Ebook: An Introduction to Scientific Computing: Twelve Computational Projects Solved with MATLAB
- Genre: Computers // Software: Systems: scientific computing
- Tags: Computational Mathematics and Numerical Analysis, Numerical and Computational Methods in Engineering, Mathematical and Computational Physics, Numerical Analysis, Applications of Mathematics
- Year: 2007
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
This book provides twelve computational projects aimed at numerically solving problems from a broad range of applications including Fluid Mechanics, Chemistry, Elasticity, Thermal Science, Computer Aided Design, Signal and Image Processing. For each project the reader is guided through the typical steps of scientific computing from physical and mathematical description of the problem, to numerical formulation and programming and finally to critical discussion of numerical results. Considerable emphasis is placed on practical issues of computational methods. The last section of each project contains the solutions to all proposed exercises and guides the reader in using the MATLAB scripts. The mathematical framework provides a basic foundation in the subject of numerical analysis of partial differential equations and main discretization techniques, such as finite differences, finite elements, spectral methods and wavelets).
The book is primarily intended as a graduate-level text in applied mathematics, but it may also be used by students in engineering or physical sciences. It will also be a useful reference for researchers and practicing engineers.
This book provides twelve computational projects aimed at numerically solving problems from a broad range of applications including Fluid Mechanics, Chemistry, Elasticity, Thermal Science, Computer Aided Design, Signal and Image Processing. For each project the reader is guided through the typical steps of scientific computing from physical and mathematical description of the problem, to numerical formulation and programming and finally to critical discussion of numerical results. Considerable emphasis is placed on practical issues of computational methods. The last section of each project contains the solutions to all proposed exercises and guides the reader in using the MATLAB scripts. The mathematical framework provides a basic foundation in the subject of numerical analysis of partial differential equations and main discretization techniques, such as finite differences, finite elements, spectral methods and wavelets).
The book is primarily intended as a graduate-level text in applied mathematics, but it may also be used by students in engineering or physical sciences. It will also be a useful reference for researchers and practicing engineers.
This book provides twelve computational projects aimed at numerically solving problems from a broad range of applications including Fluid Mechanics, Chemistry, Elasticity, Thermal Science, Computer Aided Design, Signal and Image Processing. For each project the reader is guided through the typical steps of scientific computing from physical and mathematical description of the problem, to numerical formulation and programming and finally to critical discussion of numerical results. Considerable emphasis is placed on practical issues of computational methods. The last section of each project contains the solutions to all proposed exercises and guides the reader in using the MATLAB scripts. The mathematical framework provides a basic foundation in the subject of numerical analysis of partial differential equations and main discretization techniques, such as finite differences, finite elements, spectral methods and wavelets).
The book is primarily intended as a graduate-level text in applied mathematics, but it may also be used by students in engineering or physical sciences. It will also be a useful reference for researchers and practicing engineers.
Content:
Front Matter....Pages I-XV
Numerical Approximation of Model Partial Differential Equations....Pages 1-32
Nonlinear Differential Equations: Application to Chemical Kinetics....Pages 33-48
Polynomial Approximation....Pages 49-83
Solving an Advection-Diffusion Equation by a Finite Element Method....Pages 85-109
Solving a Differential Equation by a Spectral Method....Pages 111-125
Signal Processing: Multiresolution Analysis....Pages 127-150
Elasticity: Elastic Deformation of a Thin Plate....Pages 151-164
Domain Decomposition Using a Schwarz Method....Pages 165-191
Geometrical Design: B?zier Curves and Surfaces....Pages 193-212
Gas Dynamics: The Riemann Problem and Discontinuous Solutions: Application to the Shock Tube Problem....Pages 213-233
Thermal Engineering: Optimization of an Industrial Furnace....Pages 235-250
Fluid Dynamics: Solving the Two-Dimensional Navier-Stokes Equations....Pages 251-284
Back Matter....Pages 285-294
This book provides twelve computational projects aimed at numerically solving problems from a broad range of applications including Fluid Mechanics, Chemistry, Elasticity, Thermal Science, Computer Aided Design, Signal and Image Processing. For each project the reader is guided through the typical steps of scientific computing from physical and mathematical description of the problem, to numerical formulation and programming and finally to critical discussion of numerical results. Considerable emphasis is placed on practical issues of computational methods. The last section of each project contains the solutions to all proposed exercises and guides the reader in using the MATLAB scripts. The mathematical framework provides a basic foundation in the subject of numerical analysis of partial differential equations and main discretization techniques, such as finite differences, finite elements, spectral methods and wavelets).
The book is primarily intended as a graduate-level text in applied mathematics, but it may also be used by students in engineering or physical sciences. It will also be a useful reference for researchers and practicing engineers.
Content:
Front Matter....Pages I-XV
Numerical Approximation of Model Partial Differential Equations....Pages 1-32
Nonlinear Differential Equations: Application to Chemical Kinetics....Pages 33-48
Polynomial Approximation....Pages 49-83
Solving an Advection-Diffusion Equation by a Finite Element Method....Pages 85-109
Solving a Differential Equation by a Spectral Method....Pages 111-125
Signal Processing: Multiresolution Analysis....Pages 127-150
Elasticity: Elastic Deformation of a Thin Plate....Pages 151-164
Domain Decomposition Using a Schwarz Method....Pages 165-191
Geometrical Design: B?zier Curves and Surfaces....Pages 193-212
Gas Dynamics: The Riemann Problem and Discontinuous Solutions: Application to the Shock Tube Problem....Pages 213-233
Thermal Engineering: Optimization of an Industrial Furnace....Pages 235-250
Fluid Dynamics: Solving the Two-Dimensional Navier-Stokes Equations....Pages 251-284
Back Matter....Pages 285-294
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