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An introduction to scientific computing for differential equations
Introduction to Computation and Modeling for Differential Equations provides a unified and integrated view of numerical analysis, mathematical modeling in applications, and programming to solve differential equations, which is essential in problem-solving across many disciplines, such as engineering, physics, and economics. This book successfully introduces readers to the subject through a unique "Five-M" approach: Modeling, Mathematics, Methods, MATLAB, and Multiphysics. This approach facilitates a thorough understanding of how models are created and preprocessed mathematically with scaling, classification, and approximation, and it also illustrates how a problem is solved numerically using the appropriate mathematical methods.
The book's approach of solving a problem with mathematical, numerical, and programming tools is unique and covers a wide array of topics, from mathematical modeling to implementing a working computer program. The author utilizes the principles and applications of scientific computing to solve problems involving:
- Ordinary differential equations
- Numerical methods for Initial Value Problems (IVPs)
- Numerical methods for Boundary Value Problems (BVPs)
- Partial Differential Equations (PDEs)
- Numerical methods for parabolic, elliptic, and hyperbolic PDEs
- Mathematical modeling with differential equations
- Numerical solution
- Finite difference and finite element methods
Real-world examples from scientific and engineering applications including mechanics, fluid dynamics, solid mechanics, chemical engineering, electromagnetic field theory, and control theory are solved through the use of MATLAB and the interactive scientific computing program Comsol Multiphysics. Numerous illustrations aid in the visualization of the solutions, and a related Web site features demonstrations, solutions to problems, MATLAB programs, and additional data.
Introduction to Computation and Modeling for Differential Equations is an ideal text for courses in differential equations, ordinary differential equations, partial differential equations, and numerical methods at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for researchers and practitioners in the fields of mathematics, engineering, and computer science who would like to refresh and revive their knowledge of the mathematical and numerical aspects as well as the applications of scientific computation.
- Sales Rank: #2793893 in Books
- Published on: 2008-07-28
- Original language: English
- Number of items: 1
- Dimensions: 9.35" h x .61" w x 6.46" l, 1.05 pounds
- Binding: Hardcover
- 235 pages
Review
"Introduction to Computation and Modeling for Differential Equations is an ideal text for course in differential equations, ordinary differential equations, partial differentials, and numerical methods at the upper-undergraduate and graduate levels. The books also serves as a valuable reference for researchers and practioners in the fields of mathematics, engineering, and computer science who would like to refresh and review their knowledge of the mathematical and numerical aspects as well as the applications of scientific computation." (Mathematical Review, Issue 2009e)
From the Back Cover
An introduction to scientific computing for differential equations
Introduction to Computation and Modeling for Differential Equations provides a unified and integrated view of numerical analysis, mathematical modeling in applications, and programming to solve differential equations, which is essential in problem-solving across many disciplines, such as engineering, physics, and economics. This book successfully introduces readers to the subject through a unique "Five-M" approach: Modeling, Mathematics, Methods, MATLAB�, and Multiphysics�. This approach facilitates a thorough understanding of how models are created and preprocessed mathematically with scaling, classification, and approximation, and it also illustrates how a problem is solved numerically using the appropriate mathematical methods.
The book's approach of solving a problem with mathematical, numerical, and programming tools is unique and covers a wide array of topics, from mathematical modeling to implementing a working computer program. The author utilizes the principles and applications of scientific computing to solve problems involving:
-
Ordinary differential equations
-
Numerical methods for Initial Value Problems (IVPs)
-
Numerical methods for Boundary Value Problems (BVPs)
-
Partial Differential Equations (PDEs)
-
Numerical methods for parabolic, elliptic, and hyperbolic PDEs
-
Mathematical modeling with differential equations
-
Numerical solution
-
Finite difference and finite element methods
Real-world examples from scientific and engineering applications including mechanics, fluid dynamics, solid mechanics, chemical engineering, electromagnetic field theory, and control theory are solved through the use of MATLAB� and the interactive scientific computing program Comsol Multiphysics�. Numerous illustrations aid in the visualization of the solutions, and a related Web site features demonstrations, solutions to problems, MATLAB� programs, and additional data.
Introduction to Computation and Modeling for Differential Equations is an ideal text for courses in differential equations, ordinary differential equations, partial differential equations, and numerical methods at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for researchers and practitioners in the fields of mathematics, engineering, and computer science who would like to refresh and revive their knowledge of the mathematical and numerical aspects as well as the applications of scientific computation.
About the Author
LENNART EDSBERG, PhD, is Associate Professor in the Department of Numerical Analysis and Computing Science (NADA) at KTH-The Royal Institute of Technology in Stockholm, Sweden, where he has also been Director of the International Master Program in Scientific Computing since 1996. Dr. Edsberg has over thirty years of academic experience and has written several journal articles in the areas of numerical methods and differential equations.
Most helpful customer reviews
0 of 0 people found the following review helpful.
Worthless and convoluted
By Libertine
Edsberg complicates simple concepts and skips over the involved parts, almost as if he does not know the area he is trying to describe. The book is short and filled with non-sequiteurs and errors. The errata at the books web page [...]. lists mainly spelling misstakes, but there are huge problems in the book. As an example, Edsberg gives the wrong definition of local error for a numerical algorithm (complete with an erraneous figure to describe it). Please, please, please chose a book on this topic from a more knowledgable author. Edsberg does is NOT a university professor.
0 of 0 people found the following review helpful.
not a good book
By Yvonne Lastra
the book is very short, some chapters are only like 4 pages long, and there are hardly any explanations or details of techniques or methods. just basically brief overviews and descriptions of things, also i think its overpriced : /
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