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5 Partner Warehouse Mathematics- Calculus

University Calculus, Part 1 (07 - Old Edition)

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University Calculus, Part 1 (07 - Old Edition) Cover

 

Synopses & Reviews

Please note that used books may not include additional media (study guides, CDs, DVDs, solutions manuals, etc.) as described in the publisher comments.

Publisher Comments:

This streamlined version of ‘Thomas’ Calculus’ provides a faster-paced, precise and accurate presentation of single variable calculus for a college-level calculus course. 'University Calculus, Part One'  is the ideal choice for professors who want a faster-paced single variable text with a more conceptually balanced exposition.  It is a blend of intuition and rigor.  Transcendental functions are introduced early and are covered in depth in subsequent chapters of the text.

About the Author

Joel Hass received his PhD from the University of California—Berkeley. He is currently a professor of mathematics at the University of California—Davis. He has coauthored six widely used calculus texts as well as two calculus study guides. He is currently on the editorial board of Geometriae Dedicata and Media-Enhanced Mathematics. He has been a member of the Institute for Advanced Study at Princeton University and of the Mathematical Sciences Research Institute, and he was a Sloan Research Fellow. Hass’s current areas of research include the geometry of proteins, three dimensional manifolds, applied math, and computational complexity. In his free time, Hass enjoys kayaking.

 

Maurice D. Weir holds a DA and MS from Carnegie-Mellon University and received his BS at Whitman College. He is a Professor Emeritus of the Department of Applied Mathematics at the Naval Postgraduate School in Monterey, California. Weir enjoys teaching Mathematical Modeling and Differential Equations. His current areas of research include modeling and simulation as well as mathematics education. Weir has been awarded the Outstanding Civilian Service Medal, the Superior Civilian Service Award, and the Schieffelin Award for Excellence in Teaching. He has coauthored eight books, including the University Calculus series and the twelfth edition of Thomas’ Calculus.

  George B. Thomas, Jr. (late) of the Massachusetts Institute of Technology, was a professor of mathematics for thirty-eight years; he served as the executive officer of the department for ten years and as graduate registration officer for five years. Thomas held a spot on the board of governors of the Mathematical Association of America and on the executive committee of the mathematics division of the American Society for Engineering Education. His book, Calculus and Analytic Geometry, was first published in 1951 and has since gone through multiple revisions. The text is now in its twelfth edition and continues to guide students through their calculus courses. He also co-authored monographs on mathematics, including the text Probability and Statistics.

Table of Contents

1 Functions

1.1 Functions and Their Graphs 1

1.2 Combining Functions; Shifting and Scaling Graphs 14

1.3 Trigonometric Functions 22

1.4 Exponential Functions 30

1.5 Inverse Functions and Logarithms 36

1.6 Graphing with Calculators and Computers 50

 

2 Limits and Continuity

2.1 Rates of Change and Tangents to Curves 55

2.2 Limit of a Function and Limit Laws 62

2.3 The Precise Definition of a Limit 74

2.4 One-Sided Limits and Limits at Infinity 84

2.5 Infinite Limits and Vertical Asymptotes 97

2.6 Continuity 103

2.7 Tangents and Derivatives at a Point 115

QUESTIONS TO GUIDE YOUR REVIEW 119

PRACTICE EXERCISES 120

ADDITIONAL AND ADVANCED EXERCISES 122

 

3 Differentiation

3.1 The Derivative as a Function 125

3.2 Differentiation Rules for Polynomials, Exponentials, Products, and Quotients 134

3.3 The Derivative as a Rate of Change 146

3.4 Derivatives of Trigonometric Functions 157

3.5 The Chain Rule and Parametric Equations 164

3.6 Implicit Differentiation 177

3.7 Derivatives of Inverse Functions and Logarithms 183

3.8 Inverse Trigonometric Functions 194

3.9 Related Rates 201

3.10 Linearization and Differentials 209

3.11 Hyperbolic Functions 221

QUESTIONS TO GUIDE YOUR REVIEW 227

PRACTICE EXERCISES 228

ADDITIONAL AND ADVANCED EXERCISES 234

 

4 Applications of Derivatives

4.1 Extreme Values of Functions 237

4.2 The Mean Value Theorem 245

4.3 Monotonic Functions and the First Derivative Test 254

4.4 Concavity and Curve Sketching 260

4.5 Applied Optimization 271

4.6 Indeterminate Forms and L’Hôpital’s Rule 283

4.7 Newton’s Method 291

4.8 Antiderivatives 296

QUESTIONS TO GUIDE YOUR REVIEW 306

PRACTICE EXERCISES 307

ADDITIONAL AND ADVANCED EXERCISES 311

 

5 Integration

5.1 Estimating with Finite Sums 315

5.2 Sigma Notation and Limits of Finite Sums 325

5.3 The Definite Integral 332

5.4 The Fundamental Theorem of Calculus 345

5.5 Indefinite Integrals and the Substitution Rule 354

5.6 Substitution and Area Between Curves 360

5.7 The Logarithm Defined as an Integral 370

QUESTIONS TO GUIDE YOUR REVIEW 381

PRACTICE EXERCISES 382

ADDITIONAL AND ADVANCED EXERCISES 386

 

6 Applications of Definite Integrals

6.1 Volumes by Slicing and Rotation About an Axis 391

6.2 Volumes by Cylindrical Shells 401

6.3 Lengths of Plane Curves 408

6.4 Areas of Surfaces of Revolution 415

6.5 Exponential Change and Separable Differential Equations 421

6.6 Work 430

6.7 Moments and Centers of Mass 437

QUESTIONS TO GUIDE YOUR REVIEW 444

PRACTICE EXERCISES 444

ADDITIONAL AND ADVANCED EXERCISES 446

 

7 Techniques of Integration

7.1 Integration by Parts 448

7.2 Trigonometric Integrals 455

7.3 Trigonometric Substitutions 461

7.4 Integration of Rational Functions by Partial Fractions 464

7.5 Integral Tables and Computer Algebra Systems 471

7.6 Numerical Integration 477

7.7 Improper Integrals 487

QUESTIONS TO GUIDE YOUR REVIEW 497

PRACTICE EXERCISES 497

ADDITIONAL AND ADVANCED EXERCISES 500

 

8 Infinite Sequences and Series

8.1 Sequences 502

8.2 Infinite Series 515

8.3 The Integral Test 523

8.4 Comparison Tests 529

8.5 The Ratio and Root Tests 533

8.6 Alternating Series, Absolute and Conditional Convergence 537

8.7 Power Series 543

8.8 Taylor and Maclaurin Series 553

8.9 Convergence of Taylor Series 559

8.10 The Binomial Series 569

QUESTIONS TO GUIDE YOUR REVIEW 572

PRACTICE EXERCISES 573

ADDITIONAL AND ADVANCED EXERCISES 575

 

9 Polar Coordinates and Conics

9.1 Polar Coordinates 577

9.2 Graphing in Polar Coordinates 582

9.3 Areas and Lengths in Polar Coordinates 586

9.4 Conic Sections 590

9.5 Conics in Polar Coordinates 599

9.6 Conics and Parametric Equations; The Cycloid 606

QUESTIONS TO GUIDE YOUR REVIEW 610

PRACTICE EXERCISES 610

ADDITIONAL AND ADVANCED EXERCISES 612

 

Appendices AP-1

A.1 Real Numbers and the Real Line AP-1

A.2 Mathematical Induction AP-7

A.3 Lines, Circles, and Parabolas AP-10

A.4 Trigonometry Formulas AP-19

A.5 Proofs of Limit Theorems AP-21

A.6 Commonly Occurring Limits AP-25

A.7 Theory of the Real Numbers AP-26

A.8 The Distributive Law for Vector Cross Products AP-29

A.9 The Mixed Derivative Theorem and the Increment Theorem AP-30

Product Details

ISBN:
9780321454201
Author:
Hass, Joel
Publisher:
Addison Wesley
Author:
Cram101 Textbook Reviews
Author:
Hass, Joel
Author:
Weir, Maurice D.
Author:
Thomas, George Brinton
Author:
Hass, Joel R.
Author:
Thomas, George B.
Subject:
Calculus
Subject:
Mathematics-Calculus
Subject:
Education-General
Copyright:
Edition Description:
Trade paper
Series:
University Calculus Series
Publication Date:
June 2006
Binding:
Paperback
Grade Level:
College/higher education:
Language:
English
Illustrations:
Y
Pages:
736
Dimensions:
9.9 x 8.4 x 1.1 in 1270 gr

Related Subjects

Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » General

University Calculus, Part 1 (07 - Old Edition) Used Trade Paper
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