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Note: Contents data are machine generated based on pre-publication provided by the publisher. Contents may have variations from the printed book or be incomplete or contain other coding. ```Preface
PART 1: MATRIX ALGEBRA AND LINEAR ECONOMIC MODELS
1.	Matrix Algebra
1.1	Basic Concepts	2
1.2	Determinants	9
1.3	The Inverse of a Matrix	17
1.4	Linear Dependence of Vectors and the Rank of a Matrix	25
*1.5	Kronecker Products and Vecs of Matrices	33
2.	Simultaneous Linear Equations
2.1	Definitions	37
2.2	Homogeneous Case	39
2.3	Nonhomogeneous Case	44
2.4	Special Case m=n	48
3.	Linear Economic Models
3.1	Introduction and Definitions	54
3.2	Examples of Linear Economic Models	56
3.3	The Use of Matrix Algebra in Statistics and Econometrics	63
4.	Quadratic Forms and Positive Definite Matrices
4.1	Introduction	69
4.2	Eigen Values of a Symmetric Matrix	70
4.3	Eigen Values of Special Matrices	73
4.4	Eigen Vectors of a Symmetric Matrix	75
4.5	Matrix whose Columns are the Eigen Vectors of a Symmetric Matrix	80
4.6	Diagonalization of Quadratic Forms	83
4.7	Eigen Values and 	85
4.8	An Alternative Approach using Determinants	86
PART 2: FUNCTIONS OF MANY VARIABLES AND OPTIMIZATION
5.	Functions of Many Variables
5.1	Functions in General	93
5.2	Partial Differentiation	95
5.3	Special Sorts of Functions	102
5.4	Comparative Statics and Nonlinear Economic Models	116
5.5	Differentials and Taylor¿s Approximation	123
6.	Optimization
6.1	Unconstrained Optimization	131
6.2	Local Optima and Global Optima	142
6.3	Constrained Optimization	146
6.4	Constrained Local Optima versus Constrained Global Optima	153
*6.5	An Introduction to Matrix Calculus	156
7.	Comparative Static Analysis in Optimization Problems
7.1	Introduction	166
7.2	Unconstrained Optimization	166
7.3	Constrained Optimization	170
7.4	Slutsky¿s Equation	174
7.5	Applications of the Envelope Theorems in Economics	178
PART 3: DYNAMIC ANALYSIS
8.	Integration
8.1	Introduction	201
8.2	Definite Integrals	202
8.3	Integration as Anti Differentiation	207
8.4	Indefinite Integrals	212
8.5	Further Considerations	215
8.6	Economic Applications	218
9.	Continuous Time: Differential Equations
9.1	Definitions	225
9.2	Linear Differential Equations	226
9.3	First Order Linear Differential Equations with Constant Coefficients	227
9.4	Economic Dynamics Using First Order Differential Equations	233
9.5	Second Order Linear Differential Equations with Constant Coefficents	243
9.6	Economic Application: A Dynamic Supply and Demand Model	250
9.7	Higher Order Linear Differential Equations	252
9.8	Descriptive Analysis of Nonlinear Differential Equations	254
10.	Discrete Time: Difference Equations
10.1	Introduction and Definitions	259
10.2	First Order Linear Difference Equations with Constant Coefficients	261
10.3	Second Order Linear Difference Equations with Constant Coefficients	262
10.4	Investigating the Nature of the Roots of a Quadratic Equation	269
10.5	Economic Applications	272
10.6	Higher Order Linear Difference Equations	280
11.	Dynamic Optimization
*11.1	Introduction		283
*11.2	Dynamic Optimization versus Static Optimization	283
*11.3	The Basic Optimal Control Problem and Pontryagin¿s Maximum Principle	285
*11.4	Extensions to the Basic Problem	293
*11.5	Economic Application: Ramsey/Solow Model	305