This
note introduces elementary programming concepts including variable types, data
structures, and flow control. After an introduction to linear algebra and
probability, it covers numerical methods relevant to mechanical engineering,
including approximation, integration, solution of linear and nonlinear equations, ordinary
differential equations, and deterministic and probabilistic approaches.
Author(s): Prof.
Anthony T. Patera, Prof. Daniel Frey and Prof. Nicholas Hadjiconstantinou
This
PDF is prepared by Gonzalo Galiano Casas and Esperanza Garcia Gonzalo from the
Department of Mathematics at Oviedo University. With a view to keeping things
compact, this document initiates with finite arithmetic and error analysis,
which forms the basis necessary for understanding the issue of numerical
precision and limitations. It considers methods for nonlinear equations,
interpolation, and approximation. Key sections on numerical differentiation and
integration give hands-on tools both for data analysis and the solution of
mathematical problems. It also covers systems of linear equations and
optimization, rounding it out for students and practitioners who might want to
apply the numerical methods through a variety of problems.
Author(s): Gonzalo Galiano Casas, Esperanza Garcia Gonzalo, Dept. of Mathematics, Oviedo University
Numerical Topics in Fluid
Dynamics Computation!!! Peter Bastian Authored - This PDF covers advanced
numerical computation topics but puts more emphasis on the solution of
computational fluid dynamics. The book starts with the modeling of immiscible
fluid flow in a composite porous medium, thus laying down the basics for the
equations of multiphase fluid flow. It then provides fully implicit methods that
have been used to find the finite volume discretization of systems for complex
algebraic equations. Two important chapters are the parallelization methods that
result in higher productivity of computation and the UG framework used for
carrying out grid computations. Numerical results are then presented, which
allow deriving some conclusions concerning practical applications and
performance. The document will be particularly useful to researchers and
engineers studying computational fluid dynamics and related numerical modeling
problems.
It gives an explanation
of all the different numerical methods of scientific computing. It starts with
the basics, which is Root Finding and Orthogonal Functions, solving equations
and analyzing functions. Finite Differences and Divided Differences included for
the needs in the process of numerical differentiation and interpolation.
Interpolation and Curve Fitting are given to outline estimation and modeling. It
also includes Z-Transforms and Summation Formulas for signal processing and
numerical summation. Quadrature Formulas and Ordinary Differential Equations are
explained for integration and the solution of differential equations. Partial
Differential Equations, Integral Equations, and Stability and Error Analysis
form the advanced topics for numerical methods coverage. Further, Monte Carlo
Techniques, Message Passing Interface, and Simulation Modeling are included to
point out methods for probabilistic simulations and parallel computing.
This
lecture series provides comprehensive foundational knowledge in the field of
numerical computational analysis. Numerical Linear Algebra covers basic matrix
operations and solutions of linear systems. The book further goes into the
Solution of Nonlinear Equations that shows methods for solving equations which
are not linear in form. Finally, it discusses Approximation Theory, showing how
functions and data may be approximated. The lectures also cover Numerical
Solution of ODEs and PDEs, giving ways to solve these two basic kinds of
equations. This resource is intended for students and professionals looking to
gain a solid understanding of basic and applied numerical analysis techniques.