Ebook: Foundations of numerical analysis (with MatLab examples). Vol. 1

Second Edition. — Sofia: University of Architecture, Civil Engineering and Geodesy, 2007. — 278 p.The first edition of these Lecture Notes appeared in 2005 and its paper version is already over. In the second edition some misprints in the first edition have been corrected and certain new material has been included.
In Volume 1 of the Lecture Notes we consider some aspects of the numerical analysis and its applications, which are connected with the effects of machine (finite) arithmetic on the result of numerical computations. We analyze the elements of the machine arithmetic and study selected issues of numerical linear algebra and some basic problems of mathematical analysis. Special attention is paid to the myths, or misconceptions, in the computational practice.
In Volume 2 we deal with the solution of differential equations (both ordinary and partial) as well as with the solution of finite equations and optimization problems.
The Lecture Notes cover parts of the discipline Applied Mathematics for the students in Hydro-Technical and Transport Engineering in both the University of Architecture, Civil Engineering and Geodesy - Sofia and the Technical University of Vienna. The lecture course is also used in the discipline Numerical Matrix Analysis for the master degree course in mathematics provideв by the Technical University of Sofia.
These Lecture Notes are also intended for the students of technical and economical universities and are connected with the courses in Linear Algebra and Analytical Geometry (Mathematics I), Mathematical Analysis I (Mathematics II) and Applied Mathematics (Mathematics IV) for the engineering faculties.
The Lecture Notes may be used by students in other mathematical disciplines as well as by engineers and specialists in the practice.
An important feature of these Notes is the systematic use of the interactive computer system MATLAB (MATLAB is a trade mark of MathWork, Inc.) for the numerical solution of all mathematical problems considered. In certain cases similar results may be obtained using the freely distributed computer systems SYSLAB and Scilab.