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 v
... Qualitative Methods 7 Further Reading 7 Problems 7 CHAPTER 4 DIFFERENTIAL EQUATIONS ASSOCIATED WITH ORTHOGONAL FUNCTIONS 75 4.1 . Trigonometric Functions 75 4.1.1 . Complex Form of the Fourier Series 75 Sturm - Liouville Problems 4.2 ...
... Qualitative Methods 7 Further Reading 7 Problems 7 CHAPTER 4 DIFFERENTIAL EQUATIONS ASSOCIATED WITH ORTHOGONAL FUNCTIONS 75 4.1 . Trigonometric Functions 75 4.1.1 . Complex Form of the Fourier Series 75 Sturm - Liouville Problems 4.2 ...
Page 7
... QUALITATIVE METHODS Many solutions can be only approximated - for instance , those of most nonlinear equations . One obvious approximation is replace- ment of the nonlinear form by a linearized one that is sufficiently accurate for a ...
... QUALITATIVE METHODS Many solutions can be only approximated - for instance , those of most nonlinear equations . One obvious approximation is replace- ment of the nonlinear form by a linearized one that is sufficiently accurate for a ...
Page 180
... qualitative analysis of the form of the solution of such cases is advis- able before the numerical solution is attempted . Several repre- sentative systems will be studied in this section . The integrals will be Example 7.11 The Finite ...
... qualitative analysis of the form of the solution of such cases is advis- able before the numerical solution is attempted . Several repre- sentative systems will be studied in this section . The integrals will be Example 7.11 The Finite ...
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