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Mathematical Modelling in One Dimension demonstrates the universality of mathematical techniques through a wide variety of applications. Learn how the same mathematical idea governs loan repayments, drug accumulation in tissues or growth of a population, or how the same argument can be used to find the trajectory of a dog pursuing a hare, the trajectory of a self-guided missile or the shape of a satellite dish. The author places equal importance on difference and differential equations, showing how they complement and intertwine in describing natural phenomena.

Differential equations, Nonlinear. --- Mathematical models. --- Models, Mathematical --- Simulation methods --- Nonlinear differential equations --- Nonlinear theories

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The aim of this volume that presents Lectures given at a joint CIME and Banach Center Summer School, is to offer a broad presentation of a class of updated methods providing a mathematical framework for the development of a hierarchy of models of complex systems in the natural sciences, with a special attention to Biology and Medicine. Mastering complexity implies sharing different tools requiring much higher level of communication between different mathematical and scientific schools, for solving classes of problems of the same nature. Today more than ever, one of the most important challenges derives from the need to bridge parts of a system evolving at different time and space scales, especially with respect to computational affordability. As a result the content has a rather general character; the main role is played by stochastic processes, positive semigroups, asymptotic analysis, kinetic theory, continuum theory and game theory.

Stochastic processes --- Numerical analysis --- Processus stochastiques --- Analyse numérique --- Congresses. --- Congrès --- Medicine --- Biological Science Disciplines --- Mathematics --- Health Occupations --- Natural Science Disciplines --- Disciplines and Occupations --- Calculus --- Mathematical Statistics --- Physical Sciences & Mathematics --- Mathematics. --- Operator theory. --- Partial differential equations. --- Game theory. --- Probabilities. --- Partial Differential Equations. --- Operator Theory. --- Probability Theory and Stochastic Processes. --- Game Theory, Economics, Social and Behav. Sciences. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Games, Theory of --- Theory of games --- Mathematical models --- Partial differential equations --- Functional analysis --- Math --- Science --- Differential equations, partial. --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities