stewart's SINGLE VARIABLE ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS offers a concise approach to teaching calculus, focusing on major concepts and supporting those with precise definitions, patient explanations, and carefully graded problems. SINGLE VARIABLE ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS is only 850 pages-two-thirds the size of Stewart's other calculus texts (CALCULUS, FIFTH EDITION AND CALCULUS, EARLY TRANSCENDENTALS, Fifth Edition)-yet it contains almost all of the same topics. The author achieved this relative brevity mainly by condensing the exposition and by putting some of the features on the website www.StewartCalculus.com. Despite the reduced size of the book, there is still a modern flavor: Conceptual understanding and technology are not neglected, though they are not as prominent as in Stewart's other books. SINGLE VARIABLE ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS has been written with the same attention to detail, eye for innovation, and meticulous accuracy that have made Stewart's textbooks the best-selling calculus texts in the world.

Table of Contents

Functions and Limits
1(72)
Functions and Their Representations
1(9)
A Catalog of Essential Functions
10(14)
The Limit of a Function
24(11)
Calculating Limits
35(10)
Continuity
45(11)
Limits Involving Infinity
56(17)
Review
69(4)
Derivatives
73(69)
Derivatives and Rates of Change
73(10)
The Derivative as a Function
83(11)
Basic Differentiation Formulas
94(12)
The Product and Quotient Rules
106(7)
The Chain Rule
113(8)
Implicit Differentiation
121(6)
Related Rates
127(6)
Linear Approximations and Differentials
133(9)
Review
138(4)
Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions
142(56)
Exponential Functions
142(6)
Inverse Functions and Logarithms
148(12)
Derivatives of Logarithmic and Exponential Functions
160(7)
Exponential Growth and Decay
167(8)
Inverse Trigonometric Functions
175(6)
Hyperbolic Functions
181(6)
Indeterminate Forms and l'Hospital's Rule
187(11)
Review
195(3)
Applications of Differentiation
198(53)
Maximum and Minimum Values
198(7)
The Mean Value Theorem
205(6)
Derivatives and the Shapes of Graphs
211(9)
Curve Sketching
220(6)
Optimization Problems
226(10)
Newton's Method
236(5)
Antiderivatives
241(10)
Review
247(4)
Integrals
251(53)
Areas and Distances
251(11)
The Definite Integral
262(12)
Evaluating Definite Integrals
274(10)
The Fundamental Theorem of Calculus
284(9)
The Substitution Rule
293(11)
Review
300(4)
Techniques of Integration
304(53)
Integration by Parts
304(6)
Trigonometric Integrals and Substitutions
310(10)
Partial Fractions
320(8)
Integration with Tables and Computer Algebra Systems
328(5)
Approximate Integration
333(12)
Improper Integrals
345(12)
Review
354(3)
Applications of Integration
357(53)
Areas between Curves
357(5)
Volumes
362(11)
Volumes by Cylindrical Shells
373(5)
Arc Length
378(6)
Applications to Physics and Engineering
384(13)
Differential Equations
397(13)
Review
407(3)
Series
410(72)
Sequences
410(10)
Series
420(9)
The Integral and Comparison Tests
429(8)
Other Convergence Tests
437(10)
Power Series
447(5)
Representing Functions as Power Series
452(6)
Taylor and Maclaurin Series
458(13)
Applications of Taylor Polynomials
471(11)
Review
479(3)
Parametric Equations and Polar Coordinates
482
Parametric Curves
482(6)
Calculus with Parametric Curves
488(8)
Polar Coordinates
496(8)
Areas and Lengths in Polar Coordinates
504(5)
Conic Sections in Polar Coordinates
509
Review
515
APPENDIXES
1
A. Trigonometry
1(9)
B. Proofs
10(13)
C. Sigma Notation
23(5)
D. The Logarithm Defined as an Integral
28(9)
E. Answers to Odd-Numbered Exercises
37
Index 69


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