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Essential Mathematics for Economic Analysis

Essential Mathematics for Economic Analysis - 02 edition

Essential Mathematics for Economic Analysis - 02 edition

ISBN13: 9780273655435

ISBN10: 0273655434

Essential Mathematics for Economic Analysis by Knut Sydsaeter - ISBN 9780273655435
Edition: 02
Copyright: 2002
Publisher: Prentice Hall, Inc.
Published:
International: No
Essential Mathematics for Economic Analysis by Knut Sydsaeter - ISBN 9780273655435

ISBN13: 9780273655435

ISBN10: 0273655434

Edition: 02

Other Editions of Essential Mathematics for Economic Analysis


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Summary

For undergraduate and graduate courses in math for economists, also suitable for general math's courses on Social Science degrees.
The first volume of this two volume series presents an introduction to mathematical analysis through comprehensive and rigorous topics ranging from elementary algebra to advanced topics, while focusing on the core topics of mathematics for economists. The major strength of this text is its mathematical reliability, and in-keeping with the growing demand, this text includes more elementary material; advanced topics will be in Volume II. A wealth of problem and answer material exist.

Table of Contents

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.
Index.

Other Editions of Essential Mathematics for Economic Analysis

Essential Mathematics for Economic Analysis by Knut Sydsaeter and Peter Hammond - ISBN 9780273681809