By Richard G. Rice, Duong D. Do
This moment variation of the go-to reference combines the classical research and smooth functions of utilized arithmetic for chemical engineers. The ebook introduces conventional innovations for fixing usual differential equations (ODEs), including new fabric on approximate answer equipment resembling perturbation innovations and common numerical recommendations. it is usually analytical how to care for very important sessions of finite-difference equations. The final part discusses numerical answer concepts and partial differential equations (PDEs). The reader will then be outfitted to use arithmetic within the formula of difficulties in chemical engineering. just like the first version, there are numerous examples supplied as homework and labored examples
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Additional info for Applied Mathematics And Modeling For Chemical Engineers, Second Edition
D. Numerical Methods for Engineers and Scientists. McGraw Hill, New York (1992). Rice, R. G. “Approximate Solutions for Batch, Packed Tube and Radial Flow Adsorbers: Comparison with Experiment,” Chem. Eng. , 37, 83–97 (1982). Walas, S. M. Modeling with Differential Equations in Chemical Engineering. Butterworth-Heinemann, Boston (1991). 1 GEOMETRIC BASIS AND FUNCTIONALITY In Chapter 1, we took the point of view that elementary differential balances gave rise to certain differential equations, and for first order systems, we could represent these in general by dy ¼ f ðx; yÞ dx ð2:1Þ where f(x,y) is some arbitrary, but known, function ((x2 þ y2)1=2, xy2, etc).
6 Gauss–Jordan Elimination: Solving Linear Equations the RHS of the augmented matrix becomes the matrix inverse AÀ1; that is, Gauss–Jordan elimination is a variation of the Gauss elimination scheme. Instead of obtaining the triangular matrix at the end of the elimination, the Gauss–Jordan has one extra step to reduce the matrix A to an identity matrix. In this way, the augmented vector b0 is simply the solution vector x. The primary use of the Gauss–Jordan method is to obtain an inverse of a matrix.
3 FIRST-ORDER EQUATIONS The most commonly occurring first-order equation in engineering analysis is the linear first-order equation (the I-factor equation) dy þ aðxÞy ¼ f ðxÞ dx ð2:13Þ ð2:12Þ Z IðxÞ ¼ exp aðxÞ dx ð2:18Þ where I(x) is called the integrating factor. This is the necessary and sufficient condition for the general solution, Eq. 15, to exist. 3 FIRST-ORDER EQUATIONS By comparing this with Eq. 2 To solve the differential equation Mðx; yÞ ¼ dy 2 À y¼x dx x ð2:19Þ Z 2 1 À dx ¼ expðÀ2 ln xÞ ¼ 2 x x @w ; @x Nðx; yÞ ¼ @w @y ð2:27Þ if w is to exist as a possible solution.