Numerical Methods for Nonlinear Engineering Models

Preface; 1 Introduction to Nonlinear Engineering Problems and Models; 1.1 Science and Engineering ; 1.2 The Engineering Method; 1.3 Some General Features of Engineering Models ; 1.4 Linear and Nonlinear; 1.5 A Brief Look Ahead ; 2 Numerical Fundamentals and Computer Programming; 2.1 Computer Programming Languages; 2.2 Lua as a Programming Language; 2.3 Data Representation and Associated Limitations; 2.4 Language Extensibility; 2.5 Some Language Enhancement Functions; 2.6 Software Coding Practices; 2.7 Summary; 3 Roots of Nonlinear Equations; 3.1 Successive Substitutions or Fixed Point Iteration; 3.2 Newton's Method or Newton-Ralphson Method; 3.3 Halley's Iteration Method; 3.4 Other Solution Methods; 3.5 Some Final Considerations for Finding Roots of Functions; 3.6 Summary; 4 Solving Sets of Equations: Linear and Nonlinear; 4.1 The Solution of Sets of Linear Equations; 4.2 Solution of Sets of Nonlinear Equations; 4.3 Some Examples of Sets of Equations; 4.4 Polynomial Equations and Roots of Polynomial Equations; 4.5 Matrix Equations and Matrix Operations; 4.6 Matrix Eigenvalue Problems; 4.7 Summary; 5 Numerical Derivatives and Numerical Integration; 5.1 Fundamentals of Numerical Derivatives; 5.2 Maximum and Minimum Problems; 5.3 Numerical Partial Derivatives and Min/Max Applications; 5.4 Fundamentals of Numerical Integration; 5.5 Integrals with Singularities and Infinite Limits; 5.6 Summary; 6 Interpolation; 6.1 Introduction to Interpolation - Linear Interpolation; 6.2 Interpolation using Local Cubic (LCB) Functions; 6.3 Interpolation using Cubic Spline Functions (CSP); 6.4 Interpolation Examples with Known Functions; 6.5 Interpolation Examples with Unknown Functions; 6.6 Summary; 7 Curve Fitting and Data Plotting; 7.1 Introduction; 7.2 Linear Least Squares Data Fitting; 7.3 General Least Squares Fitting with Linear Coefficients; 7.4 The Fourier Series Method; 7.5 Nonlinear Least Squares Curve Fitting; 7.6 Data Fitting and Plotting with Known Functional Foms;7.7

From the reviews:"This voluminous book by Hauser ... covers numerical topics ranging from roots of nonlinear equations to introductory finite element method. The advantage of this work lies in the author's approach of show-and-tell or 'learning by example.' ... The examples are almost exclusively in the area of nonlinear electronics ... which may be quite advantageous for electronics engineers. ... Summing Up: Recommended. Upper-division undergraduate through professional collections." (R. N. Laoulache, Choice, Vol. 47 (3), November, 2009)"The book represents a comprehensive guide for the exploitation of standard numerical tools in nonlinear engineering problems. The presentation style ensures a balanced construction in providing mathematical knowledge illustrated by relevant examples. ... suitable for self-study and teaching support at the first postgraduate level. The book is recommended to educators interested in preparing or upgrading lecture notes and seminars, students specializing in different fields of engineering, and practitioners working with various types of nonlinear models." (Octavian Pastravanu, Zentralblatt MATH, Vol. 1173, 2009)