Introduction to Partial Differential Equations A Computational Approach /

• Main Authors: Tveito, Aslak (Author), Winther, Ragnar (Author)
• Corporate Author: SpringerLink (Online service)
• Other Authors: Marsden, J.E (Editor), Sirovich, L. (Editor), Golubitsky, M. (Editor), Jäger, W. (Editor)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005.
• Series: Texts in Applied Mathematics, 29
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Partial differential equations.; Computer mathematics.; Analysis.; Partial Differential Equations.; Computational Science and Engineering.

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the cl- sical techniques of applied mathematics. This renewal of interest, both in resea...

Table of Contents:

• Setting the Scene
• Two-Point Boundary Value Problems
• The Heat Equation
• Finite Difference Schemes for the Heat Equation
• The Wave Equation
• Maximum Principles
• Poisson's Equation in Two Space Dimensions
• Orthogonality and General Fourier Series
• Convergence of Fourier Series
• The Heat Equation Revisited
• Reaction-Diffusion Equations
• Applications of the Fourier Transform.