Mathematics for economists: an elementary survey/ Taro Yamane

CHAPTER 1 Sets
1.1 Sets -- 1.2 Set operations -- 1.3 Finite and infinite sets -- 1.4 Non-denumerable sets -- 1.5 Cartesian product -- 1.6 Relations -- 1.7 Functions -- 1.8 Ordered sets -- 1.9 Linear point sets -- Notes and References

CHAPTER 2 Functions and Limits
2.1 Metric space -- 2.2 Neighborhood and point of accumulation -- 2.3 Sequence -- 2.4 Limit of sequence -- 2.5 Cauchy sequence -- 2.6 Limit of a function -- 2.7 Continuity -- 2.8 Necessary and sufficient conditions 67, Notes and References

CHAPTER 3 Differentiation
3.1 The derivative -- 3.2 Rules of differentiation -- 3.3 Differentials -- 3.4 Logarithms -- 3.5 Derivative of exponential functions -- 3.6 Cost curves -- 3.7 Demand curve -- 3.8 Other illustrations -- Notes and References

CHAPTER 4 Functions of Several Variables
4.1 Functions of two variables -- 4.2 Partial derivatives -- 4.3 Geometrical presentation of partial derivatives -- 4.4 Differentials, total differential -- 4.5 Second and higher-order differentials -- 4.6 Functions—total derivative -- 4.7 Implicit functions -- 4.8 Higher-order differentiation of implicit functions -- 4.9 Homogeneous functions -- 4.10 Elder"s theorem -- 4.11 Partial elasticities -- Notes and References

CHAPTER 5 Maxima and Minima of Functions
5.1 Increasing and decreasing functions -- 5.2 Convexity of curves -- 5.3 Maxima and minima of functions of one variable -- 5.4 Maxima and minima of functions of two or more variables -- 5.5 Maxima and minima with subsidiary conditions—Lagrange multiplier method -- 5.6 Maxinia and minima with subsidiary conditions (II) -- 5.7 Combining the Lagrange multiplier method and the differential method -- 5.8 Competitive equilibrium of a firm -- 5.9 Monopoly price and output -- 5.10 Dis-criminating monopolist -- 5.11 Equilibrium conditions for a producer -- 5.12 Adding-up theorem -- 5.13 Method of least squares -- Notes and References

CHAPTER 6 Integration
6.1 Riemann integral -- 6.2 Numerical methods for evaluating the integral -- 6.3 Fundamental theorem of the calculus -- 6.4 Techniques of integration -- 6.5 Improper integrals -- 6.6 Multiple integrals -- 6.7 Evaluation of multiple integrals
-- 6.8 Total cost, marginal cost -- 6 9 Law of growth 265, 6.10 Domar's model of public debt and national income -- 6.11 Domar's capital expansion model 272, 6.12 Capitalization -- Paret distribution -- Notes and Reference

CHAPTER 7 Series
7.1 Series -- 7.2 Geometric series -- 7.3 Taylor"s theorem -- 7.4 Taylor series -- 7.5 Exponential series -- 7.6 Taylor''s theorem for several Independent variables -- 7.7 Complex numbers -- 7.8 Inequalities -- Notes and References

CHAPTER 8 Differential Equations
8.1 Introduction -- 8.2 Solutions -- 8.3 Nonlinear differential equations of the first order and first degree -- 8.4 Case I—variables separable case -- 8.5 Case II—differential equation with homogeneous coefficients -- 8.6 Case III—exact differential equations -- 8.7 Linear differential equations of the first order -- 8.8 Linear differential equation of second order with constant coefficient -- 8.9 Domar's capital expansion model -- Notes and References

CHAPTER 9 Difference Equations
9.1 Finite differences -- 9.2 Some operators -- 9.3 Difference equations -- 9.4 Solutions -- 9.5 Homogeneous linear difference equation with constant coefficients -- 9.6 Geometric interpretation of solutions -- 9.7 Particular solutions of non-homogeneous linear equations -- 9.8 Linear first-order difference equations --, 9.9 Linear second-order difference equations with constant coefficients -- 9.10 Interaction between the multiplier and acceleration principle -- Notes and References

CHAPTER 10 Vectors and Matrices (Part I)
10.1 Vectors --10.2 Vector spaces --10.3 Linear dependence -- 10.4 Basis --10.5 A matrix -- 10.6 Elementary operations -- 10.7 Matrix algebra -- 10.8 Equivalence --
10.9 Determinants (I) -- 10.10 Determinants (II) -- 10.11 Inverse matrix -- 10.12 Linear and quadratic forms -- 10.13 Linear transformations -- 10.14 Orthogonal transformations -- 10.15 Rank of a matrix -- Notes and References

CHAPTER 11 Vectors and Matrices (Part II)
11.1 Characteristic equation of a square matrix -- 11.2 Similar matrices -- 11.3 Characteristic rector -- 11.4 Diagonalization of a square matrix -- 11.5 Orthogonal transformations -- 11.6 Diagonalization of real, symmetric matrices -- 11.7 Non-negative quadratic forms -- 11.8 Determining the sign of a quadratic form -- 11.9 Maxima and minima of functions -- 11.10 Partitioned matrices -- 11.11 Partitioned inverse -- 11.12 Differentiation of matrices and determinants -- 11.13 Differentiation
of determinants -- 11.14 Idempotent matrix -- 11.15 Matrix series -- 11.16 Non-negative square matrices -- Notes and References

CHAPTER 12 Vectors and Matrices (Part III)
12.1 Introduction -- 12.2 Descartes' ride of sign -- 12.3 Expansion of a characteristic equation -- 13.4 Solution of simultaneous linear equations -- 12.5 Stability conditions (I) -Schur theorem -- 12.6 Translation of a higher-order difference equation to a lower order -- 12.7 Solving simultaneous difference
equations -- 12.8 Stability conditions (II) -- 12.9 Stability conditions (III) -- 12.10 Stability conditions (IV)-Routh theorem -- 12.11 Stability conditions (V) -- 12.12 Stability conditions (VI) -- 12.13 Convex sets --, Notes and References

CHAPIER 13 Probability and Distributions

13.1 Sample space -- 13.2 A class of sets -- 13.3 .Axioms -- 13.4 Random variable (Part I) -- 13.5 Conditional probability -- 13.6 Distribution function -- 13.7 Expectation variance -- 13.8 Distributions -- 13.9 The central limit theorem -- 13.10 Random variable (Part II) -- 13.11 Jacobian transformations -- Notes and references

CHAPTER 14 Statistical Concepts—Estimation
14.1 Introduction --14.2 Unbiasedness -- 14.3 Consistency -- 4 Efficiency -- 14.5 Sufficiency -- 14.6 Method of maximum likelihood (ML) -- 14.7 Interval estimation -- Notes and References

CHAPTER 15 Testing Hypotheses
15.1 The two-decision problem --15.2 Decision rules and sample space -- 15.3 Appraisal of decision rules -- 15.4 Admissible rules -- 15.5 The Newman-Pearson theory -- 15.6 The minimax rule -- 15.7 The likelihood-ratio test 633, Notes and
References

CHAPTER 16 Regression Analysis
16.1 Introduction -- 16.2 Model I—one independent variable case -- 16.3 Model 1—two independent variable case -- 16.4 Model 2 -- 16.5 Model 2—continued -- 16.6 Estimate of the variances -- 16.7 Bivariate normal distribution -- 16.8 Matrix notation -- 16.9 Moment notation -- Notes and References

CHAPTER 17 Correlation
17.1 Introduction -- 17.2 Simple correlation coefficient --17.3 Partial correlation coefficients -- 17.4 Multiple correlation coefficient -- Notes and
References

CHAPTER 18 Game Theory
18.1 Introduction -- 18.2 Rectangular game -- 18.3 Rectangular game with saddle points -- 18.4 Mixed strategies 696, Notes and References