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Uses mathematical, numerical, and programming tools to solve differential equations for physical phenomena and engineering problems
Introduction to Computation and Modeling for Differential Equations, Second Edition features the essential principles and applications of problem solving across disciplines such as engineering, physics, and chemistry. The Second Edition integrates the science of solving differential equations with mathematical, numerical, and programming tools, specifically with methods 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 solutions; and finite difference and finite element methods.
The author features a unique “Five-M” approach: Modeling, Mathematics, Methods, MATLAB®, and Multiphysics, which facilitates a thorough understanding of how models are created and preprocessed mathematically with scaling, classification, and approximation and also demonstrates how a problem is solved numerically using the appropriate mathematical methods. With numerous real-world examples to aid in the visualization of the solutions, Introduction to Computation and Modeling for Differential Equations, Second Edition includes:
- New sections on topics including variational formulation, the finite element method, examples of discretization, ansatz methods such as Galerkin’s method for BVPs, parabolic and elliptic PDEs, and finite volume methods
- Numerous practical examples with applications in mechanics, fluid dynamics, solid mechanics, chemical engineering, heat conduction, electromagnetic field theory, and control theory, some of which are solved with computer programs MATLAB and COMSOL Multiphysics®
- Additional exercises that introduce new methods, projects, and problems to further illustrate possible applications
- A related website with select solutions to the exercises, as well as the MATLAB data sets for ordinary differential equations (ODEs) and PDEs
Introduction to Computation and Modeling for Differential Equations, Second Edition is a useful textbook for upper-undergraduate and graduate-level courses in scientific computing, differential equations, ordinary differential equations, partial differential equations, and numerical methods. The book is also an excellent self-study guide for mathematics, science, computer science, physics, and engineering students, as well as an excellent reference for practitioners and consultants who use differential equations and numerical methods in everyday situations.
- Sales Rank: #2694496 in Books
- Published on: 2015-10-05
- Original language: English
- Number of items: 1
- Dimensions: 9.60" h x .92" w x 6.40" l, 1.00 pounds
- Binding: Hardcover
- 288 pages
From the Back Cover
Uses mathematical, numerical, and programming tools to solve differential equations for physical phenomena and engineering problems
Introduction to Computation and Modeling for Differential Equations, Second Edition features the essential principles and applications to problem solving across disciplines such as engineering, physics, and chemistry. The Second Edition integrates the science of solving differential equations with mathematical, numerical, and programming tools, specifically with methods 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 solutions; and finite difference and finite element methods.
The author features a unique "Five-M" approach: Modeling, Mathematics, Methods, MATLAB®, and Multiphysics, which facilitates a thorough understanding of how models are created and preprocessed mathematically with scaling, classification, and approximation and also demonstrates how a problem is solved numerically using the appropriate mathematical methods. With numerous real-world examples to aid readers in the visualization of the solutions, Introduction to Computation and Modeling for Differential Equations, Second Edition includes:
- New sections on topics such as variational formulation, the finite element method, examples of discretization, Ansatz methods for parabolic PDEs and elliptic PDEs, Galerkin's method for the model problem, and finite volume methods
- Numerous practical examples with applications in mechanics, fluid dynamics, solid mechanics, chemical engineering, electromagnetic field theory, and control theory, all of which are solved with computer programs MATLAB and Comsol Multiphysics®
- Additional exercises that introduce new methods, projects, and problems to further illustrate possible applications
- A related website with select solutions to the exercises, as well as the MATLAB data sets for IVPs and BVPs
Introduction to Computation and Modeling for Differential Equations, Second Edition is a useful textbook for upper-undergraduate and graduate-level courses in scientific computing, differential equations, ordinary differential equations, partial differential equations, and numerical methods. The book is also an excellent self-study guide for mathematics, science, computer science, physics, and engineering students, as well as an excellent reference for practitioners and consultants who use differential equations and numerical methods in everyday situations.
Lennart Edsberg, PhD, is Associate Professor in the Department of Numerical Analysis and Computing Science (NADA) in the School of Computer Science and Communication 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 is the author of over twenty journal articles in the areas of numerical methods and differential equations.
About the Author
Lennart Edsberg, PhD, is Associate Professor in the Department of Numerical Analysis and Computing Science (NADA) in the School of Computer Science and Communication 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 is the author of over twenty journal articles in the areas of numerical methods and differential equations.
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