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- Title: Numerical methods with worked examples : Matlab edition / C. Woodford, C. Phillips.
- Author: Chris Woodford 1943-
- Edition: 2nd ed.
- Publisher: Dordrecht ; New York : Springer
- Date: c2012
- Is Part Of: SpringerLink ebooks - Mathematics and Statistics (2012)
- Subjects: Numerical analysis; Numerical analysis -- Problems, exercises, etc; Electronic books
- Contributor(s): Chris Phillips 1950-; SpringerLink ebooks - Mathematics and Statistics (2012)
- Language: English
This book is a survey of the numerical methods that are common to undergraduatecourses in Science, Computing, Engineering and Technology. The aim is to presentsufficient methods to facilitate the numerical analysis of mathematical models likelyto be encountered in practice. Examples of such models include the linear equationsdescribing the stress on girders, bridges and other civil engineering structures, thedifferential equations of chemical and thermal reactions, and the inferences to bedrawn from observed data.The book is written primarily for the student, experimental scientist and designengineer for whom it should provide a range of basic tools. The presentation isnovel in that mathematical justification follows rather than precedes the descriptionof any method. We encourage the reader first to gain a familiarity with a particularmethod through experiment. This is the approach we use when teaching this materialin university courses. We feel it is a necessary precursor to understanding theunderlying mathematics. The aim at all times is to use the experience of numericalexperiment and a feel for the mathematics to apply numerical methods efficientlyand effectively.Methods are presented in a problem–solution–discussion order. The solution maynot be the most elegant but it represents the one most likely to suggest itself on thebasis of preceding material. The ensuing discussion may well point the way to betterthings. Dwelling on practical issues we have avoided traditional problems havingneat, analytical solutions in favour of those drawn from more realistic modellingsituations which generally have no analytic solution.It is accepted that the best way to learn is to teach. But even more so, the bestway to understand a mathematical procedure is to implement the method on a totallyunforgiving computer. Matlab enables mathematics as it is written on paperto be transferred to a computer with unrivalled ease and so offers every encouragement.The book will show how programs for a wide range of problems from solvingequations to finding optimum solutions may be developed. However we are not recommendingre-inventing the wheel. Matlab provides an enormous range of ready touse programs. Our aim is to give insight into which programs to use, what may beexpected and how results are to be interpreted. To this end we will include details ofthe Matlab versions of the programs we develop and how they are to be employed.vvi PrefaceWe hope that readers will enjoy our book. It has been a refreshing experience toreverse the usual form of presentation. We have tried to simplify the mathematicsas far as possible, and to use inference and experience rather than formal proof as afirst step towards a deeper understanding. Numerical analysis is as much an art as ascience and like its best practitioners we should be prepared to pick and choose fromthe methods at our disposal to solve the problem at hand. Experience, a readiness toexperiment and not least a healthy scepticism when examining computer output arequalities to be encouraged.Chris WoodfordChris Phillips
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