Numerical Methods in Engineering with Python 3
This book is an introduction to numerical methods for students in engineering. It covers the usual topics found in an engineering course: solution of equations, interpolation and data fitting, solution of differential equations, eigenvalue problems, and optimization. The algorithms are implemented in Python 3, a high-level programming language that rivals MATLABŪ in readability and ease of use. All methods include programs showing how the computer code is utilized in the solution of problems. The book is based on Numerical Methods in Engineering with Python, which used Python 2. This new text demonstrates the use of Python 3 and includes an introduction to the Python plotting package Matplotlib. This comprehensive book is enhanced by the addition of numerous examples and problems throughout.
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Systems of Linear Algebraic Equations 31
Interpolation and Curve Fitting 104
Problem Set 3 2
Initial Value Problems
TwoPoint Boundary Value Problems
Symmetric Matrix Eigenvalue Problems
Introduction to Optimization
List of Program Modules by Chapter
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algorithm array back substitution bisection boundary conditions boundary value problem bracketed coefﬁcient matrix column Compute constraints convergence cubic spline data points deﬁned deﬁnite derivatives Determine diagonal differential equation displacement efﬁcient eigenvalue problem eigenvectors elements equations Ax evaluate EXAM PLE example ﬁgure ﬁle ﬁnd ﬁnding ﬁnite difference approximations ﬁrst ﬁrst-order ﬁt ﬁtting formula Gauss elimination Gauss-Legendre quadrature Gauss-Seidel method I/usr/bin/python import math import numpy initial conditions initial value problem input("\nPress return interpolation inverse power method linear loop LU decomposition midpoint minimization module Newton-Raphson method nodes numpy as np numpy import obtained output panels pivot plot polynomial polynomial interpolation Prob PROBLEM SET Python range(n result return to exit Richardson extrapolation Romberg integration root Runge-Kutta method shown solution Solve the equations speciﬁed symmetric Table Taylor series tion transformation trapezoidal rule triangular tridiagonal tridiagonal matrix truncation error vector Write a program XStop yields zero