عنوان

Differential equations as models in science and engineering /

شابک

9789814656962

شابک

9789814656979

شابک

9814656968

شابک

9814656976

عنوان اصلي

Differential equations as models in science and engineering /

نام عام مواد

[Book]

نام نخستين پديدآور

Gregory Baker, the Ohio State University, USA.

محل نشرو پخش و غیره

New Jersey :

نام ناشر، پخش کننده و غيره

World Scientific,

تاریخ نشرو بخش و غیره

2016.

نام خاص و کميت اثر

xxi, 368 pages ;

ابعاد

25 cm

متن يادداشت

Includes index.

متن يادداشت

Machine generated contents note: 1.Linear Ordinary Differential Equations -- 1.1.Growth and decay -- 1.1.1.Bacterial growth -- 1.1.2.From discrete to continuous -- 1.1.3.Conservation of quantity -- 1.1.4.Simple electric circuits -- 1.1.5.Abstract viewpoint -- 1.1.6.Exercises -- 1.1.7.Additional deliberations -- 1.2.Forcing effects -- 1.2.1.Constant inflow as an input -- 1.2.2.Periodic inflow as an input -- 1.2.3.Discontinuous inflow as an input -- 1.2.4.Abstract viewpoint -- 1.2.5.Exercises -- 1.2.6.General forcing terms -- 1.3.Coefficients with time variation -- 1.3.1.Variable river flow -- 1.3.2.Abstract viewpoint -- 1.3.3.Exercises -- 1.3.4.Summary -- 1.3.5.Flowchart: Linear, first-order differential equations -- 1.4.Second-order equations: Growth and decay -- 1.4.1.A simple chain of chemical reactions -- 1.4.2.Chained chemical reactions with forcing -- 1.4.3.Abstract viewpoint -- 1.4.4.Exercises -- 1.4.5.Time-varying coefficients in the differential equation

متن يادداشت

Note continued: 1.5.Second-order equations: Oscillations -- 1.5.1.Exponentials with complex arguments -- 1.5.2.Application to differential equations -- 1.5.3.The LCR circuit -- 1.5.4.Abstract viewpoint -- 1.5.5.Exercises -- 1.5.6.Higher-order differential equations -- 1.6.Forcing terms: Resonances -- 1.6.1.LCR circuit with constant applied voltage -- 1.6.2.LCR circuit with alternating applied voltage -- 1.6.3.Complex solutions -- 1.6.4.Resonance -- 1.6.5.Abstract view -- 1.6.6.Exercises -- 1.6.7.General forcing terms -- 1.6.8.Summary -- 1.6.9.Flowchart: Linear, second-order differential equations -- 2.Periodic Behavior -- 2.1.Periodic functions -- 2.1.1.Mathematical expression -- 2.1.2.Periodic forcing of an LCR circuit -- 2.1.3.Abstract view -- 2.1.4.Exercises -- 2.1.5.Periodic complex functions -- 2.2.The Fourier series -- 2.2.1.Construction of a Fourier series -- 2.2.2.Calculation of the Fourier coefficients -- 2.2.3.Abstract view -- 2.2.4.Exercises

متن يادداشت

Note continued: 2.2.5.Complex Fourier coefficients -- 2.3.Symmetry in the Fourier series -- 2.3.1.Even and odd functions -- 2.3.2.Fourier coefficients for even and odd periodic functions -- 2.3.3.Abstract view -- 2.3.4.Exercises -- 2.3.5.Other symmetries -- 3.Boundary Value Problems -- 3.1.Spatially varying steady states -- 3.1.1.Steady state transport -- 3.1.2.Diffusion -- 3.1.3.Abstract view -- 3.1.4.Exercises -- 3.2.Bifurcation -- 3.2.1.Column buckling -- 3.2.2.Abstract viewpoint -- 3.2.3.Summary -- 3.2.4.Exercises -- 3.3.Forcing effects -- 3.3.1.Cooling fins -- 3.3.2.Heated plate; homogeneous boundary conditions -- 3.3.3.Heated plate; inhomogeneous boundary conditions -- 3.3.4.Abstract viewpoint -- 3.3.5.Exercises -- 3.3.6.Flowchart: Linear, second-order boundary-value problems -- 4.Linear Partial Differential Equations -- 4.1.Diffusion: Part I -- 4.1.1.Transport equations -- 4.1.2.Initial and boundary conditions -- 4.1.3.Exponential solutions

متن يادداشت

Note continued: 4.1.4.Separation of variables -- 4.1.5.Abstract view -- 4.1.6.Exercises -- 4.2.Diffusion: Part II -- 4.2.1.Inhomogeneous boundary conditions -- 4.2.2.Homogeneous solution -- 4.2.3.Time-dependent boundary conditions -- 4.2.4.Abstract view -- 4.2.5.Exercises -- 4.3.Propagation -- 4.3.1.Transmission line -- 4.3.2.Initial and boundary conditions -- 4.3.3.The homogeneous solution -- 4.3.4.Inhomogeneous boundary conditions -- 4.3.5.No resistance -- 4.3.6.Abstract view -- 4.3.7.Exercises -- 4.3.8.Inhomogeneous partial differential equations -- 4.4.Laplace's equation -- 4.4.1.Heat transport in two dimensions -- 4.4.2.Steady state solution as a particular solution -- 4.4.3.Electrostatic potential -- 4.4.4.Abstract view -- 4.4.5.Exercises -- 4.4.6.Heat transport in two dimensions -- continued -- 5.Systems of Differential Equations -- 5.1.First-order equations -- 5.1.1.Population dynamics -- 5.1.2.Abstract view -- 5.1.3.Exercises

متن يادداشت

Note continued: 5.2.Homogeneous linear equations -- 5.2.1.Basic concepts -- 5.2.2.Chemical reactions -- 5.2.3.The LCR circuit -- 5.2.4.Abstract viewpoint -- 5.2.5.Exercises -- 5.2.6.Higher dimensional systems -- 5.3.Inhomogeneous linear equations -- 5.3.1.LCR circuit with constant applied voltage -- 5.3.2.LCR circuit with alternating applied voltage -- 5.3.3.Stability -- 5.3.4.Abstract view -- 5.3.5.Exercises -- 5.3.6.General forcing term -- 5.4.Nonlinear autonomous equations -- 5.4.1.Predator-prey model -- 5.4.2.Abstract view -- 5.4.3.Exercises -- Appendix A The Exponential Function -- A.1.A review of its properties -- Appendix B The Taylor Series -- B.1.A derivation of the Taylor series -- B.2.Accuracy of the truncated Taylor series -- B.3.Standard examples -- Appendix C Systems of Linear Equations -- C.1.Algebraic equations -- C.2.Gaussian elimination -- C.3.Matrix form -- C.4.Eigenvalues and eigenvectors -- Appendix D Complex Variables -- D.1.Basic properties

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متن يادداشت

This textbook develops a coherent view of differential equations by progressingthrough a series of typical examples in science and engineering that arise asmathematical models. All steps of the modeling process are covered: formulationof a mathematical model; the development and use of mathematical concepts that lead to construct constructive solutions; validation of the solutions; and consideration of the consequences. The volume engages students in thinking mathematically, while emphasizing the power and relevance of mathematics in science and engineering. There are just a few guidelines that bring coherence to the construction of solutions as the book progresses through ordinary to partial differential equations using examples from mixing, electric circuits, chemical reactions and transport processes, among others. The development of differential equations as mathematical models and the construction of their solutions are places center stage in this volume.

موضوع مستند نشده

Differential equations-- Numerical solutions, Textbooks.

موضوع مستند نشده

Differential equations, Textbooks.

موضوع مستند نشده

Engineering-- Mathematical models, Textbooks.

موضوع مستند نشده

Science-- Mathematical models, Textbooks.

موضوع مستند نشده

Differential equations-- Numerical solutions.

موضوع مستند نشده

Differential equations.

موضوع مستند نشده

Differentialgleichung

موضوع مستند نشده

Engineering-- Mathematical models.

موضوع مستند نشده

Mathematische Modellierung

موضوع مستند نشده

Science-- Mathematical models.

شماره

ويراست

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Baker, Gregory R., (Gregory Richard)

تاريخ عمليات

20200823232231.0

قواعد فهرست نويسي ( بخش توصيفي )

rda

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y