Thomas’ Calculus – George B. Thomas’ – 13th Edition


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 (access kit available separately)–an online homework, tutorial, and study solution designed for today’s students. 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.


  • 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 analogues studied earlier in the book.
  • A complete suite of instructor and student supplements saves class preparation time for instructors and improves students’ learning.

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
  • 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
  • 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
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  • 1. Functions
    1.1 Functions and Their Graphs
    1.2 Combining Functions; Shifting and Scaling Graphs
    1.3 Trigonometric Functions
    1.4 Graphing with Software

    2. Limits and Continuity
    2.1 Rates of Change and Tangents to Curves
    2.2 Limit of a Function and Limit Laws
    2.3 The Precise Definition of a Limit
    2.4 One-Sided Limits
    2.5 Continuity
    2.6 Limits Involving Infinity; Asymptotes of Graphs

    3. Differentiation
    3.1 Tangents and the Derivative at a Point
    3.2 The Derivative as a Function
    3.3 Differentiation Rules
    3.4 The Derivative as a Rate of Change
    3.5 Derivatives of Trigonometric Functions
    3.6 The Chain Rule
    3.7 Implicit Differentiation
    3.8 Related Rates
    3.9 Linearization and Differentials

    4. Applications of Derivatives
    4.1 Extreme Values of Functions
    4.2 The Mean Value Theorem
    4.3 Monotonic Functions and the First Derivative Test
    4.4 Concavity and Curve Sketching
    4.5 Applied Optimization
    4.6 Newton's Method
    4.7 Antiderivatives

    5. Integration
    5.1 Area and Estimating with Finite Sums
    5.2 Sigma Notation and Limits of Finite Sums
    5.3 The Definite Integral
    5.4 The Fundamental Theorem of Calculus
    5.5 Indefinite Integrals and the Substitution Method
    5.6 Substitution and Area Between Curves

    6. Applications of Definite Integrals
    6.1 Volumes Using Cross-Sections
    6.2 Volumes Using Cylindrical Shells
    6.3 Arc Length
    6.4 Areas of Surfaces of Revolution
    6.5 Work and Fluid Forces
    6.6 Moments and Centers of Mass

    7. Transcendental Functions
    7.1 Inverse Functions and Their Derivatives
    7.2 Natural Logarithms
    7.3 Exponential Functions
    7.4 Exponential Change and Separable Differential Equations
    7.5 Indeterminate Forms and L'Hôpital's Rule
    7.6 Inverse Trigonometric Functions
    7.7 Hyperbolic Functions
    7.8 Relative Rates of Growth

    8. Techniques of Integration
    8.1 Using Basic Integration Formulas
    8.2 Integration by Parts
    8.3 Trigonometric Integrals
    8.4 Trigonometric Substitutions
    8.5 Integration of Rational Functions by Partial Fractions
    8.6 Integral Tables and Computer Algebra Systems
    8.7 Numerical Integration
    8.8 Improper Integrals
    8.9 Probability

    9. First-Order Differential Equations
    9.1 Solutions, Slope Fields, and Euler's Method
    9.2 First-Order Linear Equations
    9.3 Applications
    9.4 Graphical Solutions of Autonomous Equations
    9.5 Systems of Equations and Phase Planes

    10. Infinite Sequences and Series
    10.1 Sequences
    10.2 Infinite Series
    10.3 The Integral Test
    10.4 Comparison Tests
    10.5 Absolute Convergence; The Ratio and Root Tests
    10.6 Alternating Series and Conditional Convergence
    10.7 Power Series
    10.8 Taylor and Maclaurin Series
    10.9 Convergence of Taylor Series
    10.10 The Binomial Series and Applications of Taylor Series

    11. Parametric Equations and Polar Coordinates
    11.1 Parametrizations of Plane Curves
    11.2 Calculus with Parametric Curves
    11.3 Polar Coordinates
    11.4 Graphing Polar Coordinate Equations
    11.5 Areas and Lengths in Polar Coordinates
    11.6 Conic Sections
    11.7 Conics in Polar Coordinates

    12. Vectors and the Geometry of Space
    12.1 Three-Dimensional Coordinate Systems
    12.2 Vectors
    12.3 The Dot Product
    12.4 The Cross Product
    12.5 Lines and Planes in Space
    12.6 Cylinders and Quadric Surfaces

    13. Vector-Valued Functions and Motion in Space
    13.1 Curves in Space and Their Tangents
    13.2 Integrals of Vector Functions; Projectile Motion
    13.3 Arc Length in Space
    13.4 Curvature and Normal Vectors of a Curve
    13.5 Tangential and Normal Components of Acceleration
    13.6 Velocity and Acceleration in Polar Coordinates

    14. Partial Derivatives
    14.1 Functions of Several Variables
    14.2 Limits and Continuity in Higher Dimensions
    14.3 Partial Derivatives
    14.4 The Chain Rule
    14.5 Directional Derivatives and Gradient Vectors
    14.6 Tangent Planes and Differentials
    14.7 Extreme Values and Saddle Points14.8 Lagrange Multipliers
    14.9 Taylor's Formula for Two Variables
    14.10 Partial Derivatives with Constrained Variables

    15. Multiple Integrals
    15.1 Double and Iterated Integrals over Rectangles
    15.2 Double Integrals over General Regions
    15.3 Area by Double Integration
    15.4 Double Integrals in Polar Form
    15.5 Triple Integrals in Rectangular Coordinates
    15.6 Moments and Centers of Mass
    15.7 Triple Integrals in Cylindrical and Spherical Coordinates
    15.8 Substitutions in Multiple Integrals

    16. Integrals and Vector Fields
    16.1 Line Integrals
    16.2 Vector Fields and Line Integrals: Work, Circulation, and Flux
    16.3 Path Independence, Conservative Fields, and Potential Functions
    16.4 Green's Theorem in the Plane
    16.5 Surfaces and Area
    16.6 Surface Integrals
    16.7 Stokes' Theorem
    16.8 The Divergence Theorem and a Unified Theory

    17. Second-Order Differential Equations (online)
    17.1 Second-Order Linear Equations
    17.2 Nonhomogeneous Linear Equations
    17.3 Applications
    17.4 Euler Equations
    17.5 Power-Series Solutions


    1. Real Numbers and the Real Line
    2. Mathematical Induction
    3. Lines, Circles, and Parabolas
    4. Proofs of Limit Theorems
    5. Commonly Occurring Limits
    6. Theory of the Real Numbers
    7. Complex Numbers
    8. The Distributive Law for Vector Cross Products
    9. The Mixed Derivative Theorem and the Increment Theorem
  • Citation

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