Introduction to the Theory and Applications of Functional Differential Equations (Mathematics and Its Applications, 463)

At the beginning of this century Emil Picard wrote: "Les equations differentielles de la mecanique classique sont telles qu 'il en resulte que le mouvement est determine par la simple connaissance des positions et des vitesses, c 'est-a-dire par l 'etat a un instant donne et a ['instant infiniment voison. Les etats anterieurs n'y intervenant pas, l'heredite y est un vain mot. L 'application de ces equations ou le passe ne se distingue pas de l 'avenir, ou les mouvements sont de nature reversible, sont done inapplicables aux etres vivants". "Nous pouvons rever d'equations fonctionnelles plus compliquees que les equations classiques parce qu 'elles renfermeront en outre des integrates prises entre un temps passe tres eloigne et le temps actuel, qui apporteront la part de l'heredite". (See "La mathematique dans ses rapports avec la physique, Actes du rv• congres international des Mathematiciens, Rome, 1908. ) Many years have passed since this publication. These years have seen substantial progress in many aspects of Functional Differential Equations (FDEs ). A distinguishing feature of the FDEs under consideration is that the evolution rate of the proc{lsses described by such equations depends on the past history. The discipline of FDEs has grown tremendously, and publication of literature has increased perhaps twofold over publication in the previous decade. Several new scientific journals have been introduced to absorb this increased productivity. These journals reflect the broadening interests of scientists, with ever greater attention being paid to applications.

this Book Covers The Most Important Issues In The Theory Of Functional Differential Equations And Their Applications For Both Deterministic And Stochastic Cases. Among The Subjects Treated Are Qualitative Theory, Stability, Periodic Solutions, Optimal Control And Estimation, The Theory Of Linear Equations, And Basic Principles Of Mathematical Modelling. The Work, Which Treats Many Concrete Problems In Detail, Gives A Good Overview Of The Entire Field And Will Serve As A Stimulating Guide To Further Research.
Audience: This Volume Will Be Of Interest To Researchers And (post)graduate Students Working In Analysis, And In Functional Analysis In Particular. It Will Also Appeal To Mathematical Engineers, Industrial Mathematicians, Mathematical System Theoreticians And Mathematical Modellers.

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covering The Significant Issues In The Theory Of Functional Differential Equations (fdes) And Their Applications For Both Deterministic And Stochastic Cases, This Volume Covers Qualitative Theory, Stability, Periodic Solutions, Optimal Control And Estimation, The Theory Of Linear Equations, And Basic Principles Of Mathematical Modelling. A Substantial Overview Of The Field Is Provided, With Many Problems Treated In Considerable Detail. The Authors Aim To Provide A Readable Account Of The Newest Developments In Fde Theory And Provide New Material On The Following Areas: Phenomena Modelling By Fdes; Boundary Value Problems; Formal Procedure For Liapunov Functionals Construction For Different Classes Of Fdes; Non-autonomous Equations Of First And Second Orders; Minimax Filtering And Estimation; And Model Reference Adaptive Control. Of Likely Use To Researchers And Postgraduate Students, As Well As Other Users Of Fdes. Annotation C. Book News, Inc., Portland, Or (booknews.com)