A Practical Guide to the Invariant CalculusThis book explains recent results in the theory of moving frames that concern the symbolic manipulation of invariants of Lie group actions. In particular, theorems concerning the calculation of generators of algebras of differential invariants, and the relations they satisfy, are discussed in detail. The author demonstrates how new ideas lead to significant progress in two main applications: the solution of invariant ordinary differential equations and the structure of Euler-Lagrange equations and conservation laws of variational problems.
Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers.
This text presents, for the first time at an elementary level, current topics in applied mathematics such as singular perturbation, nonlinear wave propagation, bifurcation, similarity methods and the numerical solution of partial differential equations. It emphasizes the interdependency of mathematics and its application to physical phenomena, and is written in a style accessible to readers with a wide range of interests and backgrounds.
An Introduction to Differential Equations: With Difference Equations, Fourier Series, and Partial Differential Equations
The same, refined Ordinary Differential Equations with Modern Applications by Finizio and Lades is the backbone of this text. In addition to this are included applications, techniques and theory of partial difference equations, difference equations and Fourier analysis.
This graduate level textbook offers graduate students a rapid introduction to the language of the subject of ordinary differential equations followed by a careful treatment of the central topics of the qualitative theory. In addition, special attention is given to the origins and applications of differential equations in physical science and engineering. Of special interest to mathematics students is a multifaceted approach to existence theory, for solutions and for invariant manifolds....
