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Introduction to applied mathematics
COMPUTER METHODS NORTH-HOLLAND
IN APPLIED
MECHANICS
AND ENGINEERING
61 (1987) 371-372
BOOK REVIEWS
Introduction to Applied Mathematics, MA, 1986) 7.58 pp.
Gilbert Strang (Wellesley-Cambridge
Press, Wellesley,
This book covers applied mathematics from a truly broad perspective: differential equations, including boundary value problems and initial value problems, the discrete counterparts of these problems, and algorithms for their solution. The book is intended as a text for students of applied mathematics and engineering mathematics at an advanced level and it represents a very different approach to the teaching of applied mathematics. For one thing, it emphasizes the tremendous importance of computers on engineering mathematics; secondly, it uses the interrelationship between discrete and continuous mathematics to provide the student with a better understanding. The list of topics treated in this book is extensive (the list below is not complete but representative): Chapter 1: “Symmetric Linear Systems” considers Gauss elimination, factorization, minimum principles, eigenvalues, and a review of matrix theory. Chapter 2: “Equilibrium Equations” includes such topics as constraints and Lagrange multipliers, electrical networks, structures in equilibrium, least squares estimation, and the Kalman filter. Chapter 3: “Equilibrium in the Continuous Case” deals with one-dimensional problems, differential equations of equilibrium, Laplace’s equation and potential flow, vector calculus in three dimensions, equilibrium of fluids and solids, and the calculus of variations. Chapter 4: “Analytical Methods” deals with Fourier series, Fourier integrals, convolutions, complex variables, and conformal mapping and complex integration. Chapter 5: “Numerical Methods” deals with linear and nonlinear equations, orthogonalization and eigenvalue problems, the finite element method, and the fast Fourier transform. Chapter 6: “Initial Value Problems” deals with ordinary differential equations, stability and chaos, Laplace and z transforms, and difference methods for initial value problems. Chapter 7: “Network Flows and Combinatorics” considers problems such as spanning trees and shortest paths, matching algorithms, maximal flow in networks, and the transportation problem. Chapter 8: “Optimization” deals with linear programming, including the simplex and Kamarkar’s method, duality, saddle points and game theory, and a short treatment of nonlinear optimization. The book makes very interesting reading and provides a unique perspective on the field of applied mathematics. It blends the algorithms with the governing equations, as the author strongly believes the algorithms support the theory. This is one of the many unique and 004%7825/87/$3.50
@ 1987, Elsevier Science Publishers B.V. (North-Holiand)
372
Book Reviews
innovative concepts that provided the motivation revolutionize the teaching of advanced mathematics
fur this book. to engineers.
It has the potential
to
Wing-Kam Liu Northwestern University Evanston, IL
computational Techniques and Applieatiuns: CTAC-85, .I. Noye and R. May, eds. (NorthHolland, Amsterdam~ 1986) 790 pp., ISBN ~-~4-87~~-1? US$~~.~~~D~~ 350.00.
This proceedings volume contains invited and contributed papers from a conference on computational methods held in Melbourne, Australia, August. 1985. There are papers from six keynote lectures (U.K., U.S.A., The Netherlands, and A.ustralia (3)) and 48 contributed papers. Australian universities, government researchers from CSIRO, and technical institutes are represented and contribute most of the papers. Further articles from Japan, U.S.., U.K., and New Zealand are included. The subject area is subdivided to: Invited Papers, Techniques for PDE’s, Techniques for ODE’s, Fltiid Flow and Heat Transfer, Flow through Porous Media, Elasticity and Structures, and Mis~ellaneuus Topics. There are interesting survey and research articles on, for example, Lagr~~an methods, ODE te~hniques~ and problems with constraints, Applications range from en~nee~ng structural analysis of bridges to accretion of a star in a hypersonic flow stream, and involve approximate analysis using finite difference, finite element, and boundary integral techniques. The collection is quite comprehensive and indicates that computational techniques are “alive and well ‘Down Under’.” There were, regretably, no numerical studies on flow problems for the local entrant in the “Australia’s (?) Cup’“.
IN APPLIED
MECHANICS
AND ENGINEERING
61 (1987) 371-372
BOOK REVIEWS
Introduction to Applied Mathematics, MA, 1986) 7.58 pp.
Gilbert Strang (Wellesley-Cambridge
Press, Wellesley,
This book covers applied mathematics from a truly broad perspective: differential equations, including boundary value problems and initial value problems, the discrete counterparts of these problems, and algorithms for their solution. The book is intended as a text for students of applied mathematics and engineering mathematics at an advanced level and it represents a very different approach to the teaching of applied mathematics. For one thing, it emphasizes the tremendous importance of computers on engineering mathematics; secondly, it uses the interrelationship between discrete and continuous mathematics to provide the student with a better understanding. The list of topics treated in this book is extensive (the list below is not complete but representative): Chapter 1: “Symmetric Linear Systems” considers Gauss elimination, factorization, minimum principles, eigenvalues, and a review of matrix theory. Chapter 2: “Equilibrium Equations” includes such topics as constraints and Lagrange multipliers, electrical networks, structures in equilibrium, least squares estimation, and the Kalman filter. Chapter 3: “Equilibrium in the Continuous Case” deals with one-dimensional problems, differential equations of equilibrium, Laplace’s equation and potential flow, vector calculus in three dimensions, equilibrium of fluids and solids, and the calculus of variations. Chapter 4: “Analytical Methods” deals with Fourier series, Fourier integrals, convolutions, complex variables, and conformal mapping and complex integration. Chapter 5: “Numerical Methods” deals with linear and nonlinear equations, orthogonalization and eigenvalue problems, the finite element method, and the fast Fourier transform. Chapter 6: “Initial Value Problems” deals with ordinary differential equations, stability and chaos, Laplace and z transforms, and difference methods for initial value problems. Chapter 7: “Network Flows and Combinatorics” considers problems such as spanning trees and shortest paths, matching algorithms, maximal flow in networks, and the transportation problem. Chapter 8: “Optimization” deals with linear programming, including the simplex and Kamarkar’s method, duality, saddle points and game theory, and a short treatment of nonlinear optimization. The book makes very interesting reading and provides a unique perspective on the field of applied mathematics. It blends the algorithms with the governing equations, as the author strongly believes the algorithms support the theory. This is one of the many unique and 004%7825/87/$3.50
@ 1987, Elsevier Science Publishers B.V. (North-Holiand)
372
Book Reviews
innovative concepts that provided the motivation revolutionize the teaching of advanced mathematics
fur this book. to engineers.
It has the potential
to
Wing-Kam Liu Northwestern University Evanston, IL
computational Techniques and Applieatiuns: CTAC-85, .I. Noye and R. May, eds. (NorthHolland, Amsterdam~ 1986) 790 pp., ISBN ~-~4-87~~-1? US$~~.~~~D~~ 350.00.
This proceedings volume contains invited and contributed papers from a conference on computational methods held in Melbourne, Australia, August. 1985. There are papers from six keynote lectures (U.K., U.S.A., The Netherlands, and A.ustralia (3)) and 48 contributed papers. Australian universities, government researchers from CSIRO, and technical institutes are represented and contribute most of the papers. Further articles from Japan, U.S.., U.K., and New Zealand are included. The subject area is subdivided to: Invited Papers, Techniques for PDE’s, Techniques for ODE’s, Fltiid Flow and Heat Transfer, Flow through Porous Media, Elasticity and Structures, and Mis~ellaneuus Topics. There are interesting survey and research articles on, for example, Lagr~~an methods, ODE te~hniques~ and problems with constraints, Applications range from en~nee~ng structural analysis of bridges to accretion of a star in a hypersonic flow stream, and involve approximate analysis using finite difference, finite element, and boundary integral techniques. The collection is quite comprehensive and indicates that computational techniques are “alive and well ‘Down Under’.” There were, regretably, no numerical studies on flow problems for the local entrant in the “Australia’s (?) Cup’“.