Calculus : Concepts and Contexts, Single Variable

by Stewart, James

• ISBN13: 9780534344504
• ISBN10: 053434450X
• Edition: CD
• Format: Paperback
• Copyright: 1997-07-17
• Publisher: Brooks Cole

Table of Contents

A PREVIEW OF CALCULUS	2	(8)
1 FUNCTIONS AND MODELS	10	(84)
1.1 Four Ways to Represent a Function	12	(14)
1.2 New Functions from Old Functions	26	(15)
1.3 Graphing Calculators and Computers	41	(7)
1.4 Parametric Curves	48	(8)
Laboratory Project: Families of Hypocycloids	55	(1)
1.5 Exponential Functions	56	(7)
1.6 Inverse Functions and Logarithms	63	(12)
1.7 Models and Curve Fitting	75	(9)
Review	84	(3)
Principles of Problem Solving	87	(7)
2 LIMITS AND DERIVATIVES	94	(96)
2.1 The Tangent and Velocity Problems	96	(5)
2.2 The Limit of a Function	101	(10)
2.3 Calculating Limits Using the Limit Laws	111	(9)
2.4 Continuity	120	(10)
2.5 Limits Involving Infinity	130	(12)
2.6 Tangents, Velocities, and Other Rates of Change	142	(9)
2.7 Derivatives	151	(7)
Writing Project: Early Methods for Finding Tangents	157	(1)
2.8 The Derivative as a Function	158	(13)
2.9 Linear Approximations	171	(4)
2.10 What Does f' Say about f?	175	(7)
Review	182	(4)
Focus on Problem Solving	186	(4)
3 DIFFERENTIATION RULES	190	(76)
3.1 Derivatives of Polynomials and Exponential Functions	192	(9)
3.2 The Product and Quotient Rules	201	(6)
3.3 Rates of Change in the Natural and Social Sciences	207	(13)
3.4 Derivatives of Trigonometric Functions	220	(7)
3.5 The Chain Rule	227	(12)
Laboratory Project: Bezier Curves	237	(1)
Applied Project: Where Should a Pilot Start Descent?	238	(1)
3.6 Implicit Differentiation	239	(8)
3.7 Derivatives of Logarithmic Functions	247	(7)
Discovery Project: Hyperbolic Functions	253	(1)
3.8 Linear Approximations and Differentials	254	(6)
Laboratory Project: Taylor Polynomials	259	(1)
Review	260	(3)
Focus on Problem Solving	263	(3)
4 APPLICATIONS OF DIFFERENTIATION	266	(82)
4.1 Related Rates	268	(6)
4.2 Maximum and Minimum Values	274	(9)
Applied Project: The Calculus of Rainbows	282	(1)
4.3 Derivatives and the Shapes of Curves	283	(11)
4.4 Graphing with Calculus and Calculators	294	(7)
4.5 Indeterminate Forms and L'Hospital's Rule	301	(9)
Writing Project: The Origins of L'Hospital's Rule	310	(1)
4.6 Optimization Problems	310	(12)
Applied Project: The Shape of a Can	321	(1)
4.7 Applications to Economics	322	(5)
4.8 Newton's Method	327	(5)
4.9 Antiderivatives	332	(8)
Review	340	(4)
Focus on Problem Solving	344	(4)
5 INTEGRALS	348	(98)
5.1 Areas and Distances	350	(11)
5.2 The Definite Integral	361	(11)
5.3 Evaluating Definite Integrals	372	(11)
Discovery Project: Area Functions	382	(1)
5.4 The Fundamental Theorem of Calculus	383	(10)
Writing Project: Newton, Leibniz, and the Invention of Calculus	392	(1)
5.5 The Substitution Rule	393	(9)
5.6 Integration by Parts	402	(6)
5.7 Integration Using Tables and Computer Algebra Systems	408	(8)
Discovery Project: Patterns in Integrals	414	(2)
5.8 Approximate Integration	416	(11)
5.9 Improper Integrals	427	(10)
Review	437	(5)
Focus on Problem Solving	442	(4)
6 APPLICATIONS OF INTEGRATION	446	(56)
6.1 More about Areas	448	(7)
6.2 Volumes	455	(9)
6.3 Arc Length	464	(5)
6.4 Average Value of a Function	469	(4)
Applied Project: Where to Sit at the Movies	472	(1)
6.5 Applications to Physics and Engineering	473	(11)
6.6 Applications to Economics and Biology	484	(5)
6.7 Probability	489	(7)
Review	496	(3)
Focus on Problem Solving	499	(3)
7 DIFFERENTIAL EQUATIONS	502	(56)
7.1 Modeling with Differential Equations	504	(5)
7.2 Direction Fields	509	(5)
7.3 Euler's Method	514	(4)
7.4 Separable Equations	518	(9)
Applied Project: Which is Faster, Going Up or Coming Down?	526	(1)
7.5 Exponential Growth and Decay	527	(10)
Applied Project: Calculus and Baseball	536	(1)
7.6 The Logistic Equation	537	(9)
7.7 Predator-Prey Systems	546	(7)
Review	553	(3)
Focus on Problem Solving	556	(2)
8 INFINITE SEQUENCES AND SERIES	558
8.1 Sequences	560	(10)
Laboratory Project: Logistic Sequences	569	(1)
8.2 Series	570	(9)
8.3 The Integral and Comparison Tests; Estimating Sums	579	(10)
8.4 Other Convergence Tests	589	(8)
8.5 Power Series	597	(6)
8.6 Representations of Functions as Power Series	603	(5)
8.7 Taylor and Maclaurin Series	608	(11)
8.8 The Binomial Series	619	(5)
Writing Project: How Newton Discovered the Binomial Series	623	(1)
8.9 Applications of Taylor Polynomials	624	(9)
Applied Project: Radiation from the Stars	632	(1)
8.10 Using Series to Solve Differential Equations	633	(4)
Review	637	(3)
Focus on Problem Solving	640
APPENDIXES	A1	(112)
A Intervals, Inequalities, and Absolute Values	A2	(5)
B Coordinate Geometry	A7	(12)
C Trigonometry	A19	(13)
D Precise Definitions of Limits	A32	(8)
E A Few Proofs	A40	(2)
F Integration of Rational Functions by Partial Fractions	A42	(9)
G Polar Coordinates	A51	(16)
H Complex Numbers	A67	(9)
I Answers to Odd-Numbered Exercises	A76	(37)
INDEX	A113