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Table of Contents

**Thomas Calculus 12th Edition PDF Book Description**

**Thomas Calculus 12th Edition PDF Book Description**

*This text is designed for 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, 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, improved conceptual flow, and the best in technology for learning and teaching.

## Thomas Calculus 12th Edition Features

**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 complex topics into manageable sections, allowing instructors to tailor their course to meet the specific needs of their students. For example, the precise definition of the limit is contained in its own section and may be skipped. **Complete and precise multivariable coverage**enhances the connections of multivariable ideas with their single-variable analogues studied earlier in the book.**A robust MyMathLab course**contains 7,900 assignable exercises, a complete e-book, and built-in tutorials so students can get help whenever they need it.**A complete suite of instructor and student supplements**saves class preparation time for instructors and improves students’ learning.

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**Thomas Calculus 12th Edition PDF Table of Contents**

**Thomas Calculus 12th Edition PDF 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

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

**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 Surface

**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 Points

14.8 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. Integration in 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

**Appendices**

- Real Numbers and the Real Line
- Mathematical Induction
- Lines, Circles, and Parabolas
- Proofs of Limit Theorems
- Commonly Occurring Limits
- Theory of the Real Numbers
- Complex Numbers
- The Distributive Law for Vector Cross Products
- The Mixed Derivative Theorem and the Increment Theorem

**Get Thomas Calculus 12th Edition PDF Free Download Below:**

**Get Thomas Calculus 12th Edition PDF Free Download Below:**

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