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Soo T. Tan

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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
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
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
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
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

xx, 1320, 25, 78 p. :
Number of pages

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