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Essential Calculus

by
Edition:
1st
ISBN13:

9780495014423

ISBN10:
0495014427
Format:
Hardcover
Pub. Date:
3/21/2006
Publisher(s):
Cengage Learning
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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 ESSENTIAL CALCULUS offers a concise approach to teaching calculus that focuses on major concepts and supports those concepts with precise definitions, patient explanations, and carefully graded problems. Essential Calculus is only 850 pages-two-thirds the size of Stewart's other calculus texts (CALCULUS, Fifth Edition and CALCULUS, EARLY TRANSCENDENTALS, Fifth Edition)-and 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. ESSENTIAL CALCULUS 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)
Applications of Differentiation
142(52)
Maximum and Minimum Values
142(7)
The Mean Value Theorem
149(6)
Derivatives and the Shapes of Graphs
155(8)
Curve Sketching
163(7)
Optimization Problems
170(9)
Newton's Method
179(6)
Antiderivatives
185(9)
Review
191(3)
Integrals
194(52)
Areas and Distances
194(11)
The Definite Integral
205(12)
Evaluating Definite Integrals
217(10)
The Fundamental Theorem of Calculus
227(9)
The Substitution Rule
236(10)
Review
242(4)
Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions
246(60)
Inverse Functions
246(8)
The Natural Logarithmic Function
254(8)
The Natural Exponential Function
262(6)
General Logarithmic and Exponential Functions
268(7)
Exponential Growth and Decay
275(8)
Inverse Trigonometric Functions
283(6)
Hyperbolic Functions
289(6)
Indeterminate Forms and l'Hospital's Rule
295(11)
Review
303(3)
Techniques of Integration
306(53)
Integration by Parts
306(6)
Trigonometric Integrals and Substitutions
312(10)
Partial Fractions
322(8)
Integration with Tables and Computer Algebra Systems
330(5)
Approximate Integration
335(12)
Improper Integrals
347(12)
Review
356(3)
Applications of Integration
359(53)
Areas between Curves
359(5)
Volumes
364(11)
Volumes by Cylindrical Shells
375(5)
Are Length
380(6)
Applications to Physics and Engineering
386(13)
Differential Equations
399(13)
Review
409(3)
Series
412(72)
Sequences
412(10)
Series
422(9)
The Integral and Comparison Tests
431(8)
Other Convergence Tests
439(10)
Power Series
449(5)
Representing Functions as Power Series
454(6)
Taylor and Maclaurin Series
460(13)
Applications of Taylor Polynomials
473(11)
Review
481(3)
Parametric Equations and Polar Coordinates
484(35)
Parametric Curves
484(6)
Calculus with Parametric Curves
490(8)
Polar Coordinates
498(8)
Areas and Lengths in Polar Coordinates
506(5)
Conic Sections in Polar Coordinates
511(8)
Review
517(2)
Vectors and the Geometry of Space
519(74)
Three-Dimensional Coordinate Systems
519(5)
Vectors
524(8)
The Dot Product
532(7)
The Cross Product
539(8)
Equations of Lines and Planes
547(8)
Cylinders and Quadric Surfaces
555(6)
Vector Functions and Space Curves
561(11)
Arc Length and Curvature
572(8)
Motion in Space: Velocity and Acceleration
580(13)
Review
589(4)
Partial Derivatives
593(72)
Functions of Several Variables
593(10)
Limits and Continuity
603(8)
Partial Derivatives
611(8)
Tangent Planes and Linear Approximations
619(8)
The Chain Rule
627(8)
Directional Derivatives and the Gradient Vector
635(11)
Maximum and Minimum Values
646(8)
Lagrange Multipliers
654(11)
Review
661(4)
Multiple Integrals
665(62)
Double Integrals over Rectangles
665(11)
Double Integrals over General Regions
676(8)
Double Integrals in Polar Coordinates
684(6)
Applications of Double Integrals
690(5)
Triple Integrals
695(10)
Triple Integrals in Cylindrical Coordinates
705(4)
Triple Integrals in Spherical Coordinates
709(6)
Change of Variables in Multiple Integrals
715(12)
Review
724(3)
Vector Calculus
727
Vector Fields
727(6)
Line Integrals
733(11)
The Fundamental Theorem for Line Integrals
744(9)
Green's Theorem
753(6)
Curl and Divergence
759(8)
Parametric Surfaces and Their Areas
767(10)
Surface Integrals
777(11)
Stokes' Theorem
788(5)
The Divergence Theorem
793
Review
799
APPENDIXES
1(72)
Trigonometry
1(9)
Proofs
10(14)
Sigma Notation
24(5)
Answers to Odd-Numbered Exercises
29(44)
Index 73


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