Partial Differential Equations With Numerical Methods

The book is suitable for advanced undergraduate and beginning graduate studentsof applied mathematics and engineering. The main theme is the integration ofthe t... » 

The book is suitable for advanced undergraduate and beginning graduate studentsof applied mathematics and engineering. The main theme is the integration ofthe theory of linear PDE and the theory of finite difference and finite elementmethods. For each type of PDE elliptic parabolic and hyperbolic the textcontains one chapter on the mathematical theory of the differential equationfollowed by one chapter on finite difference methods and one on finite elementmethods. The chapters on elliptic equations are preceded by a chapter on thetwopoint boundary value problem for ordinary differential equations.Similarly the chapters on timedependent problems are preceded by a chapter onthe initialvalue problem for ordinary differential equations. There is alsoone chapter on the elliptic eigenvalue problem and eigenfunction expansion. Thepresentation does not presume a deep knowledge of mathematical and functionalanalysis. The required background on linear functional analysis and Sobolevspaces is reviewed in an appendix. «