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Prentice Hall
Essential Mathematics for Economic Analysis / Edition 2

Essential Mathematics for Economic Analysis / Edition 2


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Product Details

ISBN-13: 9780273681809
Publisher: Prentice Hall
Publication date: 09/28/2005
Edition description: REV
Pages: 728
Product dimensions: 7.40(w) x 9.60(h) x 1.00(d)

Table of Contents

1. Introductory Topics: Algebra.
The Real Numbers. Integer Powers. Rules of Algebra. Fractions. Fractional Powers. Inequalities. Intervals and Absolute Values.

2. Introductory Topics: Equations.
How to Solve Simple Equations. Equations with Parameters. Quadratic Equations. Linear Equations in Two Unknowns. Nonlinear Equations.

3. Introductory Topics: Miscellaneous.
Summation Notation. Rules for Sums. Newton's Formula. Double Sums. Products. A Few Aspects of Logic. Mathematical Proofs. Essentials of Set Theory. Mathematical Induction.

4. Functions of One Variable.
Introduction. Basic Definitions. Graphs of Functions. Linear Functions. Linear Models. Quadratic Functions. Polynomials. Power Functions. Exponential Functions. The Natural Logarithmic Function.

5. Properties of Functions.
Shifting Graphs. New Functions from Old. Symmetry. Inverse Functions I. Inverse Functions II. Graphs of Equations in Two Variables. Distance in the Plane. Circles. General Functions.

6. Differentiation, Slopes of Curves.
Tangents. Increasing and Decreasing Functions. Rates of Change. A Dash of Limits. Simple Rules for Differentiation. Sums, Products, and Quotients. Chain Rule. Higher-Order Derivatives. Exponential Functions. Logarithmic Functions.

7. Implicit Differentiation and Continuity.
Implicit Differentiation I. Implicit Differentiation II. Linear Approximations. Differentials. Quadratic and Polynomial Approximations. Taylor's Formula. Why Economists Use Elasticities. Continuity. More on Limits. Intermediate Value Theorem. Newton's Method. Infinite Sequences. Indeterminate Forms and L'Hôpital's Rule.

8. Single-Variable Optimization.
Introduction. Simple Tests. Extreme-Value Theorem. Economic Examples. Local Extreme Points. Inflection Points.

9. Integration.
Antiderivatives. Indefinite Integrals. Areas and Definite Integrals. Properties of Definite Integrals. Economic Applications. Integration by Parts. Integration by Substitution. More Complicated Integrals. Extensions. Income Distribution and Lorenz Curves. A Glimpse at Differential Equations.

10. Mathematics of Finance.
Interest Rates. Continuous Compounding. Present Values. Geometric Series. Present Values of Payment Streams. Mortgages and Annuities. Investment Projects.

11. Functions of Several Variables, Functions of Two Variables.
Partial Derivatives with Two Variables. Geometric Representation. Surfaces and Distances. Functions of Several Variables. Partial Derivatives. Several Variables. Economic Applications. Partial Elasticity.

12. Tools for Comparative Statics.
Chain Rule. More General Chain Rules. Implicit Differentiation. Elasticity of Substitution. More on Implicit Differentiation. Linear Approximations. Differentials. Systems of Equations. Differentiation Systems of Equations. Homogeneous Functions I. Homogeneous Functions II.

13. Multivariable Optimization.
Two Variables. Local Extreme Points. Examples. Extreme-Value Theorem. More Variables.

14. Equality Constraints.
Lagrange's Method. Why Lagrange's Method Works. Sufficient Conditions. More Variables. More Constraints. Comparative Statics A Geometric Formulas and Results, The Greek Alphabet.

Answers to Odd-Numbered Problems.

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