This book provides an introduction to discrete dynamical systems - a framework of analysis that is commonly used in the ?elds of biology, demography, ecology, economics, engineering, ?nance, and physics. The book characterizes the fundamental factors that govern the quantitative and qualitative trajectories of a variety of deterministic, discrete dynamical systems, providing solution methods for systems that can be solved analytically and methods of qualitative analysis for those systems that do not permit or necessitate an explicit solution. The analysis focuses initially on the characterization of the factors that govern the evolution of state variables in the elementary context of one-dimensional, ?rst-order, linear, autonomous systems. The f- damental insights about the forces that a?ect the evolution of these - ementary systems are subsequently generalized, and the determinants of the trajectories of multi-dimensional, nonlinear, higher-order, non- 1 autonomous dynamical systems are established. Chapter 1 focuses on the analysis of the evolution of state variables in one-dimensional, ?rst-order, autonomous systems. It introduces a method of solution for these systems, and it characterizes the traj- tory of a state variable, in relation to a steady-state equilibrium of the system, examining the local and global (asymptotic) stability of this steady-state equilibrium. The ?rst part of the chapter characterizes the factors that determine the existence, uniqueness and stability of a steady-state equilibrium in the elementary context of one-dimensional, ?rst-order, linear autonomous systems.

This book provides an introduction to discrete dynamical systems - a framework of analysis that is commonly used in the ?elds of biology, demography, ecology, economics, engineering, ?nance, and physics. The book characterizes the fundamental factors that govern the quantitative and qualitative trajectories of a variety of deterministic, discrete dynamical systems, providing solution methods for systems that can be solved analytically and methods of qualitative analysis for those systems that do not permit or necessitate an explicit solution. The analysis focuses initially on the characterization of the factors that govern the evolution of state variables in the elementary context of one-dimensional, ?rst-order, linear, autonomous systems. The f- damental insights about the forces that a?ect the evolution of these - ementary systems are subsequently generalized, and the determinants of the trajectories of multi-dimensional, nonlinear, higher-order, non- 1 autonomous dynamical systems are established. Chapter 1 focuses on the analysis of the evolution of state variables in one-dimensional, ?rst-order, autonomous systems. It introduces a method of solution for these systems, and it characterizes the traj- tory of a state variable, in relation to a steady-state equilibrium of the system, examining the local and global (asymptotic) stability of this steady-state equilibrium. The ?rst part of the chapter characterizes the factors that determine the existence, uniqueness and stability of a steady-state equilibrium in the elementary context of one-dimensional, ?rst-order, linear autonomous systems.

This breakthrough scientific masterwork - and INTERNATIONAL BESTSELLER - reveals the underlying forces that have shaped human history and will secure our future... 'Masterful. Galor answers the ultimate mystery' Lewis Dartnell The stunning advances that have transformed human experience in recent centuries are no accident of history - they are the result of universal and timeless forces, operating since the dawn of our species. Drawing on a lifetime's scientific investigation, Oded Galor's ground-breaking new vision overturns a host of long-held assumptions to reveal the deeper causes that have shaped the journey of humanity: Education rather than industrialisation Family size and gender equality as much as inventions and technology Geography and diversity rather than wars, disease and famine 'Unparalleled in its scope and ambition . . . All readers will learn something' Washington Post 'An inspiring, readable, jargon-free and almost impossibly erudite masterwork' New Statesman 'His optimism about humanity shines through' Observer 'If you need an evidence-based antidote to doomscrolling, here it is' Guardian

For most of the vast span of human history, economic growth was all but nonexistent. Then, about two centuries ago, some nations began to emerge from this epoch of economic stagnation, experiencing sustained economic growth that led to significant increases in standards of living and profoundly altered the level and distribution of wealth, population, education, and health across the globe. The question ever since has been--why?

This is the first book to put forward a unified theory of economic growth that accounts for the entire growth process, from the dawn of civilization to today. Oded Galor, who founded the field of unified growth theory, identifies the historical and prehistorical forces behind the differential transition timing from stagnation to growth and the emergence of income disparity around the world. Galor shows how the interaction between technological progress and population ultimately raised the importance of education in coping with the rapidly changing technological environment, brought about significant reduction in fertility rates, and enabled some economies to devote greater resources toward a steady increase in per capita income, paving the way for sustained economic growth.Presents a unified theory of economic growth from the dawn of civilization to today Explains the worldwide disparities in living standards and population we see today Provides a comprehensive overview of the three phases of the development process Analyzes the Malthusian theory and its empirical support Examines theories of demographic transition and their empirical significance Explores the interaction between economic development and human evolution