Linear Partial Differential and Difference Equations and Simultaneous Systems: With Constant or Homogeneous Coefficients is part of the series "Mathematics and Physics for Science and Technology", which combines rigorous mathematics with general physical principles to model practical engineering systems with a detailed derivation and interpretation of results. Volume V presents the mathematical theory of partial differential equations and methods of solution satisfying initial and boundary conditions, and includes applications to: acoustic, elastic, water, electromagnetic and other waves; the diffusion of heat, mass, and electricity; and their interactions. This is the third book of the volume.
The book starts with six different methods of solution of linear partial differential equations (P.D.E.s) with constant coefficients. One of the methods, namely characteristic polynomial, is then extended to a further five classes, including linear P.D.E.s with homogeneous power coefficients and finite difference equations and simultaneous systems of both (S.P.D.E.s and S.F.D.E.s). The applications include detailed solutions of the most important P.D.E.s in physics and engineering, including the Laplace, heat, diffusion, telegraph, bar, and beam equations. The free and forced solutions are considered together with boundary, initial, asymptotic, starting, and other conditions.
The book is intended for graduate students and engineers working with mathematical models and can be applied to problems in mechanical, aerospace, electrical, and other branches of engineering dealing with advanced technology, and also in the physical sciences and applied mathematics.
1. Method of Separation of Variables.
2. Method of Similarity Functions.
3. Method of Symbolic Differentiation Operators.
4. Method of Exponentials of Several Variables.
5. Simultaneous Systems of P.D.E.s with Constant Coefficients.
6. Linear Equation with Homogenous Partial Derivatives.
7. Simultaneous Systems of P.D.E.s with Power Coefficients.
8. Partial Finite Difference Equations.
9. Simultaneous System of Partial Finite Difference Equations.