Single Variable Calculus (Non-InfoTrac Version)

by Stewart, James

• ISBN13: 9780534355623
• ISBN10: 0534355625
• Edition: 4th
• Format: Hardcover
• Copyright: 1999-01-26
• Publisher: Brooks Cole

Summary

Success in your calculus course starts here! James Stewarts CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS, Sixth Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course!

Table of Contents

A Preview of Calculus	2	(8)
1 Functions and Models	10	(56)
1.1 Four Ways to Represent a Function	11	(13)
1.2 Mathematical Models	24	(14)
1.3 New Functions from Old Functions	38	(12)
1.4 Graphing Calculators and Computers	50	(6)
Review	56	(3)
Principles of Problem Solving	59	(7)
2 Limits and Rates of Change	66	(62)
2.1 The Tangent and Velocity Problems	67	(5)
2.2 The Limit of a Function	72	(12)
2.3 Calculating Limits Using the Limit Laws	84	(10)
2.4 The Precise Definition of a Limit	94	(10)
2.5 Continuity	104	(10)
2.6 Tangents, Velocities, and Other Rates of Change	114	(10)
Review	124	(2)
Problems Plus	126	(2)
3 Derivatives	128	(94)
3.1 Derivatives	129	(7)
Writing Project Early Methods for Finding Tangents	135	(1)
3.2 The Derivative as a Function	136	(11)
3.3 Differentiation Formulas	147	(11)
3.4 Rates of Change in the Natural and Social Sciences	158	(12)
3.5 Derivatives of Trigonometric Functions	170	(7)
3.6 The Chain Rule	177	(8)
Applied Project Where Should a Pilot Start Descent?	199
3.7 Implicit Differentiation	185	(7)
3.8 Higher Derivatives	192	(7)
3.9 Related Rates	199	(6)
3.10 Linear Approximations and Differentials	205	(9)
Laboratory Project Taylor Polynomials	213	(1)
Review	214	(4)
Problems Plus	218	(4)
4 Applications of Differentiation	222	(90)
4.1 Maximum and Minimum Values	223	(11)
Applied Project The Calculus of Rainbows	232	(2)
4.2 The Mean Value Theorem	234	(6)
4.3 How Derivatives Affect the Shape of a Graph	240	(9)
4.4 Limits at Infinity; Horizontal Asymptotes	249	(14)
4.5 Summary of Curve Sketching	263	(8)
4.6 Graphing with Calculus and Calculators	271	(6)
4.7 Optimization Problems	277	(11)
Applied Project The Shape of a Can	287	(1)
4.8 Applications to Economics	288	(5)
4.9 Newton's Method	293	(6)
4.10 Antiderivatives	299	(7)
Review	306	(4)
Problems Plus	310	(2)
5 Integrals	312	(58)
5.1 Areas and Distances	313	(11)
5.2 The Definite Integral	324	(13)
Discovery Project Area Functions	336	(1)
5.3 The Fundamental Theorem of Calculus	337	(9)
5.4 Indefinite Integrals and the Total Change Theorem	346	(10)
Writing Project Newton, Leibniz, and the Invention of Calculus	355	(1)
5.5 The Substitution Rule	356	(7)
Review	363	(4)
Problems Plus	367	(3)
6 Applications of Integration	370	(36)
6.1 Areas between Curves	371	(7)
6.2 Volumes	378	(11)
6.3 Volumes by Cylindrical Shells	389	(5)
6.4 Work	394	(4)
6.5 Average Value of a Function	398	(3)
Review	401	(2)
Problems Plus	403	(3)
7 Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions	406	(96)
7.1 Inverse Functions	407	(9)
Instructors may cover either Sections 7.2-7.4 or Sections 7.2(*)-7.4(*). See the Preface.
7.2 Exponential Functions and Their Derivatives	416	(12)
7.3 Logarithmic Functions	428	(76)
7.4 Derivatives of Logarithmic Functions	435	(10)
7.2(*) The Natural Logarithmic Function	445	(8)
7.3(*) The Natural Exponential Function	453	(7)
7.4(*) General Logarithmic and Exponential Functions	460	(9)
7.5 Inverse Trigonometric Functions	469	(9)
Applied Project Where To Sit at the Movies	478	(1)
7.6 Hyperbolic Functions	478	(7)
7.7 Indeterminate Forms and L'Hospital's Rule	485	(11)
Writing Project The Origins of L'Hospital's Rule	496	(1)
Review	496	(4)
Problems Plus	500	(2)
8 Techniques of Integration	502	(72)
8.1 Integration by Parts	503	(7)
8.2 Trigonometric Integrals	510	(7)
8.3 Trigonometric Substitution	517	(7)
8.4 Integration of Rational Functions by Partial Fractions	524	(9)
8.5 Strategy for Integration	533	(6)
8.6 Integration Using Tables and Computer Algebra Systems	539	(7)
Discovery Project Patterns in Integrals	545	(1)
8.7 Approximate Integration	546	(11)
8.8 Improper Integrals	557	(11)
Review	568	(2)
Problems Plus	571	(3)
9 Further Applications of Integration	574	(40)
9.1 Arc Length	575	(7)
9.2 Area of a Surface of Revolution	582	(7)
Discovery Project Rotating on a Slant	588	(1)
9.3 Applications to Physics and Engineering	589	(9)
9.4 Applications to Economics and Biology	598	(5)
9.5 Probability	603	(7)
Review	610	(2)
Problems Plus	612	(2)
10 Differential Equations	614	(60)
10.1 Modeling with Differential Equations	615	(5)
10.2 Direction Fields and Euler's Method	620	(9)
10.3 Separable Equations	629	(8)
Applied Project Which Is Faster, Going Up or Coming Down?	636	(1)
10.4 Exponential Growth and Decay	637	(10)
Applied Project Calculus and Baseball	646	(1)
10.5 The Logistic Equation	647	(9)
10.6 Linear Equations	656	(6)
10.7 Predator-Prey Systems	662	(6)
Review	668	(4)
Problems Plus	672	(2)
11 Parametric Equations and Polar Coordinates	674	(52)
11.1 Curves Defined by Parametric Equations	675	(7)
Laboratory Project Families of Hypocycloids	682	(1)
11.2 Tangents and Areas	682	(7)
Laboratory Project Bezier Curves	689	(1)
11.3 Arc Length and Surface Area	689	(5)
11.4 Polar Coordinates	694	(10)
11.5 Areas and Lengths in Polar Coordinates	704	(5)
11.6 Conic Sections	709	(7)
11.7 Conic Sections in Polar Coordinates	716	(6)
Review	722	(2)
Problems Plus	724	(2)
12 Infinite Sequences and Series	726
12.1 Sequences	727	(11)
Laboratory Project Logistic Sequences	738	(1)
12.2 Series	738	(10)
12.3 The Integral Test and Estimates of Sums	748	(7)
12.4 The Comparison Tests	755	(5)
12.5 Alternating Series	760	(5)
12.6 Absolute Convergence and the Ratio and Root Tests	765	(7)
12.7 Strategy for Testing Series	772	(2)
12.8 Power Series	774	(5)
12.9 Representations of Functions as Power Series	779	(6)
12.10 Taylor and Maclaurin Series	785	(11)
12.11 The Binomial Series	796	(4)
Writing Project How Newton Discovered the Binomial Series	799	(1)
12.12 Applications of Taylor Polynomials	800	(10)
Applied Project Radiation from the Stars	808	(2)
Review	810	(2)
Problems Plus	812
Appendixes	A1	(104)
A Intervals, Inequalities, and Absolute Values	A2	(8)
B Coordinate Geometry and Lines	A10	(6)
C Graphs of Second-Degree Equations	A16	(8)
D Trigonometry	A24	(10)
E Sigma Notation	A34	(5)
F Proofs of Theorems	A39	(7)
G Complex Numbers	A46	(8)
H Answers to Odd-Numbered Exercises	A54	(51)
Index	A105