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Download e-book for iPad: A numerical primer for the chemical engineer by Edwin Zondervan

By Edwin Zondervan

ISBN-10: 1482229447

ISBN-13: 9781482229448

"This booklet emphasizes the deriviation and use of various numerical tools for fixing chemical engineering difficulties. The algorithms are used to unravel linear equations, nonlinear equations, usual differential equations and partial differential equations. it is also chapters on linear- and nonlinear regression and ond optimizaiton. MATLAB is followed because the programming atmosphere during the book. Read more...

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Example text

In MATLAB, a program or subprogram is called a function. 3 Gaussian elimination You have probably seen Gaussian elimination before, so the following may be just a review for you. 1)     A31 x1 b1 A23   x2  =  b2  , A33 x3 b3 A21 A22 A23 A31 A32 A33  | b1 | b2  . 3) Elimination methods 27 In order to simplify our system, we can perform row operations, that is, adding multiples of equations together in order to eliminate variables. For example, we could eliminate element A21 by subtracting A21 /A11 = d21 times row 1 from row 2.

35) We will use this spectral decomposition later on. , det(A − λI) = 0 has repeated roots. 36) where Λ = diag(λ1 , λ2 , · · · , λN ). Proof : We first write A as a Schur decomposition: A = U RU H . 38) we then form the two matrix products: AAH = U RU H (U RH U H ) = U RRH U H AH A = U RH U H (U RU H ) = U RH RU H . 40) 22 A Numerical Primer for the Chemical Engineer For A to be normal, AAH must be normal  R11 R12 R13  R22 R23   R33 R=   and RH     =   ¯ 11 R ¯ 12 R ¯ 13 R .. ¯ 1N R ¯ 22 R ¯ 23 R ..

The solution of this problem is y = [2, −2]. 0002]. Apparently this system is ill conditioned ; a small error in the inputs result in a big error in the outputs. If you calculate the condition criterion, you would find C ≈ 2 ∗ 108 . Also, for bigger systems, small errors in the inputs can produce tremendous errors in the solution vectors. Such badly conditioned systems are not easy to solve accurately. Sometimes it is possible to reformulate the problem in order to improve the conditioning. Sometimes the solution method can be improved.

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A numerical primer for the chemical engineer by Edwin Zondervan


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