Thomas’ Calculus Single Variable – George B. Thoma’s – 12th Edition


Calculus hasn’t changed, but your students have. Today’s students have been raised on immediacy and the desire for relevance, and they come to calculus with varied mathematical backgrounds.

Thomas’ Calculus, Twelfth Edition, helps your students successfully generalize and apply the key ideas of calculus through clear and precise explanations, clean design, thoughtfully chosen examples, and superior exercise sets. Thomas offers the right mix of basic, conceptual, and challenging exercises, along with meaningful applications. This significant revision features more examples, more mid-level exercises, more figures, and improved conceptual flow.

The complete text contains Chapters 1-16. Separate versions are available, This is the Single Variable topics (contains Chapters 1-11), and Multivariable topics (contains Chapters 11-16).

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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 Calculators and Computers

    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 Integration by Parts
    8.2 Trigonometric Integrals
    8.3 Trigonometric Substitutions
    8.4 Integration of Rational Functions by Partial Fractions
    8.5 Integral Tables and Computer Algebra Systems
    8.6 Numerical Integration
    8.7 Improper Integrals

    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 The Ratio and Root Tests
    10.6 Alternating Series, Absolute 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 in Polar Coordinates
    11.5 Areas and Lengths in Polar Coordinates
    11.6 Conic Sections
    11.7 Conics in Polar Coordinates
  • Citation

Download now Calculus Single Variable

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