Modeling with Differential Equations in Chemical Engineering'Modelling with Differential Equations in Chemical Engineering' covers the modelling of rate processes of engineering in terms of differential equations. While it includes the purely mathematical aspects of the solution of differential equations, the main emphasis is on the derivation and solution of major equations of engineering and applied science. Methods of solving differential equations by analytical and numerical means are presented in detail with many solved examples, and problems for solution by the reader. Emphasis is placed on numerical and computer methods of solution. A key chapter in the book is devoted to the principles of mathematical modelling. These principles are applied to the equations in important engineering areas. The major disciplines covered are thermodynamics, diffusion and mass transfer, heat transfer, fluid dynamics, chemical reactions, and automatic control. These topics are of particular value to chemical engineers, but also are of interest to mechanical, civil, and environmental engineers, as well as applied scientists. The material is also suitable for undergraduate and beginning graduate students, as well as for review by practising engineers. |
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Page 36
... function is obtained by multiplying the transform y of the input by the transfer function G. The great value of this concept is due in part to the ease with which systems involving several transfer functions in series and paral- lel and ...
... function is obtained by multiplying the transform y of the input by the transfer function G. The great value of this concept is due in part to the ease with which systems involving several transfer functions in series and paral- lel and ...
Page 75
... functions are also needed in some applications . An important aspect of orthogonality is that it permits ready evaluation of the coefficients of the expansion of an arbitrary function in terms of a series of orthogonal functions ...
... functions are also needed in some applications . An important aspect of orthogonality is that it permits ready evaluation of the coefficients of the expansion of an arbitrary function in terms of a series of orthogonal functions ...
Page 349
... function also has real and imaginary parts , but the term is restricted to combinations w ( z ) = $ ( x , y ) + ių ( x , y ) ( 13.41 ) whose right - hand side can be derived from proper mathematical operations on z . That requirement is ...
... function also has real and imaginary parts , but the term is restricted to combinations w ( z ) = $ ( x , y ) + ių ( x , y ) ( 13.41 ) whose right - hand side can be derived from proper mathematical operations on z . That requirement is ...
Common terms and phrases
a₁ a²u applied arctan auxiliary conditions ax² ay² b₁ becomes Bessel equation Bessel functions boundary conditions C₁ C₂ chemical coefficients convergence coordinates curve d²y derivative diffusion diskette dx dy dx/dt dx² dy/dx eigenvalues equa Example Figure finite first-order flow fluid formulas Gaussian elimination heat equation heat transfer homogeneous independent variables initial conditions input integral equation inverse k₁ Laplace equation Laplace transform linear differential equations linear equations mathematical method nodes nonhomogeneous nonlinear numerical ODEs orthogonal parameters Partial Differential Equations phase plane plane polynomials problem reaction reactor region result roots second-order separation of variables sinh solution solved substitution T₁ Table temperature tion u₁ V₁ values vector velocity x₁ x²y y₁ zero ди др ду дх