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Calculus with Analytic Geometry, Brief Edition,9780471594956
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Calculus with Analytic Geometry, Brief Edition

by
Edition:
5th
ISBN13:

9780471594956

ISBN10:
0471594954
Format:
Hardcover
Pub. Date:
1/1/1995
Publisher(s):
WILEY JOHN & SONS INC
List Price: $109.35

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Summary

The aim of this major revision is to create a contemporary text which incorporates the best features of calculus reform yet preserves the main structure of an established and well-tested calculus course. The multivariate calculus material is completely rewritten to include the concept of a vector field and focuses on major physics and engineering applications of vector analysis. Covers such new topics as Jacobians, Kepler's laws, conics in polar coordinates and parametric representation of surfaces. Contains expanded use of calculator computations and numerous exercises.

Table of Contents

Coordinates, Graphs, Lines
1(50)
Real Numbers, Intervals, and Inequalities (A Review)
1(11)
Absolute Value
12(6)
Coordinate Planes and Graphs
18(9)
Lines
27(11)
Distance; Circles; Equations of the Form y = ax2 + bx + c
38(13)
Functions and Limits
51(70)
Functions
51(10)
Operations on Functions
61(6)
Graphs of Functions
67(11)
Limits (An Intuitive Introduction)
78(9)
Limits (Computational Techniques)
87(11)
Limits: A Rigorous Approach
98(6)
Continuity
104(7)
Limits and Continuity of Trigonometric Functions
111(10)
Differentiation
121(58)
Tangent Lines and Rates of Change
121(8)
The Derivative
129(11)
Techniques of Differentiation
140(12)
Derivatives of Trigonometric Functions
152(4)
The Chain Rule
156(7)
Implicit Differentiation
163(6)
Δ-Notation; Differentials
169(10)
Applications of Differentiation
179(68)
Related Rates
179(6)
Intervals of Increase and Decrease; Concavity
185(6)
Relative Extrema; First and Second Derivative Tests
191(6)
Graphs of Polynomials and Rational Functions
197(8)
Other Graphing Problems
205(2)
Maximum and Minimum Values of a Function
207(8)
Applied Maximum and Minimum Problems
215(14)
Newton's Method
229(4)
Rolle's Theorem; Mean-Value Theorem
233(5)
Motion Along a Line (Rectilinear Motion)
238(9)
Integration
247(60)
Introduction
247(3)
Antiderivatives; The Indefinite Integral
250(7)
Integration by Substitution
257(5)
Sigma Notation
262(7)
Areas as Limits
269(6)
The Definite Integral
275(11)
The First Fundamental Theorem of Calculus
286(7)
Evaluating Definite Integrals by Substitution; Approximation by Riemann Sums
293(5)
The Second Fundamental Theorem of Calculus
298(9)
Applications of the Definite Integral
307(42)
Area Between Two Curves
307(6)
Volumes by Slicing; Disks and Washers
313(8)
Volumes by Cylindrical Shells
321(5)
Length of a Plane Curve
326(3)
Area of a Surface of Revolution
329(4)
Application of Integration to Rectilinear Motion
333(5)
Work
338(4)
Fluid Pressure and Force
342(7)
Logarithmic and Exponential Functions
349(64)
Logarithms and Exponents (An Overview)
349(10)
Derivatives and Integrals of Logarithmic and Exponential Functions
359(9)
Graphs Involving Exponentials and Logarithms
368(6)
Inverse Functions
374(9)
Logarithmic and Exponential Functions (Rigorous Approach)
383(9)
The Hyperbolic Functions
392(5)
First-Order Differential Equations and Applications
397(16)
Inverse Trigonometric and Hyperbolic Functions
413(22)
Inverse Trigonometric Functions
413(8)
Derivatives and Integrals Involving Inverse Trigonometric Functions
421(6)
Inverse Hyperbolic Functions
427(8)
Techniques of Integration
435(50)
Review; Integration Using Tables and Computer Algebra Systems
435(6)
Integration by Parts
441(6)
Integrating Powers of Sine and Cosine
447(4)
Integrating Powers of Secant and Tangent
451(3)
Trigonometric Substitutions
454(5)
Integrating Rational Functions; Partial Fractions
459(9)
Miscellaneous Substitutions
468(4)
Numerical Integration; Simpson's Rule
472(13)
Improper Integrals; L'Hopital's Rule
485(24)
Improper Integrals
485(7)
L'Hopital's Rule (Indeterminate Forms of Type 0/0)
492(6)
Other Indeterminate Forms (∞/∞, 0.&ingin;, 0°, ∞°, 1∞, &infin -- ∞)
498(11)
Infinite Series
509(82)
Sequences
509(7)
Monotone Sequences
516(7)
Infinite Series
523(8)
Convergence Tests
531(6)
Additional Convergence Tests
537(5)
The Limit Comparison Test
542(6)
Alternating Series; Conditional Convergence
548(8)
Power Series
556(5)
Taylor and Maclaurin Series
561(7)
Taylor Formula with Remainder; Convergence of Taylor Series
568(9)
Computations Using Taylor Series
577(5)
Differentiation and Integration of Power Series
582(9)
Topics in Analytic Geometry
591(32)
Introduction to the Conic Sections
591(2)
The Parabola; Translation of Coordinate Axes
593(6)
The Ellipse
599(7)
The Hyperbola
606(8)
Rotation of Axes; Second-Degree Equations
614(9)
Polar Coordinates and Parametric Equations
623(34)
Polar Coordinates
623(4)
Graphs in Polar Coordinates
627(9)
Area in Polar Coordinates
636(5)
Parametric Equations
641(10)
Tangent Lines and Arc Length in Polar Coordinates
651(6)
Three-Dimensional Space; Vectors
657(58)
Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces
657(6)
Vectors
663(9)
Dot Product; Projections
672(7)
Cross Product
679(7)
Parametric Equations of Lines
686(5)
Planes in 3-Space
691(7)
Quadric Surfaces
698(10)
Cylindrical and Spherical Coordinates
708(7)
Vector-Valued Functions
715(54)
Introduction of Vector-Valued Functions
715(5)
Calculus of Vector-Valued Functions
720(8)
Change of Parameter; Arc Length
728(8)
Unit Tangent and Normal Vectors
736(4)
Curvature
740(7)
Motion Along a Curve
747(13)
Kepler's Laws of Planetary Motion
760(9)
Partial Derivatives
769(82)
Functions of Two or More Variables
769(14)
Limits and Continuity
783(7)
Partial Derivatives
790(9)
Differentiability and Chain Rules for Functions of Two Variables
799(10)
Tangent Planes; Total Differentials for Functions of Two Variables
809(6)
Directional Derivatives and Gradients for Functions of Two Variables
815(7)
Differentiability, Directional Derivatives, and Gradients for Functions of Three Variables
822(6)
Functions of n Variables; More on the Chain Rule
828(5)
Maxima and Minima of Functions of Two Variables
833(11)
Lagrange Multipliers
844(7)
Multiple Integrals
851(68)
Double Integrals
851(7)
Double Integrals Over Nonrectangular Regions
858(8)
Double Integrals in Polar Coordinates
866(6)
Surface Area
872(6)
Triple Integrals
878(7)
Centroid, Center of Gravity, Theorem of Pappus
885(9)
Triple Integrals in Cylindrical and Spherical Coordinates
894(11)
Change of Variables in Multiple Integrals; Jacobians
905(14)
Topics in Vector Calculus
919(64)
Vector Fields
919(8)
Line Integrals
927(11)
Independence of Path; Conservative Vector Fields
938(8)
Green's Teorem
946(6)
Introduction to Surface Integrals
952(7)
Surface Integrals of Vector Fields; Flux
959(8)
The Divergence Theorem
967(8)
Stokes' Theorem
975(8)
Second-Order Differential Equations
983(14)
Second-Order Linear Homogeneous Differential Equations with Constant Coefficients
983(6)
Second-Order Linear Nonhomogeneous Differential Equations with Constant Coefficients; Undetermined Coefficients
989(6)
Variation of Parameters
995(2)
Vibration of a Spring
997
Appendix A. Review of Sets A1
Appendix B. Trigonometry Review A3
Appendix C. Proofs A19
Appendix D. Cramer's Rule A30
Appendix E. Complex Numbers A34
Answers A45
Index I-1
Photo Credits P1


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