University Calculus, Part One (Single Variable, Chap 1-9)

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  • Edition: 1st
  • Format: Paperback
  • Copyright: 2007-01-01
  • Publisher: Addison Wesley
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University Calculus: Alternate Edition Part One, Single Variable answers the demand for a more streamlined, less expensive version of the highly acclaimed Thomas' Calculus, Eleventh Edition.& The text retains the same quality and quantity of exercises as the eleventh edition while using a faster-paced presentation. This text focuses on the thinking behind calculus and uses the same precise, accurate exposition for which the Thomas series is well known. The elegant art program helps today's readers visualize important concepts.KEY TOPICS Functions; Limits and Continuity; Differentiation; Applications of Derivatives; Integration; Applications of Definite Integrals; Transcendental Functions; Techniques of Integration; Infinite Sequences and Series; Polar Coordinates and Conics. MARKET For all readers interested in Calculus.

Table of Contents

Prefacep. ix
Functionsp. 1
Functions and Their Graphsp. 1
Combining Functions; Shifting and Scaling Graphsp. 14
Trigonometric Functionsp. 22
Exponential Functionsp. 30
Inverse Functions and Logarithmsp. 36
Graphing with Calculators and Computersp. 50
Limits and Continuityp. 55
Rates of Change and Tangents to Curvesp. 55
Limit of a Function and Limit Lawsp. 62
The Precise Definition of a Limitp. 74
One-Sided Limits and Limits at Infinityp. 84
Infinite Limits and Vertical Asymptotesp. 97
Continuityp. 103
Tangents and Derivatives at a Pointp. 115
Questions to Guide Your Reviewp. 119
Practice Exercisesp. 120
Additional and Advanced Exercisesp. 122
Differentiationp. 125
The Derivative as a Functionp. 125
Differentiation Rules for Polynomials, Exponentials, Products, and Quotientsp. 134
The Derivative as a Rate of Changep. 146
Derivatives of Trigonometric Functionsp. 157
The Chain Rule and Parametric Equationsp. 164
Implicit Differentiationp. 177
Derivatives of Inverse Functions and Logarithmsp. 183
Inverse Trigonometric Functionsp. 194
Related Ratesp. 201
Linearization and Differentialsp. 209
Hyperbolic Functionsp. 221
Questions to Guide Your Reviewp. 227
Practice Exercisesp. 228
Additional and Advanced Exercisesp. 234
Applications of Derivativesp. 237
Extreme Values of Functionsp. 237
The Mean Value Theoremp. 245
Monotonic Functions and the First Derivative Testp. 254
Concavity and Curve Sketchingp. 260
Applied Optimizationp. 271
Indeterminate Forms and L'Hopital's Rulep. 283
Newton's Methodp. 291
Antiderivativesp. 296
Questions to Guide Your Reviewp. 306
Practice Exercisesp. 307
Additional and Advanced Exercisesp. 311
Integrationp. 315
Estimating with Finite Sumsp. 315
Sigma Notation and Limits of Finite Sumsp. 325
The Definite Integralp. 332
The Fundamental Theorem of Calculusp. 345
Indefinite Integrals and the Substitution Rulep. 354
Substitution and Area Between Curvesp. 360
The Logarithm Defined as an Integralp. 370
Questions to Guide Your Reviewp. 381
Practice Exercisesp. 382
Additional and Advanced Exercisesp. 386
Applications of Definite Integralsp. 391
Volumes by Slicing and Rotation About an Axisp. 391
Volumes by Cylindrical Shellsp. 401
Lengths of Plane Curvesp. 408
Areas of Surfaces of Revolutionp. 415
Exponential Change and Separable Differential Equationsp. 421
Workp. 430
Moments and Centers of Massp. 437
Questions to Guide Your Reviewp. 444
Practice Exercisesp. 444
Additional and Advanced Exercisesp. 446
Techniques of Integrationp. 448
Integration by Partsp. 448
Trigonometric Integralsp. 455
Trigonometric Substitutionsp. 461
Integration of Rational Functions by Partial Fractionsp. 464
Integral Tables and Computer Algebra Systemsp. 471
Numerical Integrationp. 477
Improper Integralsp. 487
Questions to Guide Your Reviewp. 497
Practice Exercisesp. 497
Additional and Advanced Exercisesp. 500
Infinite Sequences and Seriesp. 502
Sequencesp. 502
Infinite Seriesp. 515
The Integral Testp. 523
Comparison Testsp. 529
The Ratio and Root Testsp. 533
Alternating Series, Absolute and Conditional Convergencep. 537
Power Seriesp. 543
Taylor and Maclaurin Seriesp. 553
Convergence of Taylor Seriesp. 559
The Binomial Seriesp. 569
Questions to Guide Your Reviewp. 572
Practice Exercisesp. 573
Additional and Advanced Exercisesp. 575
Polar Coordinates and Conicsp. 577
Polar Coordinatesp. 577
Graphing in Polar Coordinatesp. 582
Areas and Lengths in Polar Coordinatesp. 586
Conic Sectionsp. 590
Conics in Polar Coordinatesp. 599
Conics and Parametric Equations; The Cycloidp. 606
Questions to Guide Your Reviewp. 610
Practice Exercisesp. 610
Additional and Advanced Exercisesp. 612
Appendicesp. AP-1
Real Numbers and the Real Linep. AP-1
Mathematical Inductionp. AP-7
Lines, Circles, and Parabolasp. AP-10
Trigonometry Formulasp. AP-19
Proofs of Limit Theoremsp. AP-21
Commonly Occurring Limitsp. AP-25
Theory of the Real Numbersp. AP-26
The Distributive Law for Vector Cross Productsp. AP-29
The Mixed Derivative Theorem and the Increment Theoremp. AP-30
Answersp. A-1
Indexp. I-1
A Brief Table of Integralsp. T-1
Creditsp. C-1
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