Fritz Schwarz Book order

The central subject of the book is the generalization of Loewy's decomposition - originally introduced by him for linear ordinary differential equations - to linear partial differential equations. Equations for a single function in two independent variables of order two or three are comprehensively discussed. A complete list of possible solution types is given. Various ad hoc results available in the literature are obtained algorithmically. The border of decidability for generating a Loewy decomposition are explicitly stated. The methods applied may be generalized in an obvious way to equations of higher order, in more variables or systems of such equations.

Focusing on Lie's theory, this book introduces methods for solving differential equations, exploring concepts like Loewy's theory and Janet bases. It delves into the symmetry analysis of quasilinear equations, categorizing them and transforming them into canonical forms for solution. The text also addresses equivalence problems and provides general solutions where feasible. Additionally, appendices feature selected exercise solutions and essential formulae, while a dedicated website offers software for complex algebraic calculations.