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Essential Mathematics for Economic Analysis

ISBN: 9780273655435 | 0273655434
Edition: 1st
Format: Paperback
Publisher: Pearson College Div
Pub. Date: 1/1/2002

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SummaryTable of Contents
For undergraduate and postgraduate courses in math's for economics and math's for econometrics at level 1 and 2 in Economics Departments, 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, whilst focusing on the core topics of mathematics for economists. The major strength of this text is its mathematical reliability, and in-keeping the growing ... MORE
Prefaceix
Introductory Topics, I: Algebra
1(36)
The Real Numbers
1(3)
... MOREInteger Powers
4(6)
Rules of Algebra
10(6)
Fractions
16(5)
Fractional Powers
21(5)
Inequalities
26(6)
Intervals and Absolute Values
32(5)
Review Problems for Chapter 1
35(2)
Introductory Topics, II: Equations
37(18)
How to Solve Simple Equations
37(3)
Equations with Parameters
40(3)
Quadratic Equations
43(6)
Linear Equations in Two Unknowns
49(3)
Nonlinear Equations
52(3)
Review Problems for Chapter 2
54(1)
Introductory Topics, III: Miscellaneous
55(28)
Summation Notation
55(4)
Rules for Sums. Newton's Binomial Formula
59(5)
Double Sums
64(2)
A Few Aspects of Logic
66(6)
Mathematical Proofs
72(2)
Essentials of Set Theory
74(5)
Mathematical Induction
79(4)
Review Problems for Chapter 3
81(2)
Functions of One Variable
83(52)
Introduction
83(1)
Basic Definitions
84(6)
Graphs of Functions
90(4)
Linear Functions
94(7)
Linear Models
101(3)
Quadratic Functions
104(8)
Polynomials
112(7)
Power Functions
119(2)
Exponential Functions
121(6)
Logarithmic Functions
127(8)
Review Problems for Chapter 4
132(3)
Properties of Functions
135(28)
Shifting Graphs
135(5)
New Functions from Old
140(4)
Inverse Functions
144(7)
Graphs of Equations
151(3)
Distance in the Plane. Circles
154(4)
General Functions
158(5)
Review Problems for Chapter 5
161(2)
Differentiation
163(52)
Slopes of Curves
163(2)
The Derivative Tangents
165(6)
Increasing and Decreasing Functions
171(2)
Rates of Change
173(4)
A Dash of Limits
177(5)
Simple Rules for Differentiation
182(4)
Sums, Products, and Quotients
186(7)
Chain Rule
193(5)
Higher-Order Derivatives
198(5)
Exponential Functions
203(4)
Logarithmic Functions
207(8)
Review Problems for Chapter 6
213(2)
Derivatives in Use
215(54)
Implicit Differentiation
215(8)
Differentiating the Inverse
223(2)
Linear Approximations
225(5)
Polynomial Approximations
230(4)
Taylor's Formula
234(4)
Why Economists Use Elasticities
238(4)
Continuity
242(5)
More on Limits
247(8)
Intermediate Value Theorem. Newton's Method
255(3)
Infinite Sequences
258(3)
Indeterminate Forms and L'Hopital's Rule
261(8)
Review Problems for Chapter 7
266(3)
Single-Variable Optimization
269(36)
Introduction
269(3)
Simple Tests for Extreme Points
272(4)
Economic Examples
276(5)
The Extreme-Value Theorem
281(6)
Further Economic Examples
287(4)
Local Extreme Points
291(6)
Inflection Points
297(8)
Review Problems for Chapter 8
302(3)
Integration
305(44)
Indefinite Integrals
305(6)
Area and Definite Integrals
311(6)
Properties of Definite Integrals
317(4)
Economic Applications
321(7)
Integration by Parts
328(4)
Integration by Substitution
332(3)
Infinite Intervals of Integration
335(6)
A Glimpse at Differential Equations
341(8)
Review Problems for Chapter 9
347(2)
Financial Topics: Interest Rates and Present Value
349(28)
Interest Periods and Effective Rates
349(4)
Continuous Compounding
353(2)
Present Value
355(2)
Geometric Series
357(5)
Total Present Value
362(5)
Mortgage Repayments
367(5)
Investment Projects
372(5)
Review Problems for Chapter 10
374(3)
Functions of Several Variables
377(36)
Functions of Two Variables
377(4)
Partial Derivatives with Two Variables
381(6)
Geometric Representation
387(7)
Surfaces and Distance
394(3)
Functions of More Variables
397(5)
Partial Derivatives with More Variables
402(4)
Economic Applications
406(2)
Partial Elasticities
408(5)
Review Problems for Chapter 11
410(3)
Tools for Comparative Statics
413(50)
A Simple Chain Rule
413(5)
Chain Rules for n Variables
418(4)
Implicit Differentiation
422(7)
Elasticity of Substitution
429(3)
Homogeneous Functions of Two Variables
432(5)
General Homogeneous and Homothetic Functions
437(5)
Linear Approximations
442(4)
Differentials
446(4)
Systems of Equations
450(4)
Differentiating Systems of Equations
454(9)
Review Problems for Chapter 12
460(3)
Multivariable Optimization
463(38)
Two Variables
463(8)
Local Extreme Points
471(6)
Linear Models with Quadratic Objectives
477(8)
The Extreme-Value Theorem
485(6)
More Variables
491(4)
Comparative Statics and the Envelope Theorem
495(6)
Review Problems for Chapter 13
499(2)
Constrained Optimization
501(46)
The Lagrange Multiplier Method
501(6)
Economic Interpretations of the Lagrange Multiplier
507(3)
Why the Lagrange Multiplier Method Works
510(5)
Sufficient Conditions
515(3)
More Variables and More Constraints
518(7)
Comparative Statics
525(5)
Nonlinear Programming: A Simple Case
530(6)
More on Nonlinear Programming
536(11)
Review Problems for Chapter 14
544(3)
Matrix and Vector Algebra
547(42)
Systems of Linear Equations
547(4)
Matrices and Matrix Operations
551(4)
Matrix Multiplication
555(4)
Rules for Matrix Multiplication
559(7)
The Transpose
566(2)
Gaussian Elimination
568(6)
Vectors
574(4)
Geometric Interpretations of Vectors
578(5)
Lines and Planes
583(6)
Review Problems for Chapter 15
587(2)
Determinants and Inverse Matrices
589(38)
Determinants of Order 2
589(4)
Determinants of Order 3
593(4)
Determinants of Order n
597(3)
Basic Rules for Determinants
600(5)
Expansion by Cofactors
605(3)
The Inverse of a Matrix
608(6)
A General Formula for the Inverse
614(4)
Cramer's Rule
618(3)
The Leontief Model
621(6)
Review Problems for Chapter 16
625(2)
Appendix: Geometry627(2)
The Greek Alphabet629(1)
Answers. Odd-Numbered Problems630(49)
Index679

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