Numerical Methods for Engineers

Numerical Methods for Engineers

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Although pseudocodes, Mathematica(R), and MATLAB(R) illustrate how algorithms work, designers of engineering systems write the vast majority of large computer programs in the Fortran language. Using Fortran 95 to solve a range of practical engineering problems, Numerical Methods for Engineers, Second Edition provides an introduction to numerical methods, incorporating theory with concrete computing exercises and programmed examples of the techniques presented. Covering a wide range of numerical applications that have immediate relevancy for engineers, the book describes forty-nine programs in Fortran 95. Many of the programs discussed use a sub-program library called nm_lib that holds twenty-three subroutines and functions. In addition, there is a precision module that controls the precision of calculations. Well-respected in their field, the authors discuss a variety of numerical topics related to engineering. Some of the chapter features include...* The numerical solution of sets of linear algebraic equations * Roots of single nonlinear equations and sets of nonlinear equations * Numerical quadrature, or numerical evaluation of integrals * An introduction to the solution of partial differential equations using finite difference and finite element approaches Describing concise programs that are constructed using sub-programs wherever possible, this book presents many different contexts of numerical analysis, forming an excellent introduction to more comprehensive subroutine libraries such as the numerical algorithm group (NAG).show more

Product details

  • Hardback | 492 pages
  • 162.6 x 236.2 x 30.5mm | 816.48g
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • Revised
  • 2nd Revised edition
  • 83 black & white illustrations, 23 black & white tables
  • 1584884010
  • 9781584884019

Table of contents

INTRODUCTION AND PROGRAMMING PRELIMINARIES Introduction Running Programs Hardware External Fortran Sub-Program Libraries A Simple Fortran Program Some Simple Fortran Constructs Intrinsic Functions User-Supplied Functions and Subroutines Errors and Accuracy Graphical Output Conclusions LINEAR ALGEBRAIC EQUATIONS Introduction Gaussian Elimination Equation Solution Using Factorization Equations with a Symmetrical Coefficient Matrix Banded Equations Compact Storage for Variable Bandwidths Pivoting Equations with Prescribed Solutions Iterative Methods Gradient Methods Unsymmetrical Systems Preconditioning Comparison of Direct and Iterative Methods Exercises NONLINEAR EQUATIONS Introduction Iterative Substitution Multiple Roots and Other Difficulties Interpolation Methods Extrapolation Methods Acceleration of Convergence Systems of Nonlinear Equations Exercises EIGENVALUE EQUATIONS Introduction Vector Iteration Intermediate Eigenvalues by Deflation The Generalized Eigenvalue Problem [K] {x} = ?[M] {x} Transformation Methods Characteristic Polynomial Methods Exercises INTERPOLATION AND CURVE FITTING Introduction Interpolating Polynomials Interpolation Using Cubic Spline Functions Numerical Differentiation Curve Fitting Exercises NUMERICAL INTEGRATION Introduction Newton-Cotes Rules Gauss-Legendre Rules Adaptive Integration Rules Special Integration Rules Multiple Integrals Exercises NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS Introduction Definitions and Types of ODE Initial Value Problems Boundary Value Problems Exercises INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS Introduction Definitions and Types of PDE First Order Equations Second Order Equations Finite Difference Method Finite Element Method Exercises APPENDIX A: Descriptions of Library Subprograms APPENDIX B: Fortran 95 Listings of Library Subprograms APPENDIX C: References and Additional Readingshow more