Beginner's Georgian with 2 Audio CDs by Dodona Kiziria

By Dodona Kiziria

This publication is designed for either school room use and self-study. all of the thirteen classes opens with a discussion approximately a regular subject, via vocabulary lists, factors of grammar, and workouts. Audio CDs accompany the teachings, delivering right pronunciation of the dialogues and vocabulary, with pauses for repetition through the coed.

Includes:

* An workout key
* Georgian-English and English-Georgian glossaries
* An creation to Georgian language, tradition, and heritage

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Extra info for Beginner's Georgian with 2 Audio CDs

Sample text

If'l U + and convex then Proof. 3. l !. 4I

Theorem 15. Proof. If E. a n > 0: a2 > - ~ n. if then i < j and a 1 < aj it is easily seen that a' a'. a' a' i i j > _J + + ai aj ai and so n a' . n a.

Theorem 20. If f: U + R is eonvex on the open eonvex set U in the f is Lipsehitz on every eompaet sub set of U, and has partial CHAPTERI 32 derivatives of the first order almost everywhere in U that are eontinuous on the set where they exist. Proof. See RV p. 93, 116-117. 'nleorem 2 1. p , n ~ 2, have f is eonvex on U is non-negative definite, if H is positive definite on U then f is strictly eonvex. Proof. See RV p. 103. SO-Sl. 3. 'nleorem 22. If'l U + and convex then Proof. 3. l !. 4I

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