Graduate-level text for science and technology students provides strong background in the more abstract and intellectually satisfying areas of dynamical theory. Topics include d’Alembert’s principle and the idea of virtual work, Hamilton’s equations, Hamilton-Jacobi theory, canonical transformations, more. Problems and references at chapter ends. 1977 edition.
Applied Linear Algebra & Introductory Numerical Methods (video)
Applied Linear Algebra & Introductory Numerical Methods - AMATH 584 Numerical methods for solving linear systems of equations, linear least squares problems, matrix eigen value problems, nonlinear systems of equations, interpolation, quadrature, and initial value ordinary differential equations.
This real-world, application-oriented outline introduces non-math majors to: linear equations and linear growth; exponential functions and geometric growth; sets; and counting. Following this material are applications using the formulas derived in topics such as: descriptive statistics; basic probability theory; graphs and networks; voting systems and apportionment; interest calculation; and systems of linear equations and games theory.
Linearity plays a critical role in the study of elementary differential equations; linear differential equations, especially systems thereof, demonstrate a fundamental application of linear algebra. In Differential Equations with Linear Algebra, we explore this interplay between linear algebra and differential equations and examine introductory and important ideas in each, usually through the lens of important problems that involve differential equations.
Superdiffusions and Positive Solutions of Nonlinear Partial Differential Equations
This book is devoted to the applications of probability theory to the theory of nonlinear partial differential equations. More precisely, it is shown that all positive solutions for a class of nonlinear elliptic equations in a domain are described in terms of their traces on the boundary of the domain.
