Calculus

by Stewart, James

• ISBN13: 9780534359492
• ISBN10: 0534359493
• Edition: 4th
• Format: Hardcover
• Copyright: 1999-05-21
• Publisher: Brooks Cole

Summary

Stewart's CALCULUS, FOURTH EDITION reflects the same old-world dedication to excellence that characterized the first three editions. It has been revised with dedication, precision, and patient care to further emphasize conceptual understanding. A phenomenon of the Stewart success is the texts' use in such a wide variety of colleges and universities throughout the world. Just as he teaches to every student in his classes from the most unprepared to the most mathematically gifted, Stewart writes to a range of students - adding the explanations that make ideas come alive as well as the problems that challenge. Stewart's heuristic examples reveal calculus to students. His examples stand out because they are not just models for problem solving or a means of demonstrating techniques - they also encourage students to develop an analytic view of the subject.

Table of Contents

A Preview of Calculus	2	(8)
Functions and Models	10	(56)
Four Ways to Represent a Function	11	(13)
Mathematical Models	24	(14)
New Functions from Old Functions	38	(12)
Graphing Calculators and Computers	50	(9)
Review	56	(3)
Principles of Problem Solving	59	(7)
Limits and Rates of Change	66	(62)
The Tangent and Velocity Problems	67	(5)
The Limit of a Function	72	(12)
Calculating Limits Using the Limit Laws	84	(10)
The Precise Definition of a Limit	94	(10)
Continuity	104	(10)
Tangents, Velocities, and Other Rates of Change	114	(12)
Review	124	(2)
Problems Plus	126	(2)
Derivatives	128	(94)
Derivatives	129	(7)
Writing Project Early Methods for Finding Tangents	135	(1)
The Derivative as a Function	136	(11)
Differentiation Formulas	147	(11)
Rates of Change in the Natural and Social Sciences	158	(12)
Derivatives of Trigonometric Functions	170	(7)
The Chain Rule	177	(8)
Implicit Differentiation	185	(7)
Higher Derivatives	192	(7)
Applied Project *** Where Should a Pilot Start Descent?	199	(1)
Related Rates	199	(6)
Linear Approximations and Differentials	205	(13)
Laboratory Project *** Taylor Polynomials	213	(1)
Review	214	(4)
Problems Plus	218	(4)
Applications of Differentiation	222	(90)
Maximum and Minimum Values	223	(11)
Applied Project *** The Calculus of Rainbows	232	(2)
The Mean Value Theorem	234	(6)
How Derivatives Affect the Shape of a Graph	240	(9)
Limits at Infinity; Horizontal Asymptotes	249	(14)
Summary of Curve Sketching	263	(8)
Graphing with Calculus and Calculators	271	(6)
Optimization Problems	277	(11)
Applied Project *** The Shape of a Can	287	(1)
Applications to Economics	288	(5)
Newton's Method	293	(6)
Antiderivatives	299	(11)
Review	306	(4)
Problems Plus	310	(2)
Integrals	312	(58)
Areas and Distances	313	(11)
The Definite Integral	324	(13)
Discovery Project *** Area Functions	336	(1)
The Fundamental Theorem of Calculus	337	(9)
Indefinite Integrals and the Total Change Theorem	346	(10)
Writing Project *** Newton, Leibniz, and the Invention of Calculus	355	(1)
The Substitution Rule	356	(11)
Review	363	(4)
Problems Plus	367	(3)
Applications of Integration	370	(36)
Areas between Curves	371	(7)
Volumes	378	(11)
Volumes by Cylindrical Shells	389	(5)
Work	394	(4)
Average Value of a Function	398	(5)
Review	401	(2)
Problems Plus	403	(3)
Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions	406	(96)
Inverse Functions	407	(9)
Instructors may cover either Sections 7.2--7.4 or Sections 7.2*--7.4*. See the Preface.
Exponential Functions and Their Derivatives	416	(12)
Logarithmic Functions	428	(7)
Derivatives of Logarithmic Functions	435	(10)
The Natural Logarithmic Function	445	(8)
The Natural Exponential Function	453	(7)
General Logarithmic and Exponential Functions	460	(9)
Inverse Trigonometric Functions	469	(9)
Applied Project *** Where to Sit at the Movies	478	(1)
Hyperbolic Functions	478	(7)
Indeterminate Forms and L'Hospital's Rule	485	(15)
Writing Project *** The Origins of L'Hospital's Rule	496	(1)
Review	496	(4)
Problems Plus	500	(2)
Techniques of Integration	502	(72)
Integration by Parts	503	(7)
Trigonometric Integrals	510	(7)
Trigonometric Substitution	517	(7)
Integration of Rational Functions by Partial Fractions	524	(9)
Strategy for Integration	533	(6)
Integration Using Tables and Computer Algebra Systems	539	(7)
Discovery Project *** Patterns in Integrals	545	(1)
Approximate Integration	546	(11)
Improper Integrals	557	(14)
Review	568	(3)
Problems Plus	571	(3)
Further Applications of Integration	574	(40)
Arc Length	575	(7)
Area of a Surface of Revolution	582	(7)
Discovery Project *** Rotating on a Slant	588	(1)
Applications to Physics and Engineering	589	(9)
Applications to Economics and Biology	598	(5)
Probability	603	(9)
Review	610	(2)
Problems Plus	612	(2)
Differential Equations	614	(60)
Modeling with Differential Equations	615	(5)
Direction Fields and Euler's Method	620	(9)
Separable Equations	629	(8)
Applied Project *** Which Is Faster, Going Up or Coming Down?	636	(1)
Exponential Growth and Decay	637	(10)
Applied Project *** Calculus and Baseball	646	(1)
The Logistic Equation	647	(9)
Linear Equations	656	(6)
Predator-Prey Systems	662	(10)
Review	668	(4)
Problems Plus	672	(2)
Parametric Equations and Polar Coordinates	674	(52)
Curves Defined by Parametric Equations	675	(7)
Laboratory Project *** Families of Hypocycloids	682	(1)
Tangents and Areas	682	(7)
Laboratory Project *** Bezier Curves	689	(1)
Arc Length and Surface Area	689	(5)
Polar Coordinates	694	(10)
Areas and Lengths in Polar Coordinates	704	(5)
Conic Sections	709	(7)
Conic Sections in Polar Coordinates	716	(8)
Review	722	(2)
Problems Plus	724	(2)
Infinite Sequences and Series	726	(90)
Sequences	727	(11)
Laboratory Project *** Logistic Sequences	738	(1)
Series	738	(10)
The Integral Test and Estimates of Sums	748	(7)
The Comparison Tests	755	(5)
Alternating Series	760	(5)
Absolute Convergence and the Ratio and Root Tests	765	(7)
Strategy for Testing Series	772	(2)
Power Series	774	(5)
Representations of Functions as Power Series	779	(6)
Taylor and Maclaurin Series	785	(11)
The Binomial Series	796	(4)
Writing Project *** How Newton Discovered the Binomial Series	799	(1)
Applications of Taylor Polynomials	800	(12)
Applied Project *** Radiation from the Stars	808	(1)
Review	809	(3)
Problems Plus	812	(4)
Vectors and the Geometry of Space	816	(54)
Three-Dimensional Coordinate Systems	817	(5)
Vectors	822	(8)
The Dot Product	830	(7)
The Cross Product	837	(9)
Discovery Project *** The Geometry of a Tetrahedron	845	(1)
Equations of Lines and Planes	846	(9)
Cylinders and Quadric Surfaces	855	(6)
Cylindrical and Spherical Coordinates	861	(8)
Laboratory Project *** Families of Surfaces	866	(1)
Review	866	(3)
Problems Plus	869	(1)
Vector Functions	870	(36)
Vector Functions and Space Curves	871	(6)
Derivatives and Integrals of Vector Functions	877	(6)
Arc Length and Curvature	883	(8)
Motion in Space: Velocity and Acceleration	891	(13)
Applied Project *** Kepler's Laws	900	(1)
Review	901	(3)
Problems Plus	904	(2)
Partial Derivatives	906	(94)
Functions of Several Variables	907	(14)
Limits and Continuity	921	(8)
Partial Derivatives	929	(13)
Tangent Planes and Linear Approximations	942	(9)
The Chain Rule	951	(9)
Directional Derivatives and the Gradient Vector	960	(13)
Maximum and Minimum Values	973	(12)
Applied Project *** Designing a Dumpster	983	(1)
Discovery Project *** Quadratic Approximations and Critical Points	984	(1)
Lagrange Multipliers	985	(13)
Applied Project *** Rocket Science	992	(1)
Applied Project *** Hydro-Turbine Optimization	993	(1)
Review	994	(4)
Problems Plus	998	(2)
Multiple Integrals	1000	(74)
Double Integrals over Rectangles	1001	(9)
Iterated Integrals	1010	(5)
Double Integrals over General Regions	1015	(8)
Double Integrals in Polar Coordinates	1023	(6)
Applications of Double Integrals	1029	(10)
Surface Area	1039	(3)
Triple Integrals	1042	(10)
Discovery Project *** Volumes of Hyperspheres	1052	(1)
Triple Integrals in Cylindrical and Spherical Coordinates	1052	(8)
Applied Project *** Roller Derby	1058	(1)
Discovery Project *** The Intersection of Three Cylinders	1059	(1)
Change of Variables in Multiple Integrals	1060	(12)
Review	1068	(4)
Problems Plus	1072	(2)
Vector Calculus	1074	(84)
Vector Fields	1075	(6)
Line Integrals	1081	(12)
The Fundamental Theorem for Line Integrals	1093	(9)
Green's Theorem	1102	(7)
Curl and Divergence	1109	(8)
Parametric Surfaces and Their Areas	1117	(10)
Surface Integrals	1127	(12)
Stokes' Theorem	1139	(6)
Writing Project *** Three Men and Two Theorems	1144	(1)
The Divergence Theorem	1145	(7)
Summary	1152	(4)
Review	1153	(3)
Problems Plus	1156	(2)
Second-Order Differential Equations	1158	(26)
Second-Order Linear Equations	1159	(6)
Nonhomogeneous Linear Equations	1165	(7)
Applications of Second-Order Differential Equations	1172	(8)
Series Solutions	1180	(4)
Review	1184
Appendixes	1	(118)
A Intervals, 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	(9)
G Complex Numbers	48	(8)
H Answers to Odd-Numbered Exercises	56	(63)
Index	119