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Focusing on the application of partial differential equations (PDEs) in engineering, this monograph offers a graduate-level exploration beginning with the geometrical interpretation of ordinary differential equations (ODEs) and their relevance to balance laws in continuum physics. It provides an in-depth analysis of first-order PDEs, including shock waves, with practical applications in traffic design and gas dynamics. Subsequent chapters cover second-order equations, emphasizing geometric insights and connections to discrete systems, while addressing uniqueness and various mathematical principles relevant to engineering contexts.
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Partial Differential Equations, Marcelo Epstein
- Language
- Released
- 2017
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- (Hardcover)
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- Title
- Partial Differential Equations
- Subtitle
- Mathematical Techniques for Engineers
- Language
- English
- Authors
- Marcelo Epstein
- Publisher
- Springer International Publishing
- Released
- 2017
- Format
- Hardcover
- Pages
- 272
- ISBN13
- 9783319552118
- Category
- Technology / Engineering, Mathematics
- Description
- Focusing on the application of partial differential equations (PDEs) in engineering, this monograph offers a graduate-level exploration beginning with the geometrical interpretation of ordinary differential equations (ODEs) and their relevance to balance laws in continuum physics. It provides an in-depth analysis of first-order PDEs, including shock waves, with practical applications in traffic design and gas dynamics. Subsequent chapters cover second-order equations, emphasizing geometric insights and connections to discrete systems, while addressing uniqueness and various mathematical principles relevant to engineering contexts.