Theory of Maxima and Minima - Tapa blanda

Klf OF MAXIMA AND MINIMA CHAPTEK II FUNCTIONS OF SEVERAL VARIABLES I. Obdinaky Maxima axd Minima Preliminary Rnhwrks L. Proper and improper extremes 1i, Cilteria for maxima and minima 1(. Dntie, sem.irA nite, and iitdtiH eforms 11. Criteiioa for a definite quadratic form 1II. Relative Maxima and Minima i. Statement of the problem. Derivation of tlie conditions 2P roblems 2CHAPTER III FUNCTIONS OF TWO VARIABLES I. Okdinaky Extremes .D efinitions and derivation of the required conditions. Statement of difieront caKes after Goursat 2. The indefinite case 2i, Tlie definite case 2. Summary of the results derived for the two cases above. Example taken from tlie theory of least squares 2P roblems 2I ntrodiwM on to tha Ambiguous Case Bj4 C0 I. Exposition of the attending difS cuities which are illustrated by means of geometric considerations due toG oursat 21. The classic example of Peano allowing when we may and may not expect extremes 3[. iNOOEJ tECTNESS OF DEDUCTIONS MAD t) BYE aULIER AND Many Mouebn Write es ). The Lagrange fallacy followed by Bertrajid, Serret, Todhunter, etc. Geometric explanation of this fallacy 3IIL DiFFBBENT Attempts to impkovb the Theory ). Failure in deriving the required conditions by studying the behavior of the function upon algebraic curves 3. Statement of theS oheefier method 8t. The method of Von Dantachor outlined 3I.
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