Mathematical models in electrical circuits : theory and applications
Author(s)
Bibliographic Information
Mathematical models in electrical circuits : theory and applications
（Mathematics and its applications, v. 66）
Kluwer Academic Publishers, c1991
Available at 20 libraries
Note
Includes bibliographical references (p. 151-160) and index
Description and Table of Contents
Description
One service mathematics has rendered the 'Et moi, ...si favait su comment en revenir, je n'y seTais point alle.' human race. It has put common sense back Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded n- sense', The series is divergent; therefore we may be Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One scrvice logic has rendered com- puter science ...'; 'One service category theory has rendcred mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'e"tre of this scries.
Table of Contents
I. Dissipative operators and differential equations on Banach spaces.- 1.0. Introduction.- 1.1. Duality type functionals.- 1.2. Dissipative operators.- 1.3. Semigroups of linear operators.- 1.4. Linear differential equations on Banach spaces.- 1.5. Nonlinear differential equations on Banach spaces.- II. Lumped parameter approach of nonlinear networks with transistors.- 2.0. Introduction.- 2.1. Mathematical model.- 2.2. Dissipativity.- 2.3. DC equations.- 2.4. Dynamic behaviour.- 2.5. An example.- III. lp-solutions of countable infinite systems of equations and applications to electrical circuits.- 3.0. Introduction.- 3.1. Statement of the problem and preliminary results.- 3.2. Properties of continuous lp-solutions.- 3.3. Existence of continuous lp-solutions for the quasiautonomous case.- 3.4. Truncation errors in linear case.- 3.5. Applications to infinite circuits.- IV. Mixed-type circuits with distributed and lumped parameters as correct models for integrated structures.- 4.0. Why mixed-type circuits?.- 4.1. Examples.- 4.2. Statement of the problem.- 4.3. Existence and uniqueness for dynamic system.- 4.4. The steady state problem.- 4.5. Other qualitative results.- 4.6. Bibliographical comments.- V. Asymptotic behaviour of mixed-type circuits. Delay time predicting.- 5.0. Introduction.- 5.1. Remarks on delay time evaluation.- 5.2. Asymptotic stability. Upper bound of delay time.- 5.3. A nonlinear mixed-type circuit.- 5.4. Comments.- VI. Numerical approximation of mixed models for digital integrated circuits.- 6.0. Introduction.- 6.1. The mathematical model.- 6.2. Construction of the system of FEM-equations.- 6.2.1. Space discretization of reg-lines.- 6.2.2. FEM-equations of lines.- 6.3. FEM-equations of the model.- 6.4. Residual evaluations.- 6.5. Steady state.- 6.6. The delay time and its a-priori upper bound.- 6.7. Examples.- 6.8. Concluding remarks.- Appendix I.- List of symbols.- References.
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