عنوان

Differential equations as models in science and engineering /

(Number (ISBN

9789814656962

(Number (ISBN

9789814656979

(Number (ISBN

9814656968

(Number (ISBN

9814656976

Title Proper

Differential equations as models in science and engineering /

General Material Designation

[Book]

First Statement of Responsibility

Gregory Baker, the Ohio State University, USA.

Place of Publication, Distribution, etc.

New Jersey :

Name of Publisher, Distributor, etc.

World Scientific,

Date of Publication, Distribution, etc.

2016.

Specific Material Designation and Extent of Item

xxi, 368 pages ;

Dimensions

25 cm

Text of Note

Includes index.

Text of Note

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

Text of Note

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

Text of Note

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

Text of Note

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

Text of Note

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

0

0

0

0

0

Text of Note

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.

Differential equations-- Numerical solutions, Textbooks.

Differential equations, Textbooks.

Engineering-- Mathematical models, Textbooks.

Science-- Mathematical models, Textbooks.

Differential equations-- Numerical solutions.

Differential equations.

Differentialgleichung

Engineering-- Mathematical models.

Mathematische Modellierung

Science-- Mathematical models.

Number

Edition

Class number

Book number

Baker, Gregory R., (Gregory Richard)

Date of Transaction

20200823232231.0

Cataloguing Rules (Descriptive Conventions))

rda

Electronic name

[Book]

Y