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Cours Année : 2006

Mathematics for Dynamicists - Lecture Notes

Thomas Michelitsch

Résumé

These notes are the essence of the lecture series "Mathematics of Dynamicists" started in November 2004 and held regularly at the University of Sheffield as a MSc course module. The module "Mathematics for Dynamicists" addresses to any students of Engineering and Natural Sciences who are interested in mathematical-analytical solution methods to tackle problems in physics and engineering dynamics. The lecture notes consist of two parts. Part I is a warmup of the basic mathematics which is prerequisite for the understanding of part II. Some students will be familiar with the basics reviewed in part I, however the experience showed that it is useful to repeat these basics before starting with dynamical problems of engineering which are described by Recurrences and Ordinary Differential Equations in part II. To ensure the appropriate maths level needed for part II, the reader is highly recommended to answer the questions to part I before going to part II. Part II is the essential part and gives a brief introduction to the theory and solution methods for linear recurrences, Ordinary Differential Equations (ODEs) and Initial Value Problems (IVPs) which are also referred to as Cauchy Problems. The main goal is less to give proofs but more on applications of the methods on dynamical problems relevant to physical and engineering sciences. Instead of strict proofs we rather confine to short derivations with emphasis on applications of the analytical techniques. The reader is referred to the standard literature for any further proofs which are beyond the scope of these lecture notes. The selection of materials for this short-term module (2 weeks time) can only be an incomplete and sometimes arbitrary selection of materials. To improve the syllabus, suggestions from anybody are highly appreciated. The enclosed lecture notes are continuously updated and extended. Any communicated discrepancies and errors will be corrected steadily. I am especially grateful to my wife Dr. Jicun Wang for proof-reading this manuscript, to Mr. Shahram Derogar (Dept. Civil \& Struct. Eng., Univ. of Sheffield) and to Dr. Andrzej F. Nowakowski (Dept. of Mech. Eng., Univ. Sheffield) for their helpful critical comments and valuable inputs which significantly improved the contents of this lecture. Sheffield, November 2006 Thomas Michael Michelitsch
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cel-01128826 , version 1 (10-03-2015)

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  • HAL Id : cel-01128826 , version 1

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Thomas Michelitsch. Mathematics for Dynamicists - Lecture Notes. Doctoral. Mathematics for Dynamicists, France. 2006. ⟨cel-01128826⟩
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