Lectures on Semi-group Theory and its Application to Cauchy's Problem in Partial Differential Equations
by K. Yosida
Publisher: Tata Institute of Fundamental Research 1957
Number of pages: 160
In these lectures, we shall be concerned with the differentiability and the representation of one-parameter semi-groups of bounded linear operators on a Banach space and with some of their applications to the initial value problem (Cauchy's problem) for differential equations, especially for the diffusion equation (heat equation) and the wave equation.
Download or read it online for free here:
by Arjeh Cohen, Rosane Ushirobira, Jan Draisma
Symmetry plays an important role in chemistry and physics. Group captures the symmetry in a very efficient manner. We focus on abstract group theory, deal with representations of groups, and deal with some applications in chemistry and physics.
by David M. Goldschmidt - American Mathematical Society
The book covers a set of interrelated topics, presenting a self-contained exposition of the algebra behind the Jones polynomial along with various excursions into related areas. Directed at graduate students and mathematicians.
by Michael Ruzhansky, Ville Turunen - Aalto TKK
Contents: Groups (Groups without topology, Group actions and representations); Topological groups (Compact groups, Haar measure, Fourier transforms on compact groups..); Linear Lie groups (Exponential map, Lie groups and Lie algebras); Hopf algebras.
by J. S. Milne
Contents: Basic Definitions and Results; Free Groups and Presentations; Coxeter Groups; Automorphisms and Extensions; Groups Acting on Sets; The Sylow Theorems; Subnormal Series; Solvable and Nilpotent Groups; Representations of Finite Groups.