University Calculus: International Edition
Autor Joel Hass, Maurice D Weir, George B. Thomas, JR.en Limba Engleză Paperback – feb 2006
University Calculus is the ideal choice for professors who want a faster-paced text with a more conceptually balanced exposition. It is a blend of intuition and rigor. Transcendental functions are introduced early, and are continually revisited in more depth in subsequent chapters of the text
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Specificații
ISBN-13: 9780321416308
ISBN-10: 0321416309
Pagini: 930
Dimensiuni: 203 x 254 mm
Greutate: 1.97 kg
Ediția:1
Editura: Pearson Education
Colecția Pearson Education
Locul publicării:Upper Saddle River, United States
ISBN-10: 0321416309
Pagini: 930
Dimensiuni: 203 x 254 mm
Greutate: 1.97 kg
Ediția:1
Editura: Pearson Education
Colecția Pearson Education
Locul publicării:Upper Saddle River, United States
Cuprins
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
10 Vectors and the Geometry of Space
10.1 Three-Dimensional Coordinate Systems 614
10.2 Vectors 619
10.3 The Dot Product 628
10.4 The Cross Product 636
10.5 Lines and Planes in Space 642
10.6 Cylinders and Quadric Surfaces 652
QUESTIONS TO GUIDE YOUR REVIEW 657
PRACTICE EXERCISES 658
ADDITIONAL AND ADVANCED EXERCISES 660
11 Vector-Valued Functions and Motion in Space
11.1 Vector Functions and Their Derivatives 663
11.2 Integrals of Vector Functions 672
11.3 Arc Length in Space 678
11.4 Curvature of a Curve 683
11.5 Tangential and Normal Components of Acceleration 689
11.6 Velocity and Acceleration in Polar Coordinates 694
QUESTIONS TO GUIDE YOUR REVIEW 698
PRACTICE EXERCISES 698
ADDITIONAL AND ADVANCED EXERCISES 700
12 Partial Derivatives
12.1 Functions of Several Variables 702
12.2 Limits and Continuity in Higher Dimensions 711
12.3 Partial Derivatives 719
12.4 The Chain Rule 731
12.5 Directional Derivatives and Gradient Vectors 739
12.6 Tangent Planes and Differentials 747
12.7 Extreme Values and Saddle Points 756
12.8 Lagrange Multipliers 765
12.9 Taylor’s Formula for Two Variables 775
QUESTIONS TO GUIDE YOUR REVIEW 779
PRACTICE EXERCISES 780
ADDITIONAL AND ADVANCED EXERCISES 783
13 Multiple Integrals
13.1 Double and Iterated Integrals over Rectangles 785
13.2 Double Integrals over General Regions 790
13.3 Area by Double Integration 799
13.4 Double Integrals in Polar Form 802
13.5 Triple Integrals in Rectangular Coordinates 807
13.6 Moments and Centers of Mass 816
13.7 Triple Integrals in Cylindrical and Spherical Coordinates 825
13.8 Substitutions in Multiple Integrals 837
QUESTIONS TO GUIDE YOUR REVIEW 846
PRACTICE EXERCISES 846
ADDITIONAL AND ADVANCED EXERCISES 848
14 Integration in Vector Fields
14.1 Line Integrals 851
14.2 Vector Fields, Work, Circulation, and Flux 856
14.3 Path Independence, Potential Functions, and Conservative Fields 867
14.4 Green’s Theorem in the Plane 877
14.5 Surfaces and Area 887
14.6 Surface Integrals and Flux 896
14.7 Stokes’Theorem 905
14.8 The Divergence Theorem and a Unified Theory 914
QUESTIONS TO GUIDE YOUR REVIEW 925
PRACTICE EXERCISES 925
ADDITIONAL AND ADVANCED EXERCISES 928
15 First-Order Differential Equations (online)
15.1 Solutions, Slope Fields, and Picard’s Theorem
15.2 First-Order Linear Equations
15.3 Applications
15.4 Euler’s Method
15.5 Graphical Solutions of Autonomous Equations
15.6 Systems of Equations and Phase Planes
16 Second-Order Differential Equations (online)
16.1 Second-Order Linear Equations
16.2 Nonhomogeneous Linear Equations
16.3 Applications
16.4 Euler Equations
16.5 Power Series Solutions
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
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
10 Vectors and the Geometry of Space
10.1 Three-Dimensional Coordinate Systems 614
10.2 Vectors 619
10.3 The Dot Product 628
10.4 The Cross Product 636
10.5 Lines and Planes in Space 642
10.6 Cylinders and Quadric Surfaces 652
QUESTIONS TO GUIDE YOUR REVIEW 657
PRACTICE EXERCISES 658
ADDITIONAL AND ADVANCED EXERCISES 660
11 Vector-Valued Functions and Motion in Space
11.1 Vector Functions and Their Derivatives 663
11.2 Integrals of Vector Functions 672
11.3 Arc Length in Space 678
11.4 Curvature of a Curve 683
11.5 Tangential and Normal Components of Acceleration 689
11.6 Velocity and Acceleration in Polar Coordinates 694
QUESTIONS TO GUIDE YOUR REVIEW 698
PRACTICE EXERCISES 698
ADDITIONAL AND ADVANCED EXERCISES 700
12 Partial Derivatives
12.1 Functions of Several Variables 702
12.2 Limits and Continuity in Higher Dimensions 711
12.3 Partial Derivatives 719
12.4 The Chain Rule 731
12.5 Directional Derivatives and Gradient Vectors 739
12.6 Tangent Planes and Differentials 747
12.7 Extreme Values and Saddle Points 756
12.8 Lagrange Multipliers 765
12.9 Taylor’s Formula for Two Variables 775
QUESTIONS TO GUIDE YOUR REVIEW 779
PRACTICE EXERCISES 780
ADDITIONAL AND ADVANCED EXERCISES 783
13 Multiple Integrals
13.1 Double and Iterated Integrals over Rectangles 785
13.2 Double Integrals over General Regions 790
13.3 Area by Double Integration 799
13.4 Double Integrals in Polar Form 802
13.5 Triple Integrals in Rectangular Coordinates 807
13.6 Moments and Centers of Mass 816
13.7 Triple Integrals in Cylindrical and Spherical Coordinates 825
13.8 Substitutions in Multiple Integrals 837
QUESTIONS TO GUIDE YOUR REVIEW 846
PRACTICE EXERCISES 846
ADDITIONAL AND ADVANCED EXERCISES 848
14 Integration in Vector Fields
14.1 Line Integrals 851
14.2 Vector Fields, Work, Circulation, and Flux 856
14.3 Path Independence, Potential Functions, and Conservative Fields 867
14.4 Green’s Theorem in the Plane 877
14.5 Surfaces and Area 887
14.6 Surface Integrals and Flux 896
14.7 Stokes’Theorem 905
14.8 The Divergence Theorem and a Unified Theory 914
QUESTIONS TO GUIDE YOUR REVIEW 925
PRACTICE EXERCISES 925
ADDITIONAL AND ADVANCED EXERCISES 928
15 First-Order Differential Equations (online)
15.1 Solutions, Slope Fields, and Picard’s Theorem
15.2 First-Order Linear Equations
15.3 Applications
15.4 Euler’s Method
15.5 Graphical Solutions of Autonomous Equations
15.6 Systems of Equations and Phase Planes
16 Second-Order Differential Equations (online)
16.1 Second-Order Linear Equations
16.2 Nonhomogeneous Linear Equations
16.3 Applications
16.4 Euler Equations
16.5 Power Series Solutions
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
Notă biografică
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.
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.
Caracteristici
- Strong examples and exercise sets: encouraging students to think clearly about the problems and reinforcing their mathematical intuition
- Early Transcendentals presentation: introducing interesting applications sooner by relating calculus concepts to real world phenomenon
- Exceptional Art: captions and multifigured images providing insight for students that supports conceptual reasoning
- Strong Multivariable Coverage: helping students progress from single variable to multivariable calculus.
- Superior Technology: MyMathLab for Calculus allows instructors to assign homework online and have it automatically graded and placed in their online grade book. Students using MyMathLab have access to:
- Online homework with guided solutions
- Automatic feedback on the work they have completed
- Algorithmically generated exercises for unlimited practice and mastery
- Multiple choice questions that aid students in their understanding and helps them develop their mathematical intuition
- Video lectures, flash cards, animations, java applets, multimedia textbook and Maple/Mathematica projects
- Comprehensive coverage of Differential Equations
- Group Projects
- The Addison-Wesley Tutor Center