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by Margaret L. Lial, Nathan P. Ritchey and Raymond N. Greenwell

Edition: 7TH 02Copyright: 2002

Publisher: Addison-Wesley Longman, Inc.

Published: 2002

International: No

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**Lial, Margaret L. : American River College**

Ritchey, Nathan P. : Youngstown State University

Greenwell, Raymond N. : Hofstra University

**R. Algebra Reference. **

R.1 Polynomials.

R.2 Factoring.

R.3 Rational Expressions.

R.4 Equations.

R.5 Inequalities.

R.6 Exponents.

R.7 Radicals.

**1. Linear Functions. **

Slopes and Equations of Lines.

Linear Functions and Applications.

The Least Squares Line.

**2. Nonlinear Functions. **

Properties of Functions.

Quadratic Functions; Translation and Reflection.

Polynomial and Rational Functions.

Exponential Functions.

Logarithmic Functions.

Applications. Growth and Decay; Mathematics of Finance.

**3. The Derivative. **

Limits.

Continuity.

Rates of Change.

Definition of the Derivative.

Graphical Differentiation.

**4. Calculating the Derivative. **

Techniques for Finding Derivatives.

Derivatives of Products and Quotients.

The Chain Rule.

Derivatives of Exponential Functions.

Derivatives of Logarithmic Functions.

**5. Graphs and the Derivative. **

Increasing and Decreasing Functions.

Relative Extrema.

Higher Derivatives, Concavity, and the Second Derivative Test.

Curve Sketching.

**6. Applications of the Derivative. **

Absolute Extrema.

Applications of Extrema.

Further Business Applications: Economic Lot Size, Economic Order Quantity; Elasticity of Demand.

Implicit Differentiation.

Related Rates.

Differentials: Linear Approximation.

**7. Integration. **

Antiderivatives.

Substitution.

Area and the Definite Integral.

The Fundamental Theorem of Calculus.

The Area Between Two Curves.

Numerical Integration.

**8. Further Techniques and Applications of Integration. **

Integration by Parts.

Volume and Average Value.

Continuous Money Flow.

Improper Integrals.

**9. Multivariable Calculus. **

Functions of Several Variables.

Partial Derivatives.

Maxima and Minima.

Lagrange Multipliers.

Total Differentials and Approximations.

Double Integrals.

**10. Differential Equations. **

Solutions of Elementary and Separable Differential Equations.

Linear First-Order Differential Equations.

Euler's Method.

Applications of Differential Equations.

**11. Probability and Calculus. **

Continuous Probability Models.

Expected Value and Variance of Continuous Random Variables.

Special Probability Density Functions.

**12. Sequences and Series. **

Geometric Sequences.

Annuities: An Application of Sequences.

Taylor Polynomials at 0.

Infinite Series.

Taylor Series.

Newton's Method.

L'Hôpital's Rule.

**13. The Trigonometric Functions. **

Definitions of the Trigonometric Functions.

Derivatives of Trigonometric Functions.

Integrals of Trigonometric Functions.

**Tables. **

Table 1. Formulas from Geometry.

Table 2. Area Under a Normal Curve.

Table 3. Integrals.

Table 4. Integrals Involving Trigonometric Functions.

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Author Bio

**Lial, Margaret L. : American River College**

Ritchey, Nathan P. : Youngstown State University

Greenwell, Raymond N. : Hofstra University

Table of Contents

**R. Algebra Reference. **

R.1 Polynomials.

R.2 Factoring.

R.3 Rational Expressions.

R.4 Equations.

R.5 Inequalities.

R.6 Exponents.

R.7 Radicals.

**1. Linear Functions. **

Slopes and Equations of Lines.

Linear Functions and Applications.

The Least Squares Line.

**2. Nonlinear Functions. **

Properties of Functions.

Quadratic Functions; Translation and Reflection.

Polynomial and Rational Functions.

Exponential Functions.

Logarithmic Functions.

Applications. Growth and Decay; Mathematics of Finance.

**3. The Derivative. **

Limits.

Continuity.

Rates of Change.

Definition of the Derivative.

Graphical Differentiation.

**4. Calculating the Derivative. **

Techniques for Finding Derivatives.

Derivatives of Products and Quotients.

The Chain Rule.

Derivatives of Exponential Functions.

Derivatives of Logarithmic Functions.

**5. Graphs and the Derivative. **

Increasing and Decreasing Functions.

Relative Extrema.

Higher Derivatives, Concavity, and the Second Derivative Test.

Curve Sketching.

**6. Applications of the Derivative. **

Absolute Extrema.

Applications of Extrema.

Further Business Applications: Economic Lot Size, Economic Order Quantity; Elasticity of Demand.

Implicit Differentiation.

Related Rates.

Differentials: Linear Approximation.

**7. Integration. **

Antiderivatives.

Substitution.

Area and the Definite Integral.

The Fundamental Theorem of Calculus.

The Area Between Two Curves.

Numerical Integration.

**8. Further Techniques and Applications of Integration. **

Integration by Parts.

Volume and Average Value.

Continuous Money Flow.

Improper Integrals.

**9. Multivariable Calculus. **

Functions of Several Variables.

Partial Derivatives.

Maxima and Minima.

Lagrange Multipliers.

Total Differentials and Approximations.

Double Integrals.

**10. Differential Equations. **

Solutions of Elementary and Separable Differential Equations.

Linear First-Order Differential Equations.

Euler's Method.

Applications of Differential Equations.

**11. Probability and Calculus. **

Continuous Probability Models.

Expected Value and Variance of Continuous Random Variables.

Special Probability Density Functions.

**12. Sequences and Series. **

Geometric Sequences.

Annuities: An Application of Sequences.

Taylor Polynomials at 0.

Infinite Series.

Taylor Series.

Newton's Method.

L'Hôpital's Rule.

**13. The Trigonometric Functions. **

Definitions of the Trigonometric Functions.

Derivatives of Trigonometric Functions.

Integrals of Trigonometric Functions.

**Tables. **

Table 1. Formulas from Geometry.

Table 2. Area Under a Normal Curve.

Table 3. Integrals.

Table 4. Integrals Involving Trigonometric Functions.

Publisher Info

Publisher: Addison-Wesley Longman, Inc.

Published: 2002

International: No

Published: 2002

International: No

**Lial, Margaret L. : American River College**

Ritchey, Nathan P. : Youngstown State University

Greenwell, Raymond N. : Hofstra University

**R. Algebra Reference. **

R.1 Polynomials.

R.2 Factoring.

R.3 Rational Expressions.

R.4 Equations.

R.5 Inequalities.

R.6 Exponents.

R.7 Radicals.

**1. Linear Functions. **

Slopes and Equations of Lines.

Linear Functions and Applications.

The Least Squares Line.

**2. Nonlinear Functions. **

Properties of Functions.

Quadratic Functions; Translation and Reflection.

Polynomial and Rational Functions.

Exponential Functions.

Logarithmic Functions.

Applications. Growth and Decay; Mathematics of Finance.

**3. The Derivative. **

Limits.

Continuity.

Rates of Change.

Definition of the Derivative.

Graphical Differentiation.

**4. Calculating the Derivative. **

Techniques for Finding Derivatives.

Derivatives of Products and Quotients.

The Chain Rule.

Derivatives of Exponential Functions.

Derivatives of Logarithmic Functions.

**5. Graphs and the Derivative. **

Increasing and Decreasing Functions.

Relative Extrema.

Higher Derivatives, Concavity, and the Second Derivative Test.

Curve Sketching.

**6. Applications of the Derivative. **

Absolute Extrema.

Applications of Extrema.

Further Business Applications: Economic Lot Size, Economic Order Quantity; Elasticity of Demand.

Implicit Differentiation.

Related Rates.

Differentials: Linear Approximation.

**7. Integration. **

Antiderivatives.

Substitution.

Area and the Definite Integral.

The Fundamental Theorem of Calculus.

The Area Between Two Curves.

Numerical Integration.

**8. Further Techniques and Applications of Integration. **

Integration by Parts.

Volume and Average Value.

Continuous Money Flow.

Improper Integrals.

**9. Multivariable Calculus. **

Functions of Several Variables.

Partial Derivatives.

Maxima and Minima.

Lagrange Multipliers.

Total Differentials and Approximations.

Double Integrals.

**10. Differential Equations. **

Solutions of Elementary and Separable Differential Equations.

Linear First-Order Differential Equations.

Euler's Method.

Applications of Differential Equations.

**11. Probability and Calculus. **

Continuous Probability Models.

Expected Value and Variance of Continuous Random Variables.

Special Probability Density Functions.

**12. Sequences and Series. **

Geometric Sequences.

Annuities: An Application of Sequences.

Taylor Polynomials at 0.

Infinite Series.

Taylor Series.

Newton's Method.

L'Hôpital's Rule.

**13. The Trigonometric Functions. **

Definitions of the Trigonometric Functions.

Derivatives of Trigonometric Functions.

Integrals of Trigonometric Functions.

**Tables. **

Table 1. Formulas from Geometry.

Table 2. Area Under a Normal Curve.

Table 3. Integrals.

Table 4. Integrals Involving Trigonometric Functions.