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Numerical linear algebra and optimization, volume 1
Book reviews
Numerical Linear Algebra and Optimization, Volume 1. P.E. Gill, W. Murray & M.H. Wright, Addison-Wesley Publishers Ltd, Finchampstead Rd, Wokingham, Berks RG11 2NZ, UK. Hardback, £38.65. ISBN: 0 2011 2649 4
This book is designed to provide a unified introduction for students and practitioners to three distinct but closely related areas: (1) fundamentals of numerical analysis and scientific computing; (2) techniques for solving linear systems and linear least-squares problems, and for updating matrix factorizations; (3) numerical optimization methods for both linear and nonliner programming. These topics not only form a coherent body of knowledge for schooling, but are also important background for anyone who wishes to understand and develop numerical methods and software. The progression of topics in Volumes I and 2 is designed to correspond to an intensive one-year course in numerical liner algebra and optimization. L. Sucharov The Shape of Space. How to Visualise Surfaces and ThreeDimensional Manifolds. Jeffrey R. Weeks, Pure and Applied Mathematics, Marcel Dekker, Inc. pp. 324. ISBN: 0 8247 7437 X
Written in a simple and informal style, this book provides an introduction to topology through the modern notation of a three-dimensional manifold. This book bridges the gap between the simplest examples, such as the M6bius strip and the Klein bottle, and the sophisticated mathematics found in college courses. It is directed primarily at the nonmathematician and will compliment existing textbooks, which often deal only in abstractions, by its numerous examples. The book presents over 140 hands-on exercises, all with complete solutions and offers more than 170 illustrations. Material presented does not aim at developing an extensive theory of three-dimensional manifolds, but acts as a visual tool for these manifolds. Furthermore, it does not provide a series of answers, but rather a series of questions designed to lead the reader to his/her own intuitive understanding of manifolds. The book is suitable as a guide for graduate and undergraduate students. Contents: Part I - - Surfaces and three-manifolds; Part II - Geometries on surfaces; Part III - - Geometries on threemanifolds; Part IV - - The universe. R. Bains Computer Graphics and Geometric Modeling Using BetaSplines. B.A. Barsky, Springer-Verlag, 1988. pp. 156, hardcover. DM78.00. ISBN: 3 540 70006 4
237
This book explains the Beta-spline representation for curves and surfaces. The Beta-spline technique follows from the earlier techniques of B~zier and B-splines, and forms the latest method in this field. The Beta-spline technique combines powerful mathematics with an intuitive specification method. In addition to the control vertices, shape parameters are introduced to indicate the shape of the object in terms of sharpness or flatness. The book is of interest to researchers, engineers and graduate students in numerical analysis, computer graphics, computer aided design and computer aided manufacturing. A. Portela
Methods of Differential Geometry in Analytical Mechanics. Edited by M. de L~on & P.R. Rodrigues, Elsevier Science Publishers B.V., 1989. pp. 484. US$110.50/Dfl.210.00. ISBN: 0 444 88017 8
This book is written for mathematicians/mathematical physicists whose interests lie in differential geometry and its applications. It makes contributions to the modern development of Lagrangian and Hamiltonian formalism of classical mechanics in terms of differential-geometric methods on differentiable manifolds. Topics covered in this volume include differential forms, the differential geometry of tangent and contangent bundles, almost tangent geometry, symplectic and pre-symplectic Lagrangian and Hamiltonian formalisms, tensors and connections on manifolds, and geometrical aspects of variational and constraint theories. The book assumes that the reader is acquainted with linear and multilinear algebra as well as advanced calculus. Contents: (1) Differential geometry; (2) Almost tangent structures and tangent bundles; (3) Structures on manifolds; (4) Connections in tangent bundles; (5) Symplectic manifolds and cotangent bundles; (6) Hamiltonian systems; (7) Lagrangian systems; (8) Presymplectic mechanical systems; Appendices: a brief summary of particle mechanics in local coordinates. Higher order tangent bundles. Generalities. R. Bains
Numerical Methods with FORTRAN 77 m A Practical Introduction. L.V. Atkinson, P.J. Harley & J.D. Hudson, Addison-Wesley Publishing Company, 1989. £14.95. ISBN: 0 201 17430 8
The book provides a clear and comprehensive account of numerical methods and their implementation in
Numerical Linear Algebra and Optimization, Volume 1. P.E. Gill, W. Murray & M.H. Wright, Addison-Wesley Publishers Ltd, Finchampstead Rd, Wokingham, Berks RG11 2NZ, UK. Hardback, £38.65. ISBN: 0 2011 2649 4
This book is designed to provide a unified introduction for students and practitioners to three distinct but closely related areas: (1) fundamentals of numerical analysis and scientific computing; (2) techniques for solving linear systems and linear least-squares problems, and for updating matrix factorizations; (3) numerical optimization methods for both linear and nonliner programming. These topics not only form a coherent body of knowledge for schooling, but are also important background for anyone who wishes to understand and develop numerical methods and software. The progression of topics in Volumes I and 2 is designed to correspond to an intensive one-year course in numerical liner algebra and optimization. L. Sucharov The Shape of Space. How to Visualise Surfaces and ThreeDimensional Manifolds. Jeffrey R. Weeks, Pure and Applied Mathematics, Marcel Dekker, Inc. pp. 324. ISBN: 0 8247 7437 X
Written in a simple and informal style, this book provides an introduction to topology through the modern notation of a three-dimensional manifold. This book bridges the gap between the simplest examples, such as the M6bius strip and the Klein bottle, and the sophisticated mathematics found in college courses. It is directed primarily at the nonmathematician and will compliment existing textbooks, which often deal only in abstractions, by its numerous examples. The book presents over 140 hands-on exercises, all with complete solutions and offers more than 170 illustrations. Material presented does not aim at developing an extensive theory of three-dimensional manifolds, but acts as a visual tool for these manifolds. Furthermore, it does not provide a series of answers, but rather a series of questions designed to lead the reader to his/her own intuitive understanding of manifolds. The book is suitable as a guide for graduate and undergraduate students. Contents: Part I - - Surfaces and three-manifolds; Part II - Geometries on surfaces; Part III - - Geometries on threemanifolds; Part IV - - The universe. R. Bains Computer Graphics and Geometric Modeling Using BetaSplines. B.A. Barsky, Springer-Verlag, 1988. pp. 156, hardcover. DM78.00. ISBN: 3 540 70006 4
237
This book explains the Beta-spline representation for curves and surfaces. The Beta-spline technique follows from the earlier techniques of B~zier and B-splines, and forms the latest method in this field. The Beta-spline technique combines powerful mathematics with an intuitive specification method. In addition to the control vertices, shape parameters are introduced to indicate the shape of the object in terms of sharpness or flatness. The book is of interest to researchers, engineers and graduate students in numerical analysis, computer graphics, computer aided design and computer aided manufacturing. A. Portela
Methods of Differential Geometry in Analytical Mechanics. Edited by M. de L~on & P.R. Rodrigues, Elsevier Science Publishers B.V., 1989. pp. 484. US$110.50/Dfl.210.00. ISBN: 0 444 88017 8
This book is written for mathematicians/mathematical physicists whose interests lie in differential geometry and its applications. It makes contributions to the modern development of Lagrangian and Hamiltonian formalism of classical mechanics in terms of differential-geometric methods on differentiable manifolds. Topics covered in this volume include differential forms, the differential geometry of tangent and contangent bundles, almost tangent geometry, symplectic and pre-symplectic Lagrangian and Hamiltonian formalisms, tensors and connections on manifolds, and geometrical aspects of variational and constraint theories. The book assumes that the reader is acquainted with linear and multilinear algebra as well as advanced calculus. Contents: (1) Differential geometry; (2) Almost tangent structures and tangent bundles; (3) Structures on manifolds; (4) Connections in tangent bundles; (5) Symplectic manifolds and cotangent bundles; (6) Hamiltonian systems; (7) Lagrangian systems; (8) Presymplectic mechanical systems; Appendices: a brief summary of particle mechanics in local coordinates. Higher order tangent bundles. Generalities. R. Bains
Numerical Methods with FORTRAN 77 m A Practical Introduction. L.V. Atkinson, P.J. Harley & J.D. Hudson, Addison-Wesley Publishing Company, 1989. £14.95. ISBN: 0 201 17430 8
The book provides a clear and comprehensive account of numerical methods and their implementation in