Thomas’ Calculus in SI Units (13th Edition)

Description

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 Pearson MyLab Mathematics® 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.

Pearson MyLab Mathematics 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.

Key Features

This title is a Pearson Global Edition. The Editorial team at Pearson has worked closely with educators around the world to include content which is especially relevant to students outside the United States.

• Strong exercise sets feature a great breadth of problems–progressing from skills problems to applied and theoretical problems–to encourage students to think about and practice the concepts until they achieve mastery.
• Figures are conceived and rendered to provide insight for students and support conceptual reasoning.
• The flexible table of contents divides topics into manageable sections, allowing instructors to tailor their course to meet the specific needs of their students.
• Complete and precise multivariable coverage enhances the connections of multivariable ideas with their single-variable analogs studied earlier in the book.

Pearson MyLab Mathematics not included. Students, if Pearson MyLab Mathematics is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN and course ID. Pearson MyLab Mathematics should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

• A robust Pearson MyLab Mathematics course contains nearly 9,000 assignable exercises, a complete eBook, and built-in tutorials so students can get help whenever they need it.

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

Thomas’ Calculus, Thirteenth Edition, introduces readers 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 readers’ 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 learners.

New to this Edition

• Two new sections:
  • Section 8.1 reviews basic integration formulas and the Substitution Rules combined with algebraic methods and trigonometric identities
  • Section 8.10 on probability as an application of improper integrals to making predictions for probabilistic models, with a wide range of applications in business and sciences
• Presentation of absolute convergence before considering the Ratio and Root Tests for convergence of a series, which allows the tests to be stated in their stronger forms (Theorems 13 and 14, Section 10.5)
• Updated and new art, and additional tables, supporting examples and exercises throughout
• Material has been rewritten or enhanced, for greater clarity or improved motivation. Here are some examples:
  • Definition of continuous at x = c
  • Geometric insight into L’Hôpital’s Rule
  • Discussion of cycloid curve
  • Introduction to differentiability for functions of several variables
  • Chain Rule for paths
  • Most chapter introductory overviews
• A variety of new examples throughout, including:
  • Predicting the rise in college tuition costs
  • Predicting the decline in tuberculosis death rates
  • Minimizing production costs
  • Integration by parts
  • Log formula for the inverse hyperbolic sine function
  • Using the Integral Test
  • Finding the perimeter of an ellipse
  • Testing multivariable critical points in an exponential function
• Updated and new exercises, including:
  • Using regression analysis to predict Federal minimum wage, median home and energy prices, and global warming
  • More limits involving rational functions
  • Interpreting derivatives from graphs
  • Growth in the Gross National Product
  • Vehicular stopping distance
  • Spread of an oil spill in gulf waters
  • Estimating concentration of a drug
  • Considering endangered species
  • Prescribing drug dosage
  • Summing infinitely many areas
  • Representing functions by a geometric series
  • Unusual polar graphs
  • Finding the distance between skew lines in space
  • Finding mass and distances in our solar system

Key Topics

Functions, Limits and Continuity, Differentiation, Applications of Derivatives, Integration, Applications of Definite Integrals, Transcendental Functions, Techniques of Integration, First-Order Differential Equations, Infinite Sequences and Series, Parametric Equations and Polar Coordinates, Vectors and the Geometry of Space, Vector-Valued Functions and Motion in Space, Partial Derivatives, Multiple Integrals, Integrals and Vector Fields, Second-Order Differential Equations

Target Audience

For all readers interested in calculus.

Table of Contents

1. Functions
   1. Functions and Their Graphs
   2. Combining Functions; Shifting and Scaling Graphs
   3. Trigonometric Functions
   4. Graphing with Software
2. Limits and Continuity
   1. Rates of Change and Tangents to Curves
   2. Limit of a Function and Limit Laws
   3. The Precise Definition of a Limit
   4. One-Sided Limits
   5. Continuity
   6. Limits Involving Infinity; Asymptotes of Graphs
3. Derivatives
   1. Tangents and the Derivative at a Point
   2. The Derivative as a Function
   3. Differentiation Rules
   4. The Derivative as a Rate of Change
   5. Derivatives of Trigonometric Functions
   6. The Chain Rule
   7. Implicit Differentiation
   8. Related Rates
   9. Linearization and Differentials
4. Applications of Derivatives
   1. Extreme Values of Functions
   2. The Mean Value Theorem
   3. Monotonic Functions and the First Derivative Test
   4. Concavity and Curve Sketching
   5. Applied Optimization
   6. Newton’s Method
   7. Antiderivatives
5. Integrals
   1. Area and Estimating with Finite Sums
   2. Sigma Notation and Limits of Finite Sums
   3. The Definite Integral
   4. The Fundamental Theorem of Calculus
   5. Indefinite Integrals and the Substitution Method
   6. Definite Integral Substitutions and the Area Between Curves
6. Applications of Definite Integrals
   1. Volumes Using Cross-Sections
   2. Volumes Using Cylindrical Shells
   3. Arc Length
   4. Areas of Surfaces of Revolution
   5. Work and Fluid Forces
   6. Moments and Centers of Mass
7. Transcendental Functions
   1. Inverse Functions and Their Derivatives
   2. Natural Logarithms
   3. Exponential Functions
   4. Exponential Change and Separable Differential Equations
   5. Indeterminate Forms and L’Hôpital’s Rule
   6. Inverse Trigonometric Functions
   7. Hyperbolic Functions
   8. Relative Rates of Growth
8. Techniques of Integration
   1. Using Basic Integration Formulas
   2. Integration by Parts
   3. Trigonometric Integrals
   4. Trigonometric Substitutions
   5. Integration of Rational Functions by Partial Fractions
   6. Integral Tables and Computer Algebra Systems
   7. Numerical Integration
   8. Improper Integrals
   9. Probability
9. First-Order Differential Equations
   1. Solutions, Slope Fields, and Euler’s Method
   2. First-Order Linear Equations
   3. Applications
   4. Graphical Solutions of Autonomous Equations
   5. Systems of Equations and Phase Planes
10. Infinite Sequences and Series
    1. Sequences
    2. Infinite Series
    3. The Integral Test
    4. Comparison Tests
    5. Absolute Convergence; The Ratio and Root Tests
    6. Alternating Series and Conditional Convergence
    7. Power Series
    8. Taylor and Maclaurin Series
    9. Convergence of Taylor Series
    10. The Binomial Series and Applications of Taylor Series
11. Parametric Equations and Polar Coordinates
    1. Parametrizations of Plane Curves
    2. Calculus with Parametric Curves
    3. Polar Coordinates
    4. Graphing Polar Coordinate Equations
    5. Areas and Lengths in Polar Coordinates
    6. Conic Sections
    7. Conics in Polar Coordinates
12. Vectors and the Geometry of Space
    1. Three-Dimensional Coordinate Systems
    2. Vectors
    3. The Dot Product
    4. The Cross Product
    5. Lines and Planes in Space
    6. Cylinders and Quadric Surfaces
13. Vector-Valued Functions and Motion in Space
    1. Curves in Space and Their Tangents
    2. Integrals of Vector Functions; Projectile Motion
    3. Arc Length in Space
    4. Curvature and Normal Vectors of a Curve
    5. Tangential and Normal Components of Acceleration
    6. Velocity and Acceleration in Polar Coordinates
14. Partial Derivatives
    1. Functions of Several Variables
    2. Limits and Continuity in Higher Dimensions
    3. Partial Derivatives
    4. The Chain Rule
    5. Directional Derivatives and Gradient Vectors
    6. Tangent Planes and Differentials
    7. Extreme Values and Saddle Points
    8. Lagrange Multipliers
    9. Taylor’s Formula for Two Variables
    10. Partial Derivatives with Constrained Variables
15. Multiple Integrals
    1. Double and Iterated Integrals over Rectangles
    2. Double Integrals over General Regions
    3. Area by Double Integration
    4. Double Integrals in Polar Form
    5. Triple Integrals in Rectangular Coordinates
    6. Moments and Centers of Mass
    7. Triple Integrals in Cylindrical and Spherical Coordinates
    8. Substitutions in Multiple Integrals
16. Integrals and Vector Fields
    1. Line Integrals
    2. Vector Fields and Line Integrals: Work, Circulation, and Flux
    3. Path Independence, Conservative Fields, and Potential Functions
    4. Green’s Theorem in the Plane
    5. Surfaces and Area
    6. Surface Integrals
    7. Stokes’ Theorem
    8. The Divergence Theorem and a Unified Theory
17. Second-Order Differential Equations online
    1. Second-Order Linear Equations
    2. Nonhomogeneous Linear Equations
    3. Applications
    4. Euler Equations
    5. Power Series Solutions
18. Appendices
19. 1. A.1 Real Numbers and the Real Line
    2. A.2 Mathematical Induction
    3. A.3 Lines, Circles, and Parabolas
    4. A.4 Proofs of Limit Theorems
    5. A.5 Commonly Occurring Limits
    6. A.6 Theory of the Real Numbers
    7. A.7 Complex Numbers
    8. A.8 The Distributive Law for Vector Cross Products
    9. A.9 The Mixed Derivative Theorem and the Increment Theorem

Authors Biography

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.

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.