Xue, Dingyü; Chen, YangQuan Scientific computing with MATLAB. 2nd edition. (English) Zbl 1344.65001 Boca Raton, FL: CRC Press (ISBN 978-1-4987-5777-5/hbk; 978-0-367-78313-6/pbk; 978-1-315-36785-9/ebook). xvii, 586 p. (2016). This is an impressive book, its subtitle could be “What you ever would like to know about using MATLAB solving problems”. The volume of nearly 600 pages, subdivided into 10 chapters with altogether 65 sections, touches on an extended variety of mathematical problems, which are taken from the fields listed under the keywords. The present second edition contains a significant amount of new material compared to the first edition [(2009; Zbl 1156.00013)]. Also compatibility with the new versions of MATLAB is supported, which especially was necessary after the MATLAB R2008b was released soon after the publication of the first edition.The aim of the book is not to present mathematics either to provide the abstract specifications of the existing MATLAB tools (for the latter there is enough material easily available). It starts with the observation “that in today’s applied science and applied engineering, one usually needs to get the mathematical problems at hand solved efficiently in a timely manner without complete understanding of the mathematical techniques involved in the solution process”. Acccordingly, an impressing large number of problems from each of the above topics is shown how to be solved using MATLAB/Simulink tools. The corresponding MATLAB programs are given and the obtained results, in most cases, are graphically displayed. In presenting the material the authors follow what say call the “three-phase solution”, by which they mean, that the physical meaning of the mathematical problem to be solved is given first, followed by the methodology to bring it in a MATLAB-compatible form and then solving it using the adequate MATLAB functions. Apart from the standard MATLAB also commercial toolboxes are considered, e.g. the Symbolic Math Toolbox, Optimization Toolbox, Partial Differential Equations Toolbox, Spline Toolbox, Statistics Toolbox, Fuzzy Logic Toolbox, Neural Network Toolbox, Wavelet Toolbox, Genetic Algorithm Toolbox, Direct Search Toolbox. (Perhaps, in the section on partial differential equations a limit of the book’s philosophy “compute without fully understanding the mechanism of numerics” can be observed: only ten pages are dedicated to this involved topic and only one example is presented.)The material of the book has been used as a fundament for university courses at the University of California and the Northeastern University (China). As a nice consequence, in each chapter a large number of exercises is given jointly with a concentrated bibliography, in most cases containing URLs of free textbooks which are concerned with the mathematical topics of the chapter.There is no official price given for how much the book sells. At the time of the present review there are found offers for $ 59.99 in the USA and EUR 48.14 in Germany. Reviewer: Rolf Dieter Grigorieff (Berlin) Cited in 2 Documents MSC: 65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis 00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.) 68-04 Software, source code, etc. for problems pertaining to computer science 68N15 Theory of programming languages 68W30 Symbolic computation and algebraic computation 65Mxx Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems 65Nxx Numerical methods for partial differential equations, boundary value problems 65Fxx Numerical linear algebra 65R10 Numerical methods for integral transforms 65E05 General theory of numerical methods in complex analysis (potential theory, etc.) 65H05 Numerical computation of solutions to single equations 65K05 Numerical mathematical programming methods 65Lxx Numerical methods for ordinary differential equations 65Dxx Numerical approximation and computational geometry (primarily algorithms) 65Cxx Probabilistic methods, stochastic differential equations 65T60 Numerical methods for wavelets Keywords:MATLAB programming; scientific visualization; introduction to Simulink; calculus problems; linear algebra; integral transforms; complex-valued functions; nonlinear equations; optimization problems; differential equations; stiff equations; differential algebraic equations; delay equations; interpolation; approximation; probability; mathematical statistics; fuzzy logic; rough set theory; neural networks; evolutionary computing; wavelet transform; fractional order calculus Citations:Zbl 1156.00013 Software:YALMIP; EISPACK; LINPACK; Robust Control Toolbox; Simulink; PSOt; fminsearchbnd; Fuzzy Logic Toolbox; Neural Network Toolbox; Wavelet Toolbox; Symbolic Math Toolbox; Matlab; BNB; Partial Differential Equation Toolbox; Ezimplot3; Decision tree for optimization software; Optimization Toolbox; Spline Toolbox; Statistics Toolbox; numerical integration toolbox; Genetic Algorithm and Direct Search Toolbox PDFBibTeX XMLCite \textit{D. Xue} and \textit{Y. Chen}, Scientific computing with MATLAB. 2nd edition. Boca Raton, FL: CRC Press (2016; Zbl 1344.65001) Full Text: DOI