# Mathematics For Economists Mukras

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mathematics for economists

eal and Unequal Roots of the Characteristic Equation 648 Real and Equal Roots of the Characteristic Equation Complex Roots of the Characteristic Equation 651 The Motion of a Spring 653 Nonhomogeneous Second Order Equations 654 24.4 EXISTENCE OF SOLUTIONS 657 The Fundamental Existence and Uniqueness Theorem hi7 Direction Fields 659 PHASE PORTRAITS AND EQUILIBRIA ON R’ Drawing Phase Portraits 666 Stability of Equilibria on the Line 66X APPENDIX: APPLICATIONS 670 Indirect Money Metric Utility Functions 672 .mathematics for economists

∂x ∂y Observe that by Young theorem if for some F (x, y ) the second order partial derivatives exists and they are continuous then F is twice di¤erentiable, hence the Hesse matrix is symmetric. The theorem is in some sense the converse to Young theorem.mathematics for economists

De¯nition 1 A set is a collection of objects thought of as a whole. ² Describe a set by enumeration: list all the elements of the set e.g. S = f2; 4; 6; 8; 10g = f4; 10; 6; 2; 8g ² Describe a set by property: state the property shared by all the elements in the set, e.g. S = fx : x is an even number between 1 and 11g ² x 2 S: x is in the set² x 62 S: x is not in the setExamples fx : x is a ¯rm producing computersg (\computer industry") fx : x is a bundle of goods a consumer can aordg (\budget set&.mathematics for economists

. than the Babylonians. Indeed, the text Nine Chapters on the Mathematical Art written during the Han Dynasty gives the first known.
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