Numerical Methods for Scientific Computing
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.
Author(s): John Henry Heinbockel
NA Pages 
Introduction to Numerical Computation
This is an exhaustive PDF written by Lars Elden, Linde Wittmeyer-Koch, and Hans Bruun Nielsen. In fact, this really is an exemplary introduction to numerical computation. The text begins with the basics like error analysis and computer arithmetic, which gives a very solid ground for the origin and handling of numerical errors. It proceeds further to explain more basic topics related to function evaluation, solutions of nonlinear equations, and interpolation techniques. Next, it describes procedures for improving numerical estimates using differentiation and Richardson extrapolation. This is followed by full details of integration, systems of linear equations, and approximation. Finally, ordinary differential equations complete a thorough course of study that will prepare the reader with both the theory and practice that will serve in carrying out numerical computations.
Author(s): Lars Elden, Linde Wittmeyer-Koch, Hans Bruun Nielsen
383 Pages
Numerical Computation by Peter Bastian
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.
Author(s): Peter Bastian
236 Pages
Numerical Computation for Mechanical Engineers
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
NA Pages
Numerical Methods for Scientific Computing
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.
Author(s): John Henry Heinbockel
NA Pages
