Mathematical Methods XIB

Physical Chemistry: An Advanced Treatise, Volume XIB: Mathematical Methods focuses on mathematical techniques that consist of concepts relating to differentiation and integration.

This book discusses the methods in lattice statistics, Pfaffian solution of the planar Ising problem, and probability theory and stochastic processes. The random variables and probability distributions, non-equilibrium problems, Brownian motion, and scattering theory are also elaborated. This text likewise covers the elastic scattering from atoms, solution of integral and differential equations, concepts in graph theory, and theory of operator equations.

This volume provides graduate and physical chemistry students a basic understanding of mathematical techniques important in chemistry.

Contenu

List of Contributors
Foreword
Preface
Contents of Previous Volumes
Chapter 9 / Methods in Lattice Statistics
I. Introduction
II. Concepts in Graph Theory
III. Evaluation of Lattice Constants
IV. Exact Series Expansions
V. The Dimer Problem
VI. Pfaffian Solution of the Planar Ising Problem
Appendix-Methods of Series Analysis
References
Chapter 10 / Probability Theory and Stochastic Processes
I. Introduction
II. Random Variables and Probability Distributions
III. Functions of Random Variables
IV. Stochastic Processes-General
V. Stochastic Processes Discrete in Both Sample Space and Time
VI. Stochastic Processes Discrete in Sample Space but Continuous in Time
VII. Stochastic Processes Continuous in Both Sample Space and Time
References
Chapter 11 / Nonequilibrium Problems-Projection Operator Techniques
I. Introduction
II. The Projection Operator Technique
III. Brownian Motion
IV. Further Applications-Lowest Order Results
V. Higher Order Results
References
Chapter 12 / Scattering Theory
I. Introduction
II. Simple Particle Scattering from a Fixed Center
III. The Green's Function and Solutions to an Inhomogeneous Differential Equation
IV. Elastic Scattering from Atoms
V. Inelastic Scattering
VI. The Multichannel Scattering Matrix
VII. Approximate Wave Functions
VIII. Autoionization
IX. The Optical Model
X. The R-Matrix Theory
References
Chapter 13 / The Solution of Integral and Differential Equations
I. Introduction
II. Theory of Operator Equations-Fundamentals
III. Integral Equations: Linear and Nonlinear
IV. Differential Equations, Mainly Nonlinear
V. Methods of Solution
References
Author Index
Subject Index