Download Engineering Analysis Interactive Methods and Programs With by Yen-Ching Pao PDF

By Yen-Ching Pao

This booklet offers a concise creation to numerical recommendations in engineering research, utilizing FORTRAN, QuickBASIC, MATLAB, and Mathematica to demonstrate the examples. Discussions include:omatrix algebra and analysisosolution of matrix equationsomethods of curve fitomethods for locating the roots of polynomials and transcendental equationsofinite adjustments and strategies for interpolation and numerical differentiationonumerical computation of unmarried and double integralsonumerical resolution of normal differential equationsEngineering Analysis:oteaches readers to develop into expert in FORTRAN or QuickBASIC programming to resolve engineering problemsoprovides an advent to MATLAB and Mathematica, allowing readers to put in writing supplementary m-files for MATLAB and toolkits for Mathematica utilizing C-like commandsThe publication emphasizes interactive operation in constructing computing device courses all through, permitting the values of the parameters all in favour of the matter to be entered via the consumer of this system through a keyboard.In introducing each one numerical technique, Engineering research provides minimal mathematical derivations yet offers a radical clarification of computational systems to unravel a particular challenge. It serves as an excellent textual content for self-study in addition to source for basic reference.

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Extra info for Engineering Analysis Interactive Methods and Programs With FORTRAN ver 2

Sample text

The Input display bar will appear on screen, applications of Mathematica can start by entering commands from keyboard and then press the Shift and Enter keys. To terminate the Mathematica application, enter Quit[] from keyboard and then press the Shift and Enter keys. Mathematica commands, statements, and functions are gradually introduced and applied in increasing degree of difficulty. Its graphic capabilities are also utilized in presentation of the computed results. For matrix operations, Mathematica can compute the sum and difference of two matrices of same order in symbolic forms, such as in the following cases of involving two matrices, A and B, both of order 2 by 2: In[1]: = A = {{1,2},{3,4}}; MatrixForm[A] Out[1]//MatrixForm = 1 2 3 4 In[1]: = is shown on screen by Mathematica while user types in A = {{1,2},{3,4}}; MatrixForm[A].

M should then be added into MATLAB. As an example of interactive application of this m file, the sample problem used in the FORTRAN and QuickBASIC versions is again solved by specifying the coefficient matrix [C] and the right hand side vector {R} to obtain the resulting display as follows: The results of the vector {X} and determinant D for the coefficient matrix [C] are same as obtained before. MATHEMATICA APPLICATIONS For solving a system of linear algebraic equations which has been arranged in matrix form as [A]{X} = {R}, Mathematica’s function LinearSolve can be applied © 2001 by CRC Press LLC to solve for {X} when the coefficient matrix [A] and the right-hand side vector {R} are both provided.

However, it should be evident here that a matrix whose order is large the task of calculating its determinant would certainly need help from computer. 5. Let us demonstrate the application of Cramer’s Rule by having a numerical case. If the two given points to be passed by the straight line y = a1 + a2x are (x1,y1) = (1,2) and (x2,y2) = (3,4). Then we can have: © 2001 by CRC Press LLC [C ] = 1 1 x1 1 = x2 1 1 = 1× 3 −1×1 = 3 −1 = 2 3 y1 x1 2 = x2 4 1 = 2 × 3 −1× 4 = 6 − 4 = 2 3 y1 1 = y2 1 2 = 1× 4 − 2 ×1 = 4 − 2 = 2 4 [c ] = y 1 2 and 1 [C ] = 1 2 Consequently, according to Equation 5 we can find the coefficients in the straight-line equation to be: a1 = [C1 ] [C ] = 2 2 = 1 and a 2 = [C2 ] [C] = 2 2 = 1 Hence, the line passing through the points (1,2) and (3,4) is y = a1 + a2x = 1 + x.

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