NumericalComputing-Chapter0 - Numerical Computing...

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Unformatted text preview: Numerical Computing Introduction and Review Dr. Nguyen V.M. Man Email: mnguyen@cse.hcmut.edu.vn Faculty of Computer Science and Engineering HCMUT Vietnam February 10, 2010 Abstract This chapter briefs selective topics for Numerical Computing, aimed for undergraduates in Power Engineering (a joint program of EEE-UT with UIUC) and in Computational Sciences at HCMC, Spring 2009-2010. The structure of the course This lecture is aimed at introducing basic techniques of calculus, analysis, algebra, laiding base for engineering and bussiness applications. The topics being discussed include parts: Part 0 : Overview of the topic- Review of basic facts Part I: Approximation of polynomials Part II: Direct and iterative methods for linear systems Part III: Eigenvalues problems Part IV: Numerically solving of non-linear system Part V: Numerical solutions of ordinary differential equations 7 tactics for successful studying I Never miss any lecture! I Look over suggested books before go to class I Understand examples in class instantly I Try to come up to reasonable questions during listening the lecture I Discuss what you dont understand with friends I Make a decent efforts in solving home-works I Employ computing packages such as Maple , Matlab , Scilab ... Part 0: Motivation- Introduction to Principles of numerical methods Main topics are: Why do we need to study Scientific Computing and Numerical Methods Three Principles of numerical methods- Scientific modeling: what, why and how?- Why applications need numerical solutions?- Categories of Numerical Problems An illustration : Determining a model of a mixtures of m evaporating substances Review of basic background Introduction to Scientific Computing and Numerical Methods Many scientific and technological problems require I good mathematical models and I efficient computing methods of major parameters of those models.- This course is designed to foster students capability in understanding and using numerical computations .- The course also is aimed to train them in practicing and implementing these methods on PC for modeling a few important classes of scientific and technological problems . Fundamental principles of Numerical Methods 1. Scientific modeling: what, why and how? Model : an artificial object which reflects and reproduces- the structure (essential features and relationships);- the functions of a concrete object or phenomenon (reality) in a simplified way Simplifying means some properties are ignored....
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This note was uploaded on 01/22/2011 for the course CS 225 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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NumericalComputing-Chapter0 - Numerical Computing...

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