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Calculus : Early Transcendentals

ISBN: 9780534251581 | 0534251587
Edition: 3rd
Format: Paperback
Publisher: Brooks Cole
Pub. Date: 3/2/1995

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SummaryTable of Contents
I have tried to write a book that assists students in discovering calculus--both for its practical power and its surprising beauty. In this edition, as in the first two editions, I aim to convey to the student a sense of the utility of calculus and to develop technical competence, but I also strive to give some appreciation for the intrinsic beauty of the subject. Newton undoubtedly experienced a sense of triumph when he made his great discoveries. I want students to share some of that excitement. - from the Preface by the author.
REVIEW AND PREVIEW2(44)
1 Functions and Their Graphs2(15)
2 Types of Functions; Shifting and Scaling17(9)
3 Graphing Calculators and Computers26(6)
4 Principles of Problem Solving... MORE32(7)
5 A Preview of Calculus39(7)
1 LIMITS AND RATES OF CHANGE
46(66)
1.1 The Tangent and Velocity Problems
46(4)
1.2 The Limit of a Function
50(11)
1.3 Calculating Limits using the Limit Laws
61(9)
1.4 The Precise Definition of a Limit
70(10)
1.5 Continuity
80(10)
1.6 Limits at Infinity; Horizontal Asymptotes
90(12)
1.7 Tangents, Velocities, and Other Rates of Change
102(7)
Review
109(3)
2 DERIVATIVES
112(82)
2.1 Derivatives
112(12)
2.2 Differentiation Formulas
124(10)
2.3 Rates of Change in the Natural and Social Sciences
134(9)
2.4 Derivatives of Trigonometric Functions
143(7)
2.5 The Chain Rule
150(8)
2.6 Implicit Differentiation
158(6)
2.7 Higher Derivatives
164(4)
2.8 Related Rates
168(6)
2.9 Differentials; Linear and Quadratic Approximations
174(8)
2.10 Newton's Method
182(5)
Review
187(3)
PROBLEMS PLUS
190(4)
3 INVERSE FUNCTIONS: Exponential, Logarithmic, and Inverse Trigonometric Functions
194(60)
3.1 Exponential Functions and Their Derivatives
194(8)
3.2 Inverse Functions
202(7)
3.3 Logarithmic Functions
209(6)
3.4 Derivatives of Logarithmic Functions
215(7)
3.5 Exponential Growth and Decay
222(6)
3.6 Inverse Trigonometric Functions
228(7)
3.7 Hyperbolic Functions
235(6)
3.8 Indeterminate Forms and l'Hospital's Rule
241(7)
Review
248(4)
APPLICATIONS PLUS
252(2)
4 THE MEAN VALUE THEOREM AND CURVE SKETCHING
254(68)
4.1 Maximum and Minimum Values
254(8)
4.2 The Mean Value Theorem
262(6)
4.3 Monotonic Functions and the First Derivative Test
268(5)
4.4 Concavity and Points of Inflection
273(6)
4.5 Curve Sketching
279(8)
4.6 Graphing with Calculus and Calculators
287(7)
4.7 Applied Maximum and Minimum Problems
294(9)
4.8 Applications to Economics
303(4)
4.9 Antiderivatives
307(8)
Review
315(4)
PROBLEM PLUS
319(3)
5 INTEGRALS
322(58)
5.1 Sigma Notation
322(6)
5.2 Area
328(8)
5.3 The Definite Integral
336(11)
5.4 The Fundamental Theorem of Calculus
347(12)
5.5 The Substitution Rule
359(7)
5.6 The Logarithm Defined as an Integral
366(8)
Review
374(3)
APPLICATIONS PLUS
377(3)
6 APPLICATIONS OF INTEGRATION
380(36)
6.1 Areas between Curves
380(7)
6.2 Volume
387(11)
6.3 Volumes by Cylindrical Shells
398(5)
6.4 Work
403(4)
6.5 Average Value of a Function
407(3)
Review
410(2)
PROBLEMS PLUS
412(4)
7 TECHNIQUES OF INTEGRATION
416(68)
7.1 Integration by Parts
417(6)
7.2 Trigonometric Integrals
423(6)
7.3 Trigonometric Substitution
429(6)
7.4 Integration of Rational Functions by Partial Fractions
435(9)
7.5 Rationalizing Substitutions
444(3)
7.6 Strategy for Integration
447(6)
7.7 Using Tables of Integrals and Computer Algebra Systems
453(4)
7.8 Approximate Integration
457(10)
7.9 Improper Integrals
467(9)
Review
476(3)
APPLICATIONS PLUS
479(5)
8 FURTHER APPLICATIONS OF INTEGRATION
484(44)
8.1 Differential Equations
484(10)
8.2 Arc Length
494(6)
8.3 Area of a Surface of Revolution
500(5)
8.4 Moments and Centers of Mass
505(7)
8.5 Hydrostatic Pressure and Force
512(3)
8.6 Applications to Economics and Biology
515(6)
Review
521(3)
PROBLEMS PLUS
524(4)
9 PARAMETRIC EQUATIONS AND POLAR COORDINATES
528(50)
9.1 Curves Defined by Parametric Equations
528(6)
9.2 Tangents and Areas
534(6)
9.3 Arc Length and Surface Area
540(4)
9.4 Polar Coordinates
544(10)
9.5 Areas and Lengths in Polar Coordinates
554(5)
9.6 Conic Sections
559(7)
9.7 Conic Sections in Polar Coordinates
566(5)
Review
571(2)
APPLICATIONS PLUS
573(5)
10 INFINITE SEQUENCES AND SERIES
578(86)
10.1 Sequences
578(11)
10.2 Series
589(9)
10.3 The Integral Test and Estimates of Sums
598(6)
10.4 The Comparison Tests
604(5)
10.5 Alternating Series
609(5)
10.6 Absolute Convergence and the Ratio and Root Tests
614(7)
10.7 Strategy for Testing Series
621(2)
10.8 Power Series
623(5)
10.9 Representation of Functions as Power Series
628(5)
10.10 Taylor and Maclaurin Series
633(11)
10.11 The Binomial Series
644(4)
10.12 Applications of Taylor Polynomials
648(7)
Review
655(3)
PROBLEMS PLUS
658(6)
11 THREE-DIMENSIONAL ANALYTIC GEOMETRY AND VECTORS
664(76)
11.1 Three-Dimensional Coordinate Systems
664(5)
11.2 Vectors
669(7)
11.3 The Dot Product
676(6)
11.4 The Cross Product
682(7)
11.5 Equations of Lines and Planes
689(9)
11.6 Quadric Surfaces
698(6)
11.7 Vector Functions and Space Curves
704(9)
11.8 Arc Length and Curvature
713(8)
11.9 Motion in Space: Velocity and Acceleration
721(8)
11.10 Cylindrical and Spherical Coordinates
729(4)
Review
733(4)
APPLICATIONS PLUS
737(3)
12 PARTIAL DERIVATIVES
740(72)
12.1 Functions of Several Variables
740(10)
12.2 Limits and Continuity
750(8)
12.3 Partial Derivatives
758(9)
12.4 Tangent Planes and Differentials
767(7)
12.5 The Chain Rule
774(8)
12.6 Directional Derivatives and the Gradient Vector
782(10)
12.7 Maximum and Minimum Values
792(9)
12.8 Lagrange Multipliers
801(6)
Review
807(3)
PROBLEMS PLUS
810(2)
13 MULTIPLE INTEGRALS
812(60)
13.1 Double Integrals over Rectangles
812(5)
13.2 Iterated Integrals
817(6)
13.3 Double Integrals over General Regions
823(8)
13.4 Double Integrals in Polar Coordinates
831(6)
13.5 Applications of Double Integrals
837(6)
13.6 Surface Area
843(2)
13.7 Triple Integrals
845(9)
13.8 Triple Integrals in Cylindrical and Spherical Coordinates
854(6)
13.9 Change of Variables in Multiple Integrals
860(7)
Review
867(3)
APPLICATIONS PLUS
870(2)
14 VECTOR CALCULUS
872
14.1 Vector Fields
872(4)
14.2 Line Integrals
876(11)
14.3 The Fundamental Theorem for Line Integrals
887(9)
14.4 Green's Theorem
896(7)
14.5 Curl and Divergence
903(8)
14.6 Parametric Surfaces and Their Areas
911(7)
14.7 Surface Integrals
918(12)
14.8 Stokes' Theorem
930(6)
14.9 The Divergence Theorem
936(5)
14.10 Summary
941(1)
Review
942(3)
PROBLEMS PLUS
945

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