## Description

**This text is designed for the single variable component of a three-semester or four-quarter calculus course (math, engineering, and science majors).**

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: Early Transcendentals, Twelfth Edition**,

(contains only chapters 1-11) 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.

This is the standalone book,(contains only chapters 1-11) if you want the book/access card order the ISBN below.

0321705408 / 9780321705402 Thomas' Calculus Early Transcendentals, Single Variable(contains only chapters 1-11) with MML/MSL Student Access Code Card

Package consists of:

0321431308 / 9780321431301 MyMathLab/MyStatLab -- Access Card

0321628837 / 9780321628831 Thomas' Calculus Early Transcendentals, Single Variable

0321654064 / 9780321654069 MyMathLab Inside Star Sticker

## Table of Contents

**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

1.5 Exponential Functions

1.6 Inverse Functions and Logarithms

**2. Limits and Derivatives**

2.1 Rates of Change and Tangents to Curves

2.2 Limit of a Function and Limit Laws

2.3 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 Rules for Polynomials, Exponentials, Products, and Quotients

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 Derivatives of Inverse Functions and Logarithms

3.9 Inverse Trigonometric Functions

3.10 Related Rates

3.11 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 Indeterminate Forms and L'Hopital's Rule

4.6 Applied Optimization

4.7 Newton's Method

4.8 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 Rule

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. Integrals and Transcendental Functions**

7.1 The Logarithm Defined as an Integral

7.2 Exponential Change and Separable Differential Equations

7.3 Hyperbolic Functions

7.4 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

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

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