Kirjahaku

Mathematical Modelling with Differential Equations aims to introduce various strategies for modelling systems using differential equations. Some of these methodologies are elementary and quite direct to comprehend and apply while others are complex in nature and require thoughtful, deep contemplation. Many topics discussed in the chapter do not appear in any of the standard textbooks and this provides users an opportunity to consider a more general set of interesting systems that can be modelled. For example, the book investigates the evolution of a "toy universe," discusses why "alternate futures" exists in classical physics, constructs approximate solutions to the famous Thomas—Fermi equation using only algebra and elementary calculus, and examines the importance of "truly nonlinear" and oscillating systems. Features Introduces, defines, and illustrates the concept of "dynamic consistency" as the foundation of modelling.Can be used as the basis of an upper-level undergraduate course on general procedures for mathematical modelling using differential equations.Discusses the issue of dimensional analysis and continually demonstrates its value for both the construction and analysis of mathematical modelling.

Mathematical Modelling with Differential Equations aims to introduce various strategies for modelling systems using differential equations. Some of these methodologies are elementary and quite direct to comprehend and apply while others are complex in nature and require thoughtful, deep contemplation. Many topics discussed in the chapter do not appear in any of the standard textbooks and this provides users an opportunity to consider a more general set of interesting systems that can be modelled. For example, the book investigates the evolution of a "toy universe," discusses why "alternate futures" exists in classical physics, constructs approximate solutions to the famous Thomas—Fermi equation using only algebra and elementary calculus, and examines the importance of "truly nonlinear" and oscillating systems. Features Introduces, defines, and illustrates the concept of "dynamic consistency" as the foundation of modelling.Can be used as the basis of an upper-level undergraduate course on general procedures for mathematical modelling using differential equations.Discusses the issue of dimensional analysis and continually demonstrates its value for both the construction and analysis of mathematical modelling.

Introduction to Qualitative Methods for Differential Equations provides an alternative approach to teaching and understanding differential equations. The basic methodology of the book is centred on finding reformulations of differential equations in such a manner that they become (partially, at least) problems in geometry. Through this approach, the book distils the critical aspects of the qualitative theory of differential equations and illustrates their application to a number of nontrivial problems.FeaturesSelf-contained with suggestions for further readingConcise and approachable exposition with only minimal pre-requisitesIdeal for self-studyAppropriate for undergraduate mathematicians, engineers, and other quantitative science students.

Introduction to Qualitative Methods for Differential Equations provides an alternative approach to teaching and understanding differential equations. The basic methodology of the book is centred on finding reformulations of differential equations in such a manner that they become (partially, at least) problems in geometry. Through this approach, the book distils the critical aspects of the qualitative theory of differential equations and illustrates their application to a number of nontrivial problems.FeaturesSelf-contained with suggestions for further readingConcise and approachable exposition with only minimal pre-requisitesIdeal for self-studyAppropriate for undergraduate mathematicians, engineers, and other quantitative science students.

Generalized Trigonometric and Hyperbolic Functions highlights, to those in the area of generalized trigonometric functions, an alternative path to the creation and analysis of these classes of functions. Previous efforts have started with integral representations for the inverse generalized sine functions, followed by the construction of the associated cosine functions, and from this, various properties of the generalized trigonometric functions are derived. However, the results contained in this book are based on the application of both geometrical phase space and dynamical systems methodologies.Features Clear, direct construction of a new set of generalized trigonometric and hyperbolic functions Presentation of why x2+y2 = 1, and related expressions, may be interpreted in three distinct ways All the constructions, proofs, and derivations can be readily followed and understood by students, researchers, and professionals in the natural and mathematical sciences

Difference Equations: Theory, Applications and Advanced Topics, Third Edition provides a broad introduction to the mathematics of difference equations and some of their applications. Many worked examples illustrate how to calculate both exact and approximate solutions to special classes of difference equations. Along with adding several advanced topics, this edition continues to cover general, linear, first-, second-, and n-th order difference equations; nonlinear equations that may be reduced to linear equations; and partial difference equations.New to the Third Edition New chapter on special topics, including discrete Cauchy–Euler equations; gamma, beta, and digamma functions; Lambert W-function; Euler polynomials; functional equations; and exact discretizations of differential equationsNew chapter on the application of difference equations to complex problems arising in the mathematical modeling of phenomena in engineering and the natural and social sciences Additional problems in all chaptersExpanded bibliography to include recently published texts related to the subject of difference equationsSuitable for self-study or as the main text for courses on difference equations, this book helps readers understand the fundamental concepts and procedures of difference equations. It uses an informal presentation style, avoiding the minutia of detailed proofs and formal explanations.

Difference Equations: Theory, Applications and Advanced Topics, Third Edition provides a broad introduction to the mathematics of difference equations and some of their applications. Many worked examples illustrate how to calculate both exact and approximate solutions to special classes of difference equations. Along with adding several advanced topics, this edition continues to cover general, linear, first-, second-, and n-th order difference equations; nonlinear equations that may be reduced to linear equations; and partial difference equations.New to the Third Edition New chapter on special topics, including discrete Cauchy–Euler equations; gamma, beta, and digamma functions; Lambert W-function; Euler polynomials; functional equations; and exact discretizations of differential equationsNew chapter on the application of difference equations to complex problems arising in the mathematical modeling of phenomena in engineering and the natural and social sciences Additional problems in all chaptersExpanded bibliography to include recently published texts related to the subject of difference equationsSuitable for self-study or as the main text for courses on difference equations, this book helps readers understand the fundamental concepts and procedures of difference equations. It uses an informal presentation style, avoiding the minutia of detailed proofs and formal explanations.