The book is suitable for advanced undergraduate and beginning graduate students
of applied mathematics and engineering. The main theme is the integration of
the theory of linear PDE and the theory of finite difference and finite element
methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text
contains one chapter on the mathematical theory of the differential equation,
followed by one chapter on finite difference methods and one on finite element
methods. The chapters on elliptic equations are preceded by a chapter on the
two-point boundary value problem for ordinary differential equations.
Similarly, the chapters on time-dependent problems are preceded by a chapter on
the initial-value problem for ordinary differential equations. There is also
one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The
presentation does not presume a deep knowledge of mathematical and functional
analysis. The required background on linear functional analysis and Sobolev
spaces is reviewed in an appendix.
