| Preface | p. xi |
| Introduction to Nonlinear Engineering Problems and Models | p. 1 |
| Science and Engineering | p. 1 |
| The Engineering Method | p. 3 |
| Some General Features of Engineering Models | p. 6 |
| Linear and Nonlinear Models | p. 8 |
| A Brief Look Ahead | p. 14 |
| Numerical Fundamentals and Computer Programming | p. 17 |
| Computer Programming Languages | p. 17 |
| Lua as a Programming Language | p. 19 |
| Data Representation and Associated Limitations | p. 23 |
| Language Extensibility | p. 29 |
| Some Language Enhancement Functions | p. 33 |
| Software Coding Practices | p. 37 |
| Summary | p. 40 |
| Roots of Nonlinear Equations | p. 43 |
| Successive Substitutions or Fixed Point Iteration | p. 45 |
| Newton's Method or Newton-Ralphson Method | p. 51 |
| Halley's Iteration Method | p. 68 |
| Other Solution Methods | p. 70 |
| Some Final Considerations for Finding Roots of Functions | p. 71 |
| Summary | p. 75 |
| Solving Sets of Equations: Linear and Nonlinear | p. 77 |
| The Solution of Sets of Linear Equations | p. 78 |
| Solution of Sets of Nonlinear Equations | p. 87 |
| Some Examples of Sets of Equations | p. 93 |
| Polynomial Equations and Roots of Polynomial Equations | p. 117 |
| Matrix Equations and Matrix Operations | p. 131 |
| Matrix Eigenvalue Problems | p. 140 |
| Summary | p. 146 |
| Numerical Derivatives and Numerical Integration | p. 147 |
| Fundamentals of Numerical Derivatives | p. 147 |
| Maximum and Minimum Problems | p. 161 |
| Numerical Partial Derivatives and Min/Max Applications | p. 164 |
| Fundamentals of Numerical Integration | p. 169 |
| Integrals with Singularities and Infinite Limits | p. 178 |
| Summary | p. 185 |
| Interpolation | p. 187 |
| Introduction to Interpolation - Linear Interpolation | p. 188 |
| Interpolation using Local Cubic (LCB) Functions | p. 192 |
| Interpolation using Cubic Spline Functions (CSP) | p. 199 |
| Interpolation Examples with Known Functions | p. 203 |
| Interpolation Examples with Unknown Functions | p. 216 |
| Summary | p. 225 |
| Curve Fitting and Data Plotting | p. 227 |
| Introduction | p. 227 |
| Linear Least Squares Data Fitting | p. 229 |
| General Least Squares Fitting with Linear Coefficients | p. 236 |
| The Fourier Series Method | p. 238 |
| Nonlinear Least Squares Curve Fitting | p. 253 |
| Data Fitting and Plotting with Known Functional Foms | p. 264 |
| General Data Fitting and Plotting | p. 275 |
| Rational Function Approximations to Implicit Functions | p. 293 |
| Weighting Factors | p. 306 |
| Summary | p. 310 |
| Statistical Methods and Basic Statistical Functions | p. 313 |
| Introduction | p. 313 |
| Basic Statistical Properties and Functions | p. 315 |
| Distributions and More Distributions | p. 326 |
| Analysis of Mean and Variance | p. 332 |
| Comparing Distribution Functions - The Kolmogorov-Smirnov Test | p. 347 |
| Monte Carlo Simulations and Confidence Limits | p. 355 |
| Non-Gaussian Distributions and Reliability Modeling | p. 361 |
| Summary | p. 367 |
| Data Models and Parameter Estimation | p. 369 |
| Introduction | p. 369 |
| Goodness of Data Fit and the 6-Plot Approach | p. 372 |
| Confidence Limits on Estimated Parameters and MC Analysis | p. 381 |
| Examples of Single Variable Data Fitting and Parameter Estimation | p. 397 |
| Data Fitting and Parameter Estimation with Weighting Factors | p. 429 |
| Data Fitting and Parameter Estimation with Transcendental Functions | p. 436 |
| Data Fitting and Parameter Estimation with Piecewise Model Equations | p. 439 |
| Data Fitting and Parameter Estimation with Multiple Independent Parameters | p. 442 |
| Response Surface Modeling and Parameter Estimation | p. 452 |
| Summary | p. 459 |
| Differential Equations: Initial Value Problems | p. 461 |
| Introduction to the Numerical Solution of Differential Equations | p. 461 |
| Systems of Differential Equations | p. 467 |
| Exploring Stability and Accuracy Issues with Simple Examples | p. 469 |
| Development of a General Differential Equation Algorithm | p. 481 |
| Variable Time Step Solutions | p. 487 |
| A More Detailed Look at Accuracy Issues with the TP Algorithm | p. 497 |
| Runge-Kutta Algorithms | p. 515 |
| An Adaptive Step Size Algorithm | p. 522 |
| Comparison with MATLAB Differential Equation Routines | p. 536 |
| Direct Solution of Second Order Differential Equations | p. 541 |
| Differential-Algebraic Systems of Equations | p. 546 |
| Examples of Initial Value Problems | p. 551 |
| Summary | p. 573 |
| Differential Equations: Boundary Value Problems | p. 575 |
| Introduction to Boundary Value Problems in One Independent Variable | p. 575 |
| Shooting(ST) Methods and Boundary Value Problems(BVP) | p. 577 |
| Accuracy of the Shooting Method for Boundary Value Problems | p. 592 |
| Eigenvalue and Eigenfunction Problems in Differential Equations | p. 600 |
| Finite Difference Methods and Boundary Value Problems | p. 620 |
| Boundary Value Problems with Coupled Second Order Differential Equations | p. 648 |
| Other Selected Examples of Boundary Value Problems | p. 681 |
| Estimating Parameters of Differential Equations | p. 688 |
| Summary | p. 701 |
| Partial Differential Equations: Finite Difference Approaches | p. 705 |
| Introduction to Single Partial Differential Equations | p. 706 |
| Introduction to Boundary Conditions | p. 707 |
| Introduction to the Finite Difference Method | p. 708 |
| Coupled Systems of Partial Differential Equations | p. 714 |
| Exploring the Accuracy of the Finite Difference Method For Partial Differential Equations | p. 727 |
| Some Examples of Partial Differential Equations of the Initial Value, Boundary Value Type | p. 735 |
| Boundary Value Problems (BVP) in Two Dimensions | p. 793 |
| Two Dimensional BVPs with One Time Dimension | p. 849 |
| Some Selected Examples of Two Dimensional BVPs | p. 860 |
| Summary | p. 879 |
| Partial Differential Equations: The Finite Element Method | p. 883 |
| An Introduction to the Finite Element Method | p. 883 |
| Selecting and Determining Finite Elements | p. 885 |
| Shape Functions and Natural Coordinates | p. 890 |
| Formulation of Finite Element Equations | p. 893 |
| Interpolation Functions and Integral Evaluation | p. 899 |
| Boundary Conditions with the Finite Element Method | p. 903 |
| The Complete Finite Element Method | p. 907 |
| Exploring the Accuracy of the Finite Element Method | p. 923 |
| Two Dimensional BVPs with One Time Dimension | p. 925 |
| Selected Examples of PDEs with the Finite Element Method | p. 935 |
| Some Final Considerations for the FE Method | p. 984 |
| Summary | p. 986 |
| A Brief Summary of the Lua Programming Language | p. 989 |
| Software Installation | p. 1001 |
| Subject Index | p. 1009 |
| Table of Contents provided by Ingram. All Rights Reserved. |