ix supplementary materials all program and data files referred to in this book are available from the book' primary web siteacknowledgments first of allwe want to thank all students who attended the courses fm modelling and simulation of dynamic systemsfm scientific computingfb mathematics and fb physics at the university college of southeast norway over the last couple of years they worked their way through early versions of this text and gave us constructive and positive feedback that helped us correct errors and improve the book in so many ways special acknowledgement goes to guandong kou and edirisinghe manjula for their careful reading of the manuscript and constructive suggestions for improvement the careful proof reading by yapi donatien achou is also highly appreciated we thank all our good colleagues at the university college of southeast norwayuniversity of osloand simula research laboratory for their continued support and interestenlightening discussionsand for providing such an inspiring environment for teaching and science in particularsvein linge is thankful to marius lysaker for their fruitful collaboration on introducing programming as an integral part of mathematics and physics bachelor courses at the university college of southeast norway finallythe authors must thank the springer team with dr martin petersthanh-ha le thiand yvonne schlatter for the effective editorial and production process the text was written in the doconce [ markup languagewhich allowed us to work with single text source for both the python and the matlab version of this bookand to produce various electronic versions of the book december svein linge and hans petter langtangen