Maxima and Minima: Theory and Economic ApplicationsSpringer Science & Business Media, 9. 11. 2013 - Počet stran: 176 |
Obsah
1 | |
CHAPTER II | 8 |
CHAPTER III | 15 |
Stationary Points | 16 |
Taylors formula in the case of one variable | 22 |
Taylors formula in the case of two variables | 29 |
Further geometric remarks concerning the coordinates of the points | 35 |
Intuitive representation and graphical illustration of a constraint | 37 |
Linear relations between functions | 91 |
These four cases correspond to the cases considered in the dis | 103 |
The characteristic equation in the case of two variables | 109 |
CHAPTER XI | 119 |
The quadratic form in the case of n variables with m constraints | 125 |
A system of n equations in n unknowns | 126 |
Provisional analysis on the hypothesis that the values satisfying | 128 |
EXAMPLES | 136 |
Formulation by means of Lagrange multipliers | 43 |
Abandonment of the investigation of a composite function | 49 |
Intuitive explanation of the Pareto optimality | 58 |
The elements of the adjoint | 66 |
Definition of a general linear system with m equations and n | 73 |
EXAMPLES | 74 |
Summary of the results concerning linear equations in two | 84 |
CHAPTER XIII | 144 |
Some remarkable relations | 150 |
Examples of the calculation of rank | 156 |
Characteristic polynomial of a matrix | 162 |
Theoretical Appendix on Complex Numbers | 171 |
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A₁ adjoint an1 an2 argument b₁ b₂ C₁ Chapter characteristic equation coefficients column complex number constraint defined definition degrees of freedom determinant of order elements equal to zero example exists a solution expression extrema extremum f₁ fact finite following theorem form Q P1 formulate function f function f(x1 ƒ x1 gives homogeneous system Lagrange multipliers least left-hand side linear equations linearly dependent local extremum local maximum log x² man-power matrix maximum minimum multiplied necessary and sufficient necessary condition neighbourhood non-zero number of equations obtain p₁ and P2 p₂ Pareto optimality partial derivatives plane point x1 problem production quadratic form quantities rank n-1 right-hand side roots satisfy simultaneously zero situated solution system square matrix strictly negative strictly positive sufficient condition system of equations system of linear unit circle v₁ variables x₁ x₁ and x2 μ₁ бу