## Thomas' Calculus in SI Units

(2016)

### Abstract

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

Thomas’ Calculus, 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.

Students, if MyMathLab is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN and course ID. Instructors can contact their Pearson representative for more information.

MyMathLab is an online homework, tutorial, and assessment product designed to personalize learning and improve results. With a wide range of interactive, engaging, and assignable activities, students are encouraged to actively learn and retain tough course concepts.

Section Title Page Action Price
Cover Cover
Thomas’ Calculus: Thirteenth Edition in SI Units 1
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
Questions to Guide Your Review 50
Practice Exercises 50
Chapter 2: Limits and Continuity 55
Rates of Change and Tangents to Curves 55
Limit of a Function and Limit Laws 62
The Precise Definition of a Limit 73
One-Sided Limits 82
Continuity 89
Limits Involving Infinity; Asymptotes of Graphs 100
Questions to Guide Your Review 113
Practice Exercises 114
Chapter 3: Derivatives 119
Tangents and the Derivative at a Point 119
The Derivative as a Function 124
Differentiation Rules 132
The Derivative as a Rate of Change 141
Derivatives of Trigonometric Functions 151
The Chain Rule 158
Implicit Differentiation 165
Related Rates 170
Linearization and Differentials 179
Questions to Guide Your Review 191
Practice Exercises 191
Chapter 4: Applications of Derivatives 199
Extreme Values of Functions 199
The Mean Value Theorem 207
Monotonic Functions and the First Derivative Test 213
Concavity and Curve Sketching 218
Applied Optimization 229
Newton’s Method 241
Antiderivatives 246
Questions to Guide Your Review 256
Practice Exercises 257
Chapter 5: Integrals 263
Area and Estimating with Finite Sums 263
Sigma Notation and Limits of Finite Sums 273
The Definite Integral 280
The Fundamental Theorem of Calculus 292
Indefinite Integrals and the Substitution Method 303
Definite Integral Substitutions and the Area Between Curves 310
Questions to Guide Your Review 320
Practice Exercises 320
Chapter 6: Applications of Definite Integrals 327
Volumes Using Cross-Sections 327
Volumes Using Cylindrical Shells 338
Arc Length 345
Areas of Surfaces of Revolution 351
Work and Fluid Forces 356
Moments and Centers of Mass 365
Questions to Guide Your Review 376
Practice Exercises 376
Chapter 7: Transcendental Functions 380
Inverse Functions and Their Derivatives 380
Natural Logarithms 388
Exponential Functions 396
Exponential Change and Separable Differential Equations 407
Indeterminate Forms and L’Hôpital’s Rule 417
Inverse Trigonometric Functions 425
Hyperbolic Functions 438
Relative Rates of Growth 447
Questions to Guide Your Review 452
Practice Exercises 453
Chapter 8: Techniques of Integration 458
Using Basic Integration Formulas 458
Integration by Parts 463
Trigonometric Integrals 471
Trigonometric Substitutions 477
Integration of Rational Functions by Partial Fractions 482
Integral Tables and Computer Algebra Systems 491
Numerical Integration 496
Improper Integrals 506
Probability 517
Questions to Guide Your Review 530
Practice Exercises 531
Chapter 9: First-Order Differential Equations 538
Solutions, Slope Fields, and Euler’s Method 538
First-Order Linear Equations 546
Applications 552
Graphical Solutions of Autonomous Equations 558
Systems of Equations and Phase Planes 565
Questions to Guide Your Review 571
Practice Exercises 571
Chapter 10: Infinite Sequences and Series 574
Sequences 574
Infinite Series 586
The Integral Test 595
Comparison Tests 602
Absolute Convergence; The Ratio and Root Tests 606
Alternating Series and Conditional Convergence 612
Power Series 618
Taylor and Maclaurin Series 628
Convergence of Taylor Series 633
The Binomial Series and Applications of Taylor Series 640
Questions to Guide Your Review 649
Practice Exercises 650
Chapter 11: Parametric Equations and Polar Coordinates 655
Parametrizations of Plane Curves 655
Calculus with Parametric Curves 663
Polar Coordinates 673
Graphing Polar Coordinate Equations 677
Areas and Lengths in Polar Coordinates 681
Conic Sections 685
Conics in Polar Coordinates 694
Questions to Guide Your Review 701
Practice Exercises 701
Chapter 12: Vectors and the Geometry of Space 706
Three-Dimensional Coordinate Systems 706
Vectors 711
The Dot Product 720
The Cross Product 728
Lines and Planes in Space 734
Questions to Guide Your Review 747
Practice Exercises 748
Chapter 13: Vector-Valued Functions and Motion in Space 753
Curves in Space and Their Tangents 753
Integrals of Vector Functions; Projectile Motion 761
Arc Length in Space 770
Curvature and Normal Vectors of a Curve 774
Tangential and Normal Components of Acceleration 780
Velocity and Acceleration in Polar Coordinates 786
Questions to Guide Your Review 790
Practice Exercises 790
Chapter 14: Partial Derivatives 795
Functions of Several Variables 795
Limits and Continuity in Higher Dimensions 803
Partial Derivatives 812
The Chain Rule 823
Directional Derivatives and Gradient Vectors 832
Tangent Planes and Differentials 841
Extreme Values and Saddle Points 850
Lagrange Multipliers 859
Taylor’s Formula for Two Variables 868
Partial Derivatives with Constrained Variables 872
Questions to Guide Your Review 877
Practice Exercises 878
Chapter 15: Multiple Integrals 884
Double and Iterated Integrals over Rectangles 884
Double Integrals over General Regions 889
Area by Double Integration 898
Double Integrals in Polar Form 902
Triple Integrals in Rectangular Coordinates 908
Moments and Centers of Mass 917
Triple Integrals in Cylindrical and Spherical Coordinates 924
Substitutions in Multiple Integrals 936
Questions to Guide Your Review 946
Practice Exercises 946
Chapter 16: Integrals and Vector Fields 952
Line Integrals 952
Vector Fields and Line Integrals: Work, Circulation, and Flux 959
Path Independence, Conservative Fields, and Potential Functions 971
Green’s Theorem in the Plane 982
Surfaces and Area 994
Surface Integrals 1005
Stokes’ Theorem 1016
The Divergence Theorem and a Unified Theory 1029
Questions to Guide Your Review 1041
Practice Exercises 1042
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