Calculus: Graphical, Numerical, Algebraic : Single Variable Version

by Finney, Ross L.; Thomas, George B.; Demana, Franklin; Waits, Bert K.

• ISBN13: 9780201554786
• ISBN10: 020155478X
• Format: Hardcover
• Copyright: 1994-04-01
• Publisher: Pearson

Table of Contents

Prerequisites for Calculus	1	(105)
Coordinates and Graphs in the Plane	1	(10)
Slope, and Equations for Lines	11	(13)
Relations, Functions, and Their Graphs	24	(19)
Geometric Transformations: Shifts, Reflections, Stretches, and Shrinks	43	(11)
Solving Equations and Inequalities Graphically	54	(13)
Relations, Functions and Their Inverses	67	(14)
A Review of Trigonometric Functions	81	(24)
Review Questions	101	(1)
Practice Exercises	102	(3)
Limits and Continuity	105	(62)
Limits	105	(11)
Continuous Functions	116	(11)
The Sandwich Theorem and (sin θ)/θ	127	(4)
Limits Involving Infinity	131	(13)
Controlling Function Outputs: Target Values	144	(7)
Defining Limits Formally with Epsilons and Deltas	151	(16)
Review Questions	163	(1)
Practice Exercises	163	(4)
Derivatives	167	(92)
Slopes, Tangent Lines, and Derivatives	167	(12)
Numerical Derivatives	179	(6)
Differentiation Rules	185	(13)
Velocity, Speed, and Other Rates of Change	198	(16)
Derivatives of Trigonometric functions	214	(6)
The Chain Rule	220	(8)
Implicit Differentiation and Fractional Powers	228	(11)
Linear Approximations and Differentials	239	(20)
Review Questions	252	(1)
Practice Exercises	253	(6)
Applications for Derivatives	259	(88)
Maxima, Minima, and the Mean Value Theorem	259	(13)
Predicting Hidden Behavior	272	(12)
Polynomial Functions, Newton's Method, and Optimization	284	(13)
Rational Functions and Economics Applications	297	(10)
Radical and Transcendental Functions	307	(9)
Related Rates of Change	316	(12)
Antiderivatives, Initial Value Problems, and Mathematical Modeling	328	(19)
Review Questions	342	(1)
Practice Exercises	342	(5)
Integration	347	(86)
Calculus and Area	347	(14)
Definite Integrals	361	(12)
Definite Integrals and Antiderivatives	373	(7)
The Fundamental Theorem of Calculus	380	(14)
Indefinite Integrals	394	(11)
Integration by Substitution - Running the Chain Rule Backward	405	(9)
Numerical Integration: The Trapezoidal Rule and Simpson's Method	414	(19)
Review Questions	428	(1)
Practice Exercises	428	(5)
Applications of Definite Integrals	433	(86)
Areas Between Curves	433	(9)
Volumes of Solids of Revolution-Disks and Washers	442	(14)
Cylindrical Shells - An Alternative to Washers	456	(10)
Lengths of Curves in the Plane	466	(7)
Areas of Surfaces of Revolution	473	(7)
Work	480	(8)
Fluid Pressures and Fluid Forces	488	(6)
Centers of Mass	494	(11)
The Basic Idea: Other Modeling Applications	505	(14)
Review Questions	515	(1)
Practice Exercises	516	(3)
The Calculus of Transcendental Functions	519	(94)
The Natural Logarithm Function	519	(10)
The Exponential Function	529	(18)
Other Exponential and Logarithmic Functions	547	(11)
The Law of Exponential change Revisited	558	(8)
Indeterminate Forms and L'Hopital's Rule	566	(8)
The Rates at Which Functions Grow	574	(7)
The Inverse Trigonometric Functions	581	(7)
Derivatives of Inverse Trigonometric Functions; Related Integrals	588	(8)
Hyperbolic Functions	596	(17)
Review Questions	606	(1)
Practice Exercises	607	(6)
Techniques of Integration	613	(66)
Formulas for Elementary Integrals	614	(6)
Integration by Parts	620	(7)
Integrals Involving Trigonometric Functions	627	(8)
Trigonometric Substitutions	635	(7)
Rational Functions and Partial Fractions	642	(6)
Improper Integrals	648	(12)
Differential Equations	660	(13)
Computer Algebra Systems(CAS)	673	(6)
Review Questions	677	(1)
Practice Exercises	677	(2)
Infinite Series	679	(88)
Limits of Sequences of Numbers	679	(13)
Infinite Series	692	(12)
Series without Negative Terms: Comparison and Integral Tests	704	(10)
Series with Nonnegative Terms: Ratio and Root Tests	714	(6)
Alternating Series and Absolute Convergence	720	(10)
Power Series	730	(13)
Taylor Series and Maclaurin Series	743	(15)
Further Calculations with Taylor Series	758	(9)
Review Questions	764	(1)
Practice Exercises	765	(2)
Plane Curves, Parametrizations, and Polar Coordinates	767	(78)
Conic Sections and Quadratic Equations	767	(16)
The Graphs of Quadratic Equations in x and y	783	(9)
Parametric Equations for Plane Curves	792	(9)
The Calculus of Parametric Equations	801	(8)
Polar Coordinates	809	(7)
Graphing in Polar Coordinates	816	(9)
Polar Equations of Conic Sections	825	(9)
Integration in Polar Coordinates	834	(11)
Review Questions	841	(1)
Practice Exercises	842	(3)
Vectors and Analytic Geometry in Space	845	(68)
Vectors in the Plane	845	(10)
Cartesian (Rectangular) Coordinates and Vectors in Space	855	(13)
Dot Products	868	(8)
Cross Products	876	(7)
Lines and Planes in Space	883	(9)
Surfaces in Space	892	(12)
Cylindrical and Spherical Coordinates	904	(9)
Review Questions	909	(1)
Practice Exercises	909	(4)
Vector-valued Functions, Parametrizations and Motion in Space	913
Vector-valued Functions and Curves in Space; Derivatives and Integrals	913	(11)
Modeling Projectile Motion	924	(13)
Directed Distance and the Unit Tangent Vector T	937	(6)
Curvature, Torsion and the TNB Frame	943	(9)
Planetary Motion and Satellites	952
Review Questions	960	(1)
Practice Exercises	961
Appendixes	APP-1	(1)
A.1 Formulas from Precalculus Mathematics	APP-1	(1)
A.2 Proofs of the Limit Theorems in Chapter 2	APP-6	(1)
A.3 A Proof of the Chain Rule for Functions of a Single Variable	APP-9	(1)
A.4 Mathematical Induction	APP-10	(1)
A.5 Limits That Arise Frequently	APP-13	(1)
A.6 Complex Numbers	APP-15	(1)
A.7 Determinants and Cramer's Rule	APP-16	(1)
A.8 Lagrange Multipliers with Two Constraints	APP-24	(1)
A.9 Path Independence of ∫ F. dr Implies That F = ∇ƒ	APP-26	(1)
Glossary	G-1	(1)
Index of Explorations	IE-1	(1)
Answers	A-1	(1)
Index	I-1	(1)
Brief Table of Integrals	T-1