Calculus, Premiere Edition / Edition 1

Calculus, Premiere Edition / Edition 1

by Robert T. Smith, Roland B. Minton
     
 

ISBN-10: 007230474X

ISBN-13: 9780072304749

Pub. Date: 01/28/2000

Publisher: McGraw-Hill Companies, The

Written for students majoring in mathematics, physics, chemistry, engineering and related fields, this text's presentation is fresh, utilizing all possible resources to help students understand calculus. Written from the ground up with technology integrated, Smith/Minton keeps calculus front and center while integrating technology where it is appropriate.The table of

Overview

Written for students majoring in mathematics, physics, chemistry, engineering and related fields, this text's presentation is fresh, utilizing all possible resources to help students understand calculus. Written from the ground up with technology integrated, Smith/Minton keeps calculus front and center while integrating technology where it is appropriate.The table of contents of this text is primarily traditional, although some minor changes have been made to reflect shifts in the importance of certain applications in engineering and science. This text also gives an early introduction to logarithms, exponentials and the trigonometric functions. Wherever practical, concepts are developed from graphical, numerical, and algebraic perspectives (the "Rule of Three") to give students a full understanding of calculus. This text places a greater emphasis on problem solving and presents more realistic applications, as well as open-ended problems.

Product Details

ISBN-13:
9780072304749
Publisher:
McGraw-Hill Companies, The
Publication date:
01/28/2000
Edition description:
Older Edition
Pages:
1115

Related Subjects

Table of Contents

Preface viii
Preliminaries
1(73)
The Real Numbers and the Cartesian Plane
2(8)
Lines and Functions
10(12)
Graphing Calculators and Computer Algebra Systems
22(9)
Solving Equations
31(6)
Trigonometric Functions
37(8)
Exponential and Logarithmic Functions
45(12)
Transformations of Functions
57(8)
Preview of Calculus
65(9)
Limits and Continuity
74(62)
The Concept of Limit
74(9)
Computation of Limits
83(10)
Continuity and Its Consequences
93(12)
Limits Involving Infinity
105(9)
Formal Definition of the Limit (Optional)
114(13)
Limits and Loss-of-Significance Errors (Optional)
127(9)
Differentiation
136(79)
Tangent Lines and Velocity
136(13)
The Derivative
149(10)
Computation of Derivatives: The Power Rule
159(9)
The Product and Quotient Rules
168(8)
Derivatives of Trigonometric Functions
176(7)
Derivatives of Exponential and Logarithmic Functions
183(7)
The Chain Rule
190(6)
Implicit Differentiation and Related Rates
196(8)
The Mean Value Theorem
204(11)
Applications of Differentiation
215(71)
Linear Approximations and Newton's Method
216(10)
Maximum and Minimum Values
226(10)
Increasing and Decreasing Functions
236(8)
Concavity
244(8)
Overview of Curve Sketching
252(11)
Optimization
263(12)
Rates of Change in Applications (Optional)
275(11)
Integration
286(68)
Antiderivatives
287(11)
Sums and Sigma Notation
298(7)
Area
305(8)
The Definite Integral
313(11)
The Fundamental Theorem of Calculus
324(10)
Integration by Substitution
334(8)
Numerical Integration
342(12)
Applications of the Definite Integral
354(64)
Area Between Curves
354(7)
Volume
361(13)
Volumes by Cylindrical Shells
374(6)
Arc Length and Surface Area
380(7)
Projectile Motion
387(9)
Work, Moments and Hydrostatic Force
396(11)
Probability (Optional)
407(11)
Exponentials, Logarithms and Other Transcendental Functions
418(63)
The Natural Logarithm
419(6)
Inverse Functions
425(6)
The Exponential Function
431(7)
Growth and Decay Problems
438(9)
Separable Differential Equations
447(7)
Euler's Method
454(7)
The Inverse Trigonometric Functions
461(5)
The Calculus of the Inverse Trigonometric Functions
466(6)
The Hyperbolic Functions
472(9)
Integration Techniques
481(59)
Review of Formulas and Techniques
481(5)
Integration by Parts
486(6)
Trigonometric Techniques of Integration
492(9)
Integration of Rational Functions Using Partial Fractions
501(7)
Integration Tables and Computer Algebra Systems
508(8)
Indeterminate Forms and L'Hopital's Rule
516(9)
Improper Integrals
525(15)
Infinite Series
540(86)
Sequences of Real Numbers
540(13)
Infinite Series
553(10)
The Integral Test and Comparison Tests
563(9)
Alternating Series
572(8)
Absolute Convergence and the Ratio Test
580(8)
Power Series
588(8)
Taylor Series
596(13)
Fourier Series
609(17)
Parametric Equations and Polar Coordinates
626(63)
Plane Curves and Parametric Equations
626(11)
Calculus and Parametric Equations
637(7)
Arc Length and Surface Area in Parametric Equations
644(9)
Polar Coordinates
653(12)
Calculus and Polar Coordinates
665(8)
Conic Sections
673(9)
Conic Sections in Polar Coordinates
682(7)
Vectors and the Geometry of Space
689(58)
Vectors in the Plane
689(9)
Vectors in Space
698(8)
The Dot Product
706(8)
The Cross Product
714(12)
Lines and Planes in Space
726(9)
Surfaces in Space
735(12)
Vector-Valued Functions
747(51)
Vector-Valued Functions
747(8)
The Calculus of Vector-Valued Functions
755(11)
Motion in Space
766(10)
Curvature
776(7)
Tangent and Normal Vectors
783(15)
Functions of Several Variables and Partial Differentiation
798(83)
Functions of Several Variables
798(11)
Limits and Continuity
809(12)
Partial Derivatives
821(10)
Tangent Planes and Linear Approximations
831(10)
The Chain Rule
841(6)
The Gradient and Directional Derivatives
847(11)
Extrema of Functions of Several Variables
858(12)
Constrained Optimization and Lagrange Multipliers
870(11)
Multiple Integrals
881(76)
Double Integrals
881(17)
Area, Volume and Center of Mass
898(8)
Double Integrals in Polar Coordinates
906(7)
Surface Area
913(5)
Triple Integrals
918(11)
Cylindrical Coordinates
929(6)
Spherical Coordinates
935(8)
Change of Variables in Multiple Integrals
943(14)
Vector Calculus
957(86)
Vector Fields
958(11)
Line Integrals
969(15)
Independence of Path and Conservative Vector Fields
984(9)
Green's Theorem
993(9)
Curl and Divergence
1002(10)
Surface Integrals
1012(12)
The Divergence Theorem
1024(7)
Stokes' Theorem
1031(12)
Appendix A: Proofs of Selected Theorems 1043(9)
Appendix B: Table of Integrals 1052(8)
Appendix C: Answers to Select Exercises 1060(38)
Bibliography 1098(9)
Index 1107

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