On a Routing Problem


Book Description

An attempt to determine an optimal route from one point to another, given a set of N cities, with every two linked by a road, and the times required to transverse these roads. The times are not directly proportional to the distances because of the varying quality of roads and quantities of traffic. The functional equation technique of dynamic programming, combined with approximation in policy space, yields an iterative algorithm which converges after a finite number if iterations bounded in advance.



















Introduction to Applied Linear Algebra


Book Description

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.







Mathematical Foundations of Statistical Mechanics


Book Description

Phase space, ergodic problems, central limit theorem, dispersion and distribution of sum functions. Chapters include Geometry and Kinematics of the Phase Space; Ergodic Problem; Reduction to the Problem of the Theory of Probability; Application of the Central Limit Theorem; Ideal Monatomic Gas; The Foundation of Thermodynamics; and more.




Mathematical Models in Population Biology and Epidemiology


Book Description

The goal of this book is to search for a balance between simple and analyzable models and unsolvable models which are capable of addressing important questions on population biology. Part I focusses on single species simple models including those which have been used to predict the growth of human and animal population in the past. Single population models are, in some sense, the building blocks of more realistic models -- the subject of Part II. Their role is fundamental to the study of ecological and demographic processes including the role of population structure and spatial heterogeneity -- the subject of Part III. This book, which will include both examples and exercises, is of use to practitioners, graduate students, and scientists working in the field.