Applied Numerical Methods with Python for Engineers and Scientists 1st Edition By Steven C. Chapra, David Clough
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Applied Numerical Methods with Python for Engineers and Scientists 1st Edition By Steven C. Chapra, David Clough

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About this ebook
The Applied Numerical Methods with Python for Engineers and Scientists (1st Edition) by Steven C. Chapra and David E. Clough is organized into six core parts. The book emphasizes practical problem-solving, engineering applications, and implementing code using Python (specifically utilizing libraries like NumPy and Matplotlib). [1, 2, 3]
The textbook covers the following topics by section: [1]
Part One: Modeling, Computers, and Error Analysis
  • Mathematical Modeling & Problem Solving: Formulation of simple engineering models and the application of conservation laws.
  • Python Fundamentals: Introduction to the Spyder/IPython environment, variables, assignments, mathematical operations, built-in functions, and basic graphics.
  • Programming in Python: Script files, structured programming, conditional statements, loops, nesting, and writing custom functions.
  • Error Analysis: Approximations, roundoff errors, truncation errors, and applications of the Taylor Series. [1, 2, 3]
Part Two: Roots and Optimization
  • Bracketing Methods for Roots: Bisection method and false-position method.
  • Open Methods for Roots: Fixed-point iteration, Newton-Raphson, and Secant methods.
  • Optimization: Finding the maxima and minima of one-dimensional and multi-dimensional functions. [1, 2, 3, 4]
Part Three: Linear Systems
  • Linear Algebraic Equations & Matrices: Matrix formulation of engineering systems.
  • Gauss Elimination: Solving linear systems, pitfalls of elimination methods, and techniques like pivoting.
  • LU Factorization & Matrix Inverse: Doolittle, Crout, and Cholesky decompositions, matrix inversion, and evaluation of condition numbers.
  • Iterative Methods: Gauss-Seidel and Jacobi iteration techniques.
  • Eigenvalues: Computation of eigenvalues and eigenvectors for physical engineering problems. [1, 2, 3, 4]
Part Four: Curve Fitting
  • Linear Regression: Straight-line regression and quantification of errors.
  • General Regression: General linear least-squares and non-linear regression models.
  • Polynomial Interpolation: Newton’s and Lagrange polynomials.
  • Splines: Linear, quadratic, and cubic splines for piecewise interpolation.
  • Fourier Analysis: Frequency-domain analysis and time-series approximation. [1]
Part Five: Integration and Differentiation
  • Numerical Integration Formulas: Newton-Cotes formulas, including the Trapezoidal rule and Simpson's rules.
  • Numerical Integration of Functions: Romberg integration and Gauss quadrature.
  • Numerical Differentiation: High-accuracy differentiation formulas and error estimation. [1, 2]
Part Six: Ordinary Differential Equations (ODEs)
  • Initial-Value Problems (IVPs): Euler's method, Heun's method, and Runge-Kutta methods.
  • Adaptive Methods & Stiff Systems: Adaptive Runge-Kutta steps and handling numerically stiff differential equations.
  • Boundary-Value Problems (BVPs): Finite-difference methods and the shooting method. [1, 2]

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9781266649615 9781266649851 9781266651496 adaptive and stiff systems Curve Fitting Details linear and nonlinear regression Integration and Differentiation Reviews Newton-Cotes integration formulas Ordinary Differential Equations Addresses initial-value problems Linear Systems Explores linear algebraic equations Modeling Computers and Error Analysis mathematical modeling Python fundamentals and programming Roots and Optimization bracketing methods
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