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

by Hass, Joel; Weir, Maurice D.; Thomas, George B.

• ISBN13: 9780321454201
• ISBN10: 0321454200
• Edition: 1st
• Format: Paperback
• Copyright: 2007-01-01
• Publisher: Addison Wesley

Summary

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

Preface	p. ix
Functions	p. 1
Functions and Their Graphs	p. 1
Combining Functions; Shifting and Scaling Graphs	p. 14
Trigonometric Functions	p. 22
Exponential Functions	p. 30
Inverse Functions and Logarithms	p. 36
Graphing with Calculators and Computers	p. 50
Limits and Continuity	p. 55
Rates of Change and Tangents to Curves	p. 55
Limit of a Function and Limit Laws	p. 62
The Precise Definition of a Limit	p. 74
One-Sided Limits and Limits at Infinity	p. 84
Infinite Limits and Vertical Asymptotes	p. 97
Continuity	p. 103
Tangents and Derivatives at a Point	p. 115
Questions to Guide Your Review	p. 119
Practice Exercises	p. 120
Additional and Advanced Exercises	p. 122
Differentiation	p. 125
The Derivative as a Function	p. 125
Differentiation Rules for Polynomials, Exponentials, Products, and Quotients	p. 134
The Derivative as a Rate of Change	p. 146
Derivatives of Trigonometric Functions	p. 157
The Chain Rule and Parametric Equations	p. 164
Implicit Differentiation	p. 177
Derivatives of Inverse Functions and Logarithms	p. 183
Inverse Trigonometric Functions	p. 194
Related Rates	p. 201
Linearization and Differentials	p. 209
Hyperbolic Functions	p. 221
Questions to Guide Your Review	p. 227
Practice Exercises	p. 228
Additional and Advanced Exercises	p. 234
Applications of Derivatives	p. 237
Extreme Values of Functions	p. 237
The Mean Value Theorem	p. 245
Monotonic Functions and the First Derivative Test	p. 254
Concavity and Curve Sketching	p. 260
Applied Optimization	p. 271
Indeterminate Forms and L'Hopital's Rule	p. 283
Newton's Method	p. 291
Antiderivatives	p. 296
Questions to Guide Your Review	p. 306
Practice Exercises	p. 307
Additional and Advanced Exercises	p. 311
Integration	p. 315
Estimating with Finite Sums	p. 315
Sigma Notation and Limits of Finite Sums	p. 325
The Definite Integral	p. 332
The Fundamental Theorem of Calculus	p. 345
Indefinite Integrals and the Substitution Rule	p. 354
Substitution and Area Between Curves	p. 360
The Logarithm Defined as an Integral	p. 370
Questions to Guide Your Review	p. 381
Practice Exercises	p. 382
Additional and Advanced Exercises	p. 386
Applications of Definite Integrals	p. 391
Volumes by Slicing and Rotation About an Axis	p. 391
Volumes by Cylindrical Shells	p. 401
Lengths of Plane Curves	p. 408
Areas of Surfaces of Revolution	p. 415
Exponential Change and Separable Differential Equations	p. 421
Work	p. 430
Moments and Centers of Mass	p. 437
Questions to Guide Your Review	p. 444
Practice Exercises	p. 444
Additional and Advanced Exercises	p. 446
Techniques of Integration	p. 448
Integration by Parts	p. 448
Trigonometric Integrals	p. 455
Trigonometric Substitutions	p. 461
Integration of Rational Functions by Partial Fractions	p. 464
Integral Tables and Computer Algebra Systems	p. 471
Numerical Integration	p. 477
Improper Integrals	p. 487
Questions to Guide Your Review	p. 497
Practice Exercises	p. 497
Additional and Advanced Exercises	p. 500
Infinite Sequences and Series	p. 502
Sequences	p. 502
Infinite Series	p. 515
The Integral Test	p. 523
Comparison Tests	p. 529
The Ratio and Root Tests	p. 533
Alternating Series, Absolute and Conditional Convergence	p. 537
Power Series	p. 543
Taylor and Maclaurin Series	p. 553
Convergence of Taylor Series	p. 559
The Binomial Series	p. 569
Questions to Guide Your Review	p. 572
Practice Exercises	p. 573
Additional and Advanced Exercises	p. 575
Polar Coordinates and Conics	p. 577
Polar Coordinates	p. 577
Graphing in Polar Coordinates	p. 582
Areas and Lengths in Polar Coordinates	p. 586
Conic Sections	p. 590
Conics in Polar Coordinates	p. 599
Conics and Parametric Equations; The Cycloid	p. 606
Questions to Guide Your Review	p. 610
Practice Exercises	p. 610
Additional and Advanced Exercises	p. 612
Appendices	p. AP-1
Real Numbers and the Real Line	p. AP-1
Mathematical Induction	p. AP-7
Lines, Circles, and Parabolas	p. AP-10
Trigonometry Formulas	p. AP-19
Proofs of Limit Theorems	p. AP-21
Commonly Occurring Limits	p. AP-25
Theory of the Real Numbers	p. AP-26
The Distributive Law for Vector Cross Products	p. AP-29
The Mixed Derivative Theorem and the Increment Theorem	p. AP-30
Answers	p. A-1
Index	p. I-1
A Brief Table of Integrals	p. T-1
Credits	p. C-1
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