Essential Calculus

by Stewart, James

• ISBN13: 9780495014423
• ISBN10: 0495014427
• Edition: 1st
• Format: Hardcover
• Copyright: 2006-03-21
• Publisher: Brooks Cole

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