- Email: [email protected]
Improperly posed boundary value problems
Mathematics and Computers 0 North-Holland Publishing
in Simulation Company
XXI (1979)
116-120
BOOKREVIEWS Edited by P. VAN REMOORTERE
1975
Power system networks are subjected to many forms of transient phenomena ranging from the relatively slow electromechanical oscillations associated with synchronous machine instability, to the comparatively fast variations in voltage and current brought about by sudden changes in the steady-state values of one or the other of these quantities. This book contains a detailed description of the mathematical methods that may be applied to the calculation of fast transient overvoltages in power system networks. Additionally, factors which influence the magnitudes and waveshapes of such transient overvoltages are discussed and methods for their inclusion in the mathematical analysis are considered. Since full-scale 3-phase systems are considered, the use of a digital computer is a necessity. Reprinted from Proc. of the IEEE, October 1977.
A. Carasso and A.P. Stone (Editors): Improperly posed boundary value problems. 1975, 160 pages, &lO.OO. FearonPitman Publishers Inc., 6 Davis Drive, Belmont, CA 94002 USA. In a developing field with impact on many important aspects of applied mathematics, this work is a collection of 12 papers invited for the National Science Foundation Regional Conference on “Improperly posed problems in partial differential equations” held at the University of New Mexico, Albuquerque, N.M. in May 1974. Relevant in particular to applied mathematicians tackling the increasingly complex problems posed by modern advances in fields such as meterorology and geophysics, elasticity and fluid dynamics, the life sciences and other areas. Postgraduate students in mathematics, physics and engineering writing dissertations in partial differential equations and numerical analysis thereof, and graduate students in geophysics will also find it useful as a reference work. Authors and contents: H.F. Walker: Well-posedness of certain elliptic problems in unbounded domains. J.A. Donaldson: A uniqueness class for two improperly posed problems arising in mathematical physics. S. Steinberg: Some unusual ill-posed Cauchy problems and their applications. H.D.Meyer: Half-plane representations and harmonic continuation. J.R. Cannon and R. Ewing: The locations and strengths of point sources. K. Miller: Efficient numerical methods for backward solution of parabolic problems with variable coefficients. H. Brezis and J.A. Goldstein: Liouville theorems for some improperly posed problems. R.E. Showalter: Quasi-reversibility of first and second order parabolic evolution equations. J.R. Cannon: A class of inverse problems: The determination of second order elliptic partial differential operators from overspecified boundary data. H.A. Levine: Nonexistence of global weak solutions to nonlinear wave equations. M. Ghil: The initialization problem in numerical weather prediction. A. Carasso: The backward beam equation and the numerical computation of dissipative equations backwards in time.
P. Faurre and M. Depeyrot: Elements of System Theory, 1976, 282 pages, Dfl. 65.00, North Holland Publishing Company, Amsterdam, New York. This textbook provides a concise, rigorous and up-to-date introduction to the theory of dynamical system and is intended to prepare the upper-level student for work with advanced and specialized texts. Although written in an applied mathematical style with precise statements and proofs, it does not demand any advanced mathematical background and is illustrated with many examples and exercises. An integrated treatment of classical and modern control science and information processing techniques is achieved by use of the main concepts of system theory. The first part deals with PID regulators and process control by computers. The external description for linear systems is given with transfer functions, impulse response, diagrams and correlation functions for second order properties. The internal description is presented next with state equation, controllability, observability and realization algorithms. System stability is discussed and simple introductions to optimal control, signal processing and identification are given. The second part, on Digital Systems, discusses mainly points of interest for both Control and Computer Sciences. Complexity of numerical systems is studied in three chapters. The first deals with logical functions and Boolean algebra, the second with functions, memories and automata, the last with basic notions of algorithms and recursive functions. Models of a Turing and a Wang machine are given. Microprogramming and diagramming are finally explained. CONTENTS: Chapters: 1. Introduction to system theory. Part One. Continuous System Teory. 2. Elementary PID control and process control. 3. Linear dynamical systems:
1976
J.P. Bickford et al. Computation of Power System Transients. 1976, International Scholarity Book Services, Forest Grove, OR., USA, g27.50. 176 pages 116
in Simulation Company
XXI (1979)
116-120
BOOKREVIEWS Edited by P. VAN REMOORTERE
1975
Power system networks are subjected to many forms of transient phenomena ranging from the relatively slow electromechanical oscillations associated with synchronous machine instability, to the comparatively fast variations in voltage and current brought about by sudden changes in the steady-state values of one or the other of these quantities. This book contains a detailed description of the mathematical methods that may be applied to the calculation of fast transient overvoltages in power system networks. Additionally, factors which influence the magnitudes and waveshapes of such transient overvoltages are discussed and methods for their inclusion in the mathematical analysis are considered. Since full-scale 3-phase systems are considered, the use of a digital computer is a necessity. Reprinted from Proc. of the IEEE, October 1977.
A. Carasso and A.P. Stone (Editors): Improperly posed boundary value problems. 1975, 160 pages, &lO.OO. FearonPitman Publishers Inc., 6 Davis Drive, Belmont, CA 94002 USA. In a developing field with impact on many important aspects of applied mathematics, this work is a collection of 12 papers invited for the National Science Foundation Regional Conference on “Improperly posed problems in partial differential equations” held at the University of New Mexico, Albuquerque, N.M. in May 1974. Relevant in particular to applied mathematicians tackling the increasingly complex problems posed by modern advances in fields such as meterorology and geophysics, elasticity and fluid dynamics, the life sciences and other areas. Postgraduate students in mathematics, physics and engineering writing dissertations in partial differential equations and numerical analysis thereof, and graduate students in geophysics will also find it useful as a reference work. Authors and contents: H.F. Walker: Well-posedness of certain elliptic problems in unbounded domains. J.A. Donaldson: A uniqueness class for two improperly posed problems arising in mathematical physics. S. Steinberg: Some unusual ill-posed Cauchy problems and their applications. H.D.Meyer: Half-plane representations and harmonic continuation. J.R. Cannon and R. Ewing: The locations and strengths of point sources. K. Miller: Efficient numerical methods for backward solution of parabolic problems with variable coefficients. H. Brezis and J.A. Goldstein: Liouville theorems for some improperly posed problems. R.E. Showalter: Quasi-reversibility of first and second order parabolic evolution equations. J.R. Cannon: A class of inverse problems: The determination of second order elliptic partial differential operators from overspecified boundary data. H.A. Levine: Nonexistence of global weak solutions to nonlinear wave equations. M. Ghil: The initialization problem in numerical weather prediction. A. Carasso: The backward beam equation and the numerical computation of dissipative equations backwards in time.
P. Faurre and M. Depeyrot: Elements of System Theory, 1976, 282 pages, Dfl. 65.00, North Holland Publishing Company, Amsterdam, New York. This textbook provides a concise, rigorous and up-to-date introduction to the theory of dynamical system and is intended to prepare the upper-level student for work with advanced and specialized texts. Although written in an applied mathematical style with precise statements and proofs, it does not demand any advanced mathematical background and is illustrated with many examples and exercises. An integrated treatment of classical and modern control science and information processing techniques is achieved by use of the main concepts of system theory. The first part deals with PID regulators and process control by computers. The external description for linear systems is given with transfer functions, impulse response, diagrams and correlation functions for second order properties. The internal description is presented next with state equation, controllability, observability and realization algorithms. System stability is discussed and simple introductions to optimal control, signal processing and identification are given. The second part, on Digital Systems, discusses mainly points of interest for both Control and Computer Sciences. Complexity of numerical systems is studied in three chapters. The first deals with logical functions and Boolean algebra, the second with functions, memories and automata, the last with basic notions of algorithms and recursive functions. Models of a Turing and a Wang machine are given. Microprogramming and diagramming are finally explained. CONTENTS: Chapters: 1. Introduction to system theory. Part One. Continuous System Teory. 2. Elementary PID control and process control. 3. Linear dynamical systems:
1976
J.P. Bickford et al. Computation of Power System Transients. 1976, International Scholarity Book Services, Forest Grove, OR., USA, g27.50. 176 pages 116