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Thomas' Calculus: Early Transcendentals in SI Units

Thomas' Calculus: Early Transcendentals in SI Units

George B. Thomas | Maurice D. Weir | Joel R. Hass

(2016)

Additional Information

Book Details

Abstract

Were you looking for the book with access to MyMathLab Global? This product is the book alone and does NOT come with access to MyMathLab Global. Buy Thomas' Calculus: Early Transcendentals in SI Units, 13th edition with MyMathLab Global access card (ISBN 9781292163543) if you need access to MyMathLab Global as well, and save money on this resource. You will also need a course ID from your instructor to access MyMathLab Global.

 

This text is designed for a three-semester or four-quarter calculus course (math, engineering, and science majors).

 

Thomas’ Calculus: Early Transcendentals, Thirteenth Edition, introduces students to the intrinsic beauty of calculus and the power of its applications. For more than half a century, this text has been revered for its clear and precise explanations, thoughtfully chosen examples, superior figures, and time-tested exercise sets. With this new edition, the exercises were refined, updated, and expanded–always with the goal of developing technical competence while furthering students’ appreciation of the subject. Co-authors Hass and Weir have made it their passion to improve the text in keeping with the shifts in both the preparation and ambitions of today's students.

 

The text is available with a robust MyMathLab® course–an online homework, tutorial, and study solution. In addition to interactive multimedia features like lecture videos and eBook, nearly 9,000 algorithmic exercises are available for students to get the practice they need.

 

 


Table of Contents

Section Title Page Action Price
Cover Cover
Thomas’ Calculus: Early Transcendentals 1
Copyright 2
Contents 3
Preface 9
Chapter 1: Functions 15
Functions and Their Graphs 15
Combining Functions; Shifting and Scaling Graphs 28
Trigonometric Functions 35
Graphing with Software 43
Exponential Functions 50
Inverse Functions and Logarithms 55
Questions to Guide Your Review 68
Practice Exercises 68
Additional and Advanced Exercises 71
Chapter 2: Limits and Continuity 73
Rates of Change and Tangents to Curves 73
Limit of a Function and Limit Laws 80
The Precise Definition of a Limit 91
One-Sided Limits 100
Continuity 107
Limits Involving Infinity; Asymptotes of Graphs 118
Questions to Guide Your Review 132
Practice Exercises 132
Additional and Advanced Exercises 134
Chapter 3: Derivatives 137
Tangents and the Derivative at a Point 137
The Derivative as a Function 142
Differentiation Rules 150
The Derivative as a Rate of Change 160
Derivatives of Trigonometric Functions 170
The Chain Rule 177
Implicit Differentiation 185
Derivatives of Inverse Functions and Logarithms 191
Inverse Trigonometric Functions 201
Related Rates 207
Linearization and Differentials 216
Questions to Guide Your Review 228
Practice Exercises 229
Additional and Advanced Exercises 233
Chapter 4: Applications of Derivatives 237
Extreme Values of Functions 237
The Mean Value Theorem 245
Monotonic Functions and the First Derivative Test 253
Concavity and Curve Sketching 258
Indeterminate Forms and L’Hôpital’s Rule 269
Applied Optimization 278
Newton’s Method 290
Antiderivatives 295
Questions to Guide Your Review 305
Practice Exercises 305
Additional and Advanced Exercises 309
Chapter 5: Integrals 313
Area and Estimating with Finite Sums 313
Sigma Notation and Limits of Finite Sums 323
The Definite Integral 330
The Fundamental Theorem of Calculus 342
Indefinite Integrals and the Substitution Method 353
Definite Integral Substitutions and the Area Between Curves 361
Questions to Guide Your Review 371
Practice Exercises 371
Additional and Advanced Exercises 375
Chapter 6: Applications of Definite Integrals 379
Volumes Using Cross-Sections 379
Volumes Using Cylindrical Shells 390
Arc Length 398
Areas of Surfaces of Revolution 404
Work and Fluid Forces 409
Moments and Centers of Mass 418
Questions to Guide Your Review 429
Practice Exercises 430
Additional and Advanced Exercises 431
Chapter 7: Integrals and Transcendental Functions 434
The Logarithm Defined as an Integral 434
Exponential Change and Separable Differential Equations 444
Hyperbolic Functions 453
Relative Rates of Growth 462
Questions to Guide Your Review 467
Practice Exercises 467
Additional and Advanced Exercises 469
Chapter 8: Techniques of Integration 470
Using Basic Integration Formulas 470
Integration by Parts 475
Trigonometric Integrals 483
Trigonometric Substitutions 489
Integration of Rational Functions by Partial Fractions 494
Integral Tables and Computer Algebra Systems 503
Numerical Integration 508
Improper Integrals 518
Probability 529
Questions to Guide Your Review 542
Practice Exercises 543
Additional and Advanced Exercises 545
Chapter 9: First-Order Differential Equations 550
Solutions, Slope Fields, and Euler’s Method 550
First-Order Linear Equations 558
Applications 564
Graphical Solutions of Autonomous Equations 570
Systems of Equations and Phase Planes 577
Questions to Guide Your Review 583
Practice Exercises 583
Additional and Advanced Exercises 584
Chapter 10: Infinite Sequences and Series 586
Sequences 586
Infinite Series 598
The Integral Test 607
Comparison Tests 614
Absolute Convergence; The Ratio and Root Tests 618
Alternating Series and Conditional Convergence 624
Power Series 630
Taylor and Maclaurin Series 640
Convergence of Taylor Series 645
The Binomial Series and Applications of Taylor Series 652
Questions to Guide Your Review 661
Practice Exercises 662
Additional and Advanced Exercises 664
Chapter 11: Parametric Equations and Polar Coordinates 667
Parametrizations of Plane Curves 667
Calculus with Parametric Curves 675
Polar Coordinates 685
Graphing Polar Coordinate Equations 689
Areas and Lengths in Polar Coordinates 693
Conic Sections 697
Conics in Polar Coordinates 706
Questions to Guide Your Review 713
Practice Exercises 713
Additional and Advanced Exercises 715
Chapter 12: Vectors and the Geometry of Space 718
Three-Dimensional Coordinate Systems 718
Vectors 723
The Dot Product 732
The Cross Product 740
Lines and Planes in Space 746
Cylinders and Quadric Surfaces 754
Questions to Guide Your Review 759
Practice Exercises 760
Additional and Advanced Exercises 762
Chapter 13: Vector-Valued Functions and Motion in Space 765
Curves in Space and Their Tangents 765
Integrals of Vector Functions; Projectile Motion 773
Arc Length in Space 782
Curvature and Normal Vectors of a Curve 786
Tangential and Normal Components of Acceleration 792
Velocity and Acceleration in Polar Coordinates 798
Questions to Guide Your Review 802
Practice Exercises 802
Additional and Advanced Exercises 804
Chapter 14: Partial Derivatives 807
Functions of Several Variables 807
Limits and Continuity in Higher Dimensions 815
Partial Derivatives 824
The Chain Rule 835
Directional Derivatives and Gradient Vectors 844
Tangent Planes and Differentials 853
Extreme Values and Saddle Points 862
Lagrange Multipliers 871
Taylor’s Formula for Two Variables 880
Partial Derivatives with Constrained Variables 884
Questions to Guide Your Review 889
Practice Exercises 890
Additional and Advanced Exercises 893
Chapter 15: Multiple Integrals 896
Double and Iterated Integrals over Rectangles 896
Double Integrals over General Regions 901
Area by Double Integration 910
Double Integrals in Polar Form 914
Triple Integrals in Rectangular Coordinates 920
Moments and Centers of Mass 929
Triple Integrals in Cylindrical and Spherical Coordinates 936
Substitutions in Multiple Integrals 948
Questions to Guide Your Review 958
Practice Exercises 958
Additional and Advanced Exercises 961
Chapter 16: Integrals and Vector Fields 964
Line Integrals 964
Vector Fields and Line Integrals: Work, Circulation, and Flux 971
Path Independence, Conservative Fields, and Potential Functions 983
Green’s Theorem in the Plane 994
Surfaces and Area 1006
Surface Integrals 1017
Stokes’ Theorem 1028
The Divergence Theorem and a Unified Theory 1041
Questions to Guide Your Review 1053
Practice Exercises 1054
Additional and Advanced Exercises 1056
Chapter 17: Second-Order Differential Equations 17-1
Second-Order Linear Equations 17-1
Nonhomogeneous Linear Equations 17-8
Applications 17-17
Euler Equations 17-23
Power Series Solutions 17-26
Appendices AP-1
Real Numbers and the Real Line AP-1
Mathematical Induction AP-6
Lines, Circles, and Parabolas AP-10
Proofs of Limit Theorems AP-19
Commonly Occurring Limits AP-22
Theory of the Real Numbers AP-23
Complex Numbers AP-26
The Distributive Law for Vector Cross Products AP-35
The Mixed Derivative Theorem and the Increment Theorem AP-36
Answers to Odd-Numbered Exercises A-1
Index I-1
Credits C-1
A Brief Table of Integrals T-1
Basic Formulas and Rules F-1