Single Variable Calculus Early Transcendentals (Non-InfoTrac Version)

by Stewart, James

• ISBN13: 9780534355630
• ISBN10: 0534355633
• Format: Hardcover
• Copyright: 1999-02-19
• Publisher: Brooks Cole

Summary

This best-selling text differs from Calculus, 4/e in that the exponential and logarithmic functions are covered earlier. These functions are introduced in the first chapter and their limits and derivatives are found in Chapters 2 and 3 at the same time as polynomials and the other elementary functions.

Table of Contents

A Preview of Calculus	2	(8)
1 Functions and Models	10	(74)
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)
1.5 Exponential Functions	56	(8)
1.6 Inverse Functions and Logarithms	64	(11)
Review	75	(3)
Principles of Problem Solving	78	(6)
2 Limits and Derivatives	84	(96)
2.1 The Tangent and Velocity Problems	85	(5)
2.2 The Limit of a Function	90	(12)
2.3 Calculating Limits Using the Limit Laws	102	(10)
2.4 The Precise Definition of a Limit	112	(10)
2.5 Continuity	122	(11)
2.6 Limits at Infinity; Horizontal Asymptotes	133	(14)
2.7 Tangents, Velocities, and Other Rates of Change	147	(9)
2.8 Derivatives	156	(7)
Writing Project Early Methods for Finding Tangents	162	(1)
2.9 The Derivative as a Function	163	(11)
Review	174	(4)
Problems Plus	178	(2)
3 Differentiation Rules	180	(96)
3.1 Derivatives of Polynomials and Exponential Functions	181	(9)
3.2 The Product and Quotient Rules	190	(6)
3.3 Rates of Change in the Natural and Social Sciences	196	(12)
3.4 Derivatives of Trigonometric Functions	208	(7)
3.5 The Chain Rule	215	(9)
3.6 Implicit Differentiation	224	(9)
3.7 Higher Derivatives	233	(7)
Applied Project Where Should a Pilot Start Descent?	240	(1)
3.8 Derivatives of Logarithmic Functions	240	(6)
3.9 Hyperbolic Functions	246	(7)
3.10 Related Rates	253	(6)
3.11 Linear Approximations and Differentials	259	(8)
Laboratory Project Taylor Polynomials	266	(1)
Review	267	(4)
Problems Plus	271	(5)
4 Applications of Differentiation	276	(90)
4.1 Maximum and Minimum Values	277	(11)
Applied Project The Calculus of Rainbows	286	(2)
4.2 The Mean Value Theorem	288	(6)
4.3 How Derivatives Affect the Shape of a Graph	294	(11)
4.4 Indeterminate Forms and L'Hospital's Rule	305	(9)
Writing Project The Origins of L'Hospital's Rule	313	(1)
4.5 Summary of Curve Sketching	314	(8)
4.6 Graphing with Calculus and Calculators	322	(7)
4.7 Optimization Problems	329	(11)
Applied Project The Shape of a Can	339	(1)
4.8 Applications to Economics	340	(5)
4.9 Newton's Method	345	(6)
4.10 Antiderivatives	351	(8)
Review	359	(4)
Problems Plus	363	(3)
5 Integrals	366	(66)
5.1 Areas and Distances	367	(11)
5.2 The Definite Integral	378	(13)
Discovery Project Area Functions	390	(1)
5.3 The Fundamental Theorem of Calculus	391	(10)
5.4 Indefinite Integrals and the Total Change Theorem	401	(9)
Writing Project Newton, Leibniz, and the Invention of Calculus	409	(1)
5.5 The Substitution Rule	410	(8)
5.6 The Logarithm Defined as an Integral	418	(7)
Review	425	(4)
Problems Plus	429	(3)
6 Applications of Integration	432	(36)
6.1 Areas between Curves	433	(7)
6.2 Volumes	440	(11)
6.3 Volumes by Cylindrical Shells	451	(5)
6.4 Work	456	(4)
6.5 Average Value of a Function	460	(3)
Applied Project Where to Sit at the Movies	463	(1)
Review	463	(2)
Problems Plus	465	(3)
7 Techniques of Integration	468	(72)
7.1 Integration by Parts	469	(7)
7.2 Trigonometric Integrals	476	(7)
7.3 Trigonometric Substitution	483	(7)
7.4 Integration of Rational Functions by Partial Fractions	490	(9)
7.5 Strategy for Integration	499	(6)
7.6 Integration Using Tables and Computer Algebra Systems	505	(7)
Discovery Project Patterns in Integrals	511	(1)
7.7 Approximate Integration	512	(11)
7.8 Improper Integrals	523	(11)
Review	534	(3)
Problems Plus	537	(3)
8 Further Applications of Integration	540	(40)
8.1 Arc Length	541	(7)
8.2 Area of a Surface of Revolution	548	(7)
Discovery Project Rotating on a Slant	554	(1)
8.3 Applications to Physics and Engineering	555	(9)
8.4 Applications to Economics and Biology	564	(5)
8.5 Probability	569	(7)
Review	576	(2)
Problems Plus	578	(2)
9 Differential Equations	580	(60)
9.1 Modeling with Differential Equations	581	(5)
9.2 Direction Fields and Euler's Method	586	(9)
9.3 Separable Equations	595	(8)
Applied Project Which Is Faster, Going Up or Coming Down?	602	(1)
9.4 Exponential Growth and Decay	603	(10)
Applied Project Calculus and Baseball	612	(1)
9.5 The Logistic Equation	613	(9)
9.6 Linear Equations	622	(6)
9.7 Predator-Prey Systems	628	(6)
Review	634	(4)
Problems Plus	638	(2)
10 Parametric Equations and Polar Coordinates	640	(52)
10.1 Curves Defined by Parametric Equations	641	(7)
Laboratory Project Families of Hypocycloids	648	(1)
10.2 Tangents and Area	648	(7)
Laboratory Project Bezier Curves	655	(1)
10.3 Arc Length and Surface Area	655	(13)
10.4 Polar Coordinates	668	(102)
10.5 Areas and Lengths in Polar Coordinates	770	(5)
10.6 Conic Sections	775	(7)
10.7 Conic Sections in Polar Coordinates	782	(6)
Review	788	(2)
Problems Plus	790
11 Infinite Sequences and Series	692
11.1 Sequences	693
Laboratory Project Logistic Sequences	704	(1)
11.2 Series	704	(10)
11.3 The Integral Test and Estimates of Sums	714	(7)
11.4 The Comparison Tests	721	(5)
11.5 Alternating Series	726	(5)
11.6 Absolute Convergence and the Ratio and Root Tests	731	(7)
11.7 Strategy for Testing Series	738	(2)
11.8 Power Series	740	(5)
11.9 Representations of Functions as Power Series	745	(6)
11.10 Taylor and Maclaurin Series	751	(11)
11.11 The Binomial Series	762	(4)
Writing Project How Newton Discovered the Binomial Series	765	(1)
11.12 Applications of Taylor Polynomials	766	(9)
Applied Project Radiation from the Stars	774	(1)
Review	775	(3)
Problems Plus	778
Appendixes	A1	(106)
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	(13)
E Sigma Notation	A37	(5)
F Proofs of Theorems	A42	(8)
G Complex Numbers	A50	(8)
H Answers to Odd-Numbered Exercises	A58	(49)
Index	A107