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Introduction to Numerical Methods in Differential Equations

Contributor(s): Holmes, Mark H [editor.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Texts in Applied Mathematics: 52Publisher: New York, NY : Springer New York, 2007.Description: XI, 239 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9780387681214.Subject(s): Mathematics | Differential equations | Partial differential equations | Numerical analysis | Mathematics | Partial Differential Equations | Ordinary Differential Equations | Numerical AnalysisDDC classification: 515.353 Online resources: Click here to access online
Contents:
Initial Value Problems -- Two-Point Boundary Value Problems -- Diffusion Problems -- Advection Equation -- Numerical Wave Propagation -- Elliptic Problems.
In: Springer eBooksSummary: This is a textbook for upper division undergraduates and beginning graduate students. Its objective is that students learn to derive, test and analyze numerical methods for solving differential equations, and this includes both ordinary and partial differential equations. In this sense the book is constructive rather than theoretical, with the intention that the students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. An essential component of this is the exercises, which develop both the analytical and computational aspects of the material. The importance of the subject of the book is that most laws of physics involve differential equations, as do the modern theories on financial assets. Moreover many computer animation methods are now based on physics based rules and are heavily invested in differential equations. Consequently numerical methods for differential equations are important for multiple areas. The author currently teaches at Rensselaer Polytechnic Institute and is an expert in his field. He has previously published a book with Springer, Introduction to Perturbation Methods.
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Item type Current location Call number Status Date due Barcode Item holds
E books E books PK Kelkar Library, IIT Kanpur
Available EBK9191
Total holds: 0

Initial Value Problems -- Two-Point Boundary Value Problems -- Diffusion Problems -- Advection Equation -- Numerical Wave Propagation -- Elliptic Problems.

This is a textbook for upper division undergraduates and beginning graduate students. Its objective is that students learn to derive, test and analyze numerical methods for solving differential equations, and this includes both ordinary and partial differential equations. In this sense the book is constructive rather than theoretical, with the intention that the students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. An essential component of this is the exercises, which develop both the analytical and computational aspects of the material. The importance of the subject of the book is that most laws of physics involve differential equations, as do the modern theories on financial assets. Moreover many computer animation methods are now based on physics based rules and are heavily invested in differential equations. Consequently numerical methods for differential equations are important for multiple areas. The author currently teaches at Rensselaer Polytechnic Institute and is an expert in his field. He has previously published a book with Springer, Introduction to Perturbation Methods.

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