##
**Calculus**

*early transcendentals*

Soo T. Tan

####
Published
**2011**
by
Brooks/Cole Cengage
in
Belmont, CA
.

Written in English.

### About the Book

This textbook provides a brief review of polynomials, trigonometric, exponential, and logarithmic functions, followed by discussion of limits, derivatives, and applications of differential calculus to real-world problem areas. This volume goes on the present an overview of integration, basic techniques for integration, a variety of applications of integration, and an introduction to (systems of) differential equations. In keeping with this emphasis on conceptual understanding, each exercise set in this three semester Calculus text begins with concept questions and each end-of-chapter review section that include fill-in-the-blank questions which are useful for mastering the definitions and theorems in each chapter. Additionally, many questions asking for the interpretation of graphical, numerical, and algebraic results are included among both the examples and the exercise sets.

### Table of Contents

Preliminaries. Lines | ||

Functions and their graphs | ||

The trigonometric functions | ||

Combining functions | ||

Graphing calculators and computers | ||

Mathematical models | ||

Inverse functions | ||

Exponential and logarithmic functions | ||

1. Limits. An intuitive introduction to limits | ||

Techniques for finding limits | ||

A precise definition of a limit | ||

Continuous functions | ||

Tangent lines and rates of change | ||

2. The derivative. The derivative | ||

Basic rules of differentiation | ||

The product and quotient rules | ||

The role of the derivative in the real world | ||

Derivatives of trigonometric functions | ||

The chain rule | ||

Implicit differentiation | ||

Derivatives of logarithmic functions | ||

Related rates | ||

Differentials and linear approximations | ||

3. Applications of the derivative. Extrema of functions | ||

The mean value theorem | ||

Increasing and decreasing functions and the first derivative test | ||

Concavity and inflection points | ||

Limits involving infinity; asymptotes | ||

Curve sketching | ||

Optimization problems | ||

Indeterminant forms and I'Ho pital's rule | ||

Newton's method | ||

4. Integration. Indefinite integrals | ||

Integration by substitution | ||

Area | ||

The definite integral | ||

The fundamental theorem of calculus | ||

Numerical integration | ||

5. Applications of the definite integral. Areas between curves | ||

Volumes : disks, washers, and cross sections | ||

Volumes using cylindrical shells | ||

Arc length and areas of surfaces of revolution | ||

Work | ||

Fluid pressure and force | ||

Moments and center of mass | ||

Hyperbolic functions | ||

6. Techniques of integration. Integration by parts | ||

Trigonometric integrals | ||

Trigonometric substitutions | ||

The method of partial fractions | ||

Integration using tables of integrals and a CAS; a summary of techniques | ||

Improper integrals | ||

7. Differential equations. Differential equations : separable equations | ||

Direction fields and Euler's method | ||

The logistic equation | ||

First-order linear differential equations | ||

Predator-prey models | ||

8. Infinite sequences and series. Sequences | ||

Series | ||

The integral test | ||

The comparison tests | ||

Alternating series | ||

Absolute convergence; the ratio and root tests | ||

Power series | ||

Taylor and Maclaurin series | ||

Approximation by Taylor polynomials | ||

9. Conic sections, plane curves, and polar coordinates. Conic sections | ||

Plane curves and parametric equations | ||

The calculus of parametric equations | ||

Polar coordinates | ||

Areas and arc lengths in polar coordinates | ||

Conic sections in polar coordinates | ||

10. Vectors and the geometry space. Vectors in the plane | ||

Coordinate systems and vectors in 3-space | ||

The dot product | ||

The cross product | ||

Lines and planes in space | ||

Surfaces in space | ||

Cylindrical and spherical coordinates | ||

11. Vector-valued functions. Vector-valued functions and space curves | ||

Differentiation and integration of vector-valued functions | ||

Arc length and curvature | ||

Velocity and acceleration | ||

Tangential and normal components of acceleration | ||

12. Functions of several variables. Functions of two or more variables | ||

Limits and continuity | ||

Partial derivatives | ||

Differentials | ||

The chain rule | ||

Directional derivatives and gradient vectors | ||

Tangent planes and normal lines | ||

Extrema of functions of two variables | ||

Lagrange multipliers | ||

13. Multiple variables. Double integrals | ||

Iterated integrals | ||

Double integrals in polar coordinates | ||

Applications of double integrals | ||

Surface area | ||

Triple integrals | ||

Triple integrals in cylindrical and spherical coordinates | ||

Change of variables in multiple integrals | ||

14. Vector analysis. Vector fields | ||

Divergence and curl | ||

Line integrals | ||

Independence of path and conservative vector fields | ||

Green's theorem | ||

Parametric surfaces | ||

Surface integrals | ||

The divergence theorem | ||

Stokes' theorem | ||

Appendix A: The real number line, inequalities, and absolute value | ||

Appendix B: Proofs of theorems | ||

Appendix C: The definition of the logarithm as an integral. |

### Edition Notes

Includes index.

### The Physical Object

## Pagination |
xx, 1320, 25, 78 p. : |

## Number of pages |
1320 |

### ID Numbers

## Open Library |
OL25567233M |

## Internet Archive |
calculusearlytra00tans |

## ISBN 10 |
0534465544 |

## ISBN 13 |
9780534465544 |

## LC Control Number |
2009941227 |

## OCLC/WorldCat |
428032502 |

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