Applied Numerical Analysis with Mathematica
Renato M. Cotta, Leonardo S. de B. Alves e Mikhail D. Mikhailov
- The first notebook (ANA0)
introduces the student to the Mathematica system, illustrating the most important
concepts and commands that will be required in the basic understanding of
the notebooks to follow.
- The second notebook
(ANA1) discusses the questions of precision and accuracy in scientific
computation, and how the system deals with fixed and variable precision arithmetic.
- The next eight notebooks
(ANA2 through ANA9) deal with the most common computational
tasks in numerical analysis, starting with polynomial interpolation and up
to the solution of boundary value problems. This material is not aimed at
reviewing the basic algorithms of numerical calculus, which should have been
covered in more elementary courses, but rather to identify and exercise the
most appropriate built-in functions for each computational task and, most
important, to introduce and stimulate the use of the software system itself
as a numerical analysis assistant, in building confidence on the numerical
results thus obtained.
- The next two notebooks
(ANA10 and ANA11) are more advanced material, which might have
to be avoided depending on the level of the course being offered and on the
maturity of the students on this software system. They include research work
by the authors on the use of the Integral Transform Method in the solution
of differential eigenvalue problems and nonlinear partial differential equations,
respectively. These two notebooks are also intended to demonstrate the advanced
programming capabilities of the Mathematica system, towards the handling of
more involved tasks not readily available as built-in functions within this
platform, while introducing and inviting the interested reader towards a more
recent electronic book by M. D. Mikhailov and R. M. Cotta, The Integral Transform
Method with Mathematica, especially devoted to such topics.
- Finally, a selection
of problems is available from the authors, extracted from the various textbooks
here considered, that includes the material covered along the above notebooks,
which offers an excellent training and examination environment in electronic
version.