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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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This book contains the written versions of lectures delivered since 1997 in the well-known weekly seminar on Applied Mathematics at the Collège de France in Paris, directed by Jacques-Louis Lions. It is the 14th and last of the series, due to the recent and untimely death of Professor Lions. The texts in this volume deal mostly with various aspects of the theory of nonlinear partial differential equations. They present both theoretical and applied results in many fields of growing importance such as Calculus of variations and optimal control, optimization, system theory and control, op

Partial differential equations --- Differential equations, Partial. --- Differential equations, Nonlinear. --- Nonlinear differential equations --- Nonlinear theories

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This is an expanded fourth edition of a classic text, including numerous worked examples, diagrams and exercises. An ideal resource for students and lecturers in engineering, mathematics and the sciences, it is published alongside a separate Problems and Solutions Sourcebook with over 500 problems and solutions.

Differential equations, Nonlinear. --- Mathematics. --- Math --- Science --- Nonlinear differential equations --- Nonlinear theories --- Equations différentielles non linéaires

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This book is the first one devoted to high-dimensional (or large-scale) diffusion stochastic processes (DSPs) with nonlinear coefficients. These processes are closely associated with nonlinear Ito's stochastic ordinary differential equations (ISODEs) and with the space-discretized versions of nonlinear Ito's stochastic partial integro-differential equations. The latter models include Ito's stochastic partial differential equations (ISPDEs). The book presents the new analytical treatment which can serve as the basis of a combined, analytical-numerical approach to greater computational efficie

Engineering --- Stochastic processes. --- Diffusion processes. --- Differential equations, Nonlinear. --- Nonlinear differential equations --- Nonlinear theories --- Markov processes --- Random processes --- Probabilities --- Mathematical models.

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The book presents a systematic and compact treatment of the qualitative theory of half-lineardifferential equations. It contains the most updated and comprehensive material and represents the first attempt to present the results of the rapidly developing theory of half-linear differential equations in a unified form. The main topics covered by the book are oscillation and asymptotic theory and the theory of boundary value problems associated with half-linear equations, but the book also contains a treatment of related topics like PDE's with p-Laplacian, half-linear difference equations and

Differential equations --- Differential equations, Linear. --- Differential equations, Nonlinear. --- Oscillation theory. --- Nonlinear differential equations --- Nonlinear theories --- Linear differential equations --- Linear systems --- 517.91 Differential equations