This text is intended for science and engineering students.
It covers most of the topics taught in a first course on numerical
analysis and requires some basic knowledge in calculus,
linear algebra and computing. The text has been
used as recommended handbook for courses taught on numerical
analysis at undergraduate level. Each chapter ends
with a number of questions. It is taken for granted if the
reader has access to computer facilities for solving some of
these questions using Mathematica. There is extensive literature
published on numerical analysis including books on
undergraduate and postgraduate levels. As the text for a
first course in numerical analysis, this handbook contains
classical content of the subject with emphases put on error
analysis, optimal algorithms and their implementation in
computer arithmetic. There is also a desire that the reader
will find interesting theorems with proofs and verity of examples
with programs in Mathematica which help reading
the text. The first chapter is designed for floating point
computer arithmetic and round-off error analysis of simple
algorithms. It also includes the notion of well conditioned
problems and concept of complexity and stability of algorithms.
Within chapter 2, interpolation of functions is discussed.
The problem of interpolation first is stated in its simplest
form for polynomials, and then is extended to generalized
polynomials. Different Chebyshev’s systems for generalized
interpolating polynomials are considered.
In chapter 3, polynomial splines are considered for uniform
approximation of an one variable function.
Fundamental theorems on uniform approximation (Taylor’s
theorem,Weierstrass theorem, Equi-Oscillation Chebeshev’s
theorem) are stated and proved in chapter 4.
Chapter 5 is an introduction to the least squares method and
contains approximation of functions in the norm of L2(a, b)
space. Also, it contains approximation of discrete data and
an analysis of experimental data.
In the chapter 6, two techniques of numerical integration are
developed, the Newton-Cotes methods and Gauss methods.
In both methods an error analysis is carried out.
For solution of non-linear algebraic equations, the most popular
methods, such as Fixed Point Iterations, NewtonMethod,
SecantMethod and BisectionMethod, are described in chapter