Numerical Methods in Engrg.practice

Preface 1. Introduction 1.1. Mathematical Models and Their Solutions 1.2. The Need for Numerical Solutions 1.3. Errors 1.4. Taylor Series 2. Matrices and Determinants 2.1. Introduction to Matrices 2.2. Special Matrices 2.3. Matrix Equality 2.4. Matrix Addition and Subtraction 2.5. Matrix Multiplication 2.6. Manipulation of Partitioned Matrices 2.7. Rules for Combined Matrix Operations 2.8. Application of Matrices to the Rotation of a Coordinate System 2.9. Determinants and Their Evaluation 2.10. Area and Volume Calculation Using Determinants 3. Mathematical Modeling of Typical Engineering Systems 3.1. Introduction 3.2. Electrcial Engineering Systems 3.3. Mechanical Engineering Systems 3.4. Civil Engineering Systems 3.5. Engineering System Response 3.6. Models Involving Partial Differential Models 3.7. Comparison of Engineering Models 4. Simulations Linear Algebraic Equations 4.1. Introduction 4.2. Cramer's Rule 4.3. Gauss's Elimination Method 4.4. Gauss-Jordan Elimination Method 4.5. Crout's Method 4.6. Square Root Method 4.7. Reducing Matrix Method 4.8. Solution of Tridiagonal Systems 4.9. Iterative Methods 4.10. Ill-Conditioned Sets and Scaling 4.11. Sets with More Unknowns Than Equations 4.12. Linear Equations Involving Fewer Unknowns Than Equations 4.13. Sets Involving Complex Coefficients 4.14. Comparison of Method Efficiencies 5. Matrix Inversion 5.1. Introduction 5.2. Cramer's Rule 5.3. Elimination Method 5.4. Reducting Matrix Method 5.5. Partitioning Method 5.6. Matrices Involving Complex Coefficients 5.7. Special Matrices 6. Nonlinear Algebraic Equations 6.1. Introduction 6.2. Graphical Method 6.3. Interval-Halving Method 6.4. False-Position Method 6.5. Newton-Raphson First Method 6.6. Newton-Raphson Second Method 6.7. Modified Newton-Raphson Methods 6.8. Lin-Bairstow Method for Roots of Polynomials 6.9. Newton-Raphson Method for Systems of Equations 6.10. Practical Considerations 7. Eigenproblems 7.1. Introduction 7.2. Characterization Equation Determination 7.3. Eigenvalues and Eigenvectors 7.4. Vector Iteration Techniques 7.5. Polynomial Iteration Method 7.6. Transformation Methods 7.7. Functions of a Matrix 7.8. Static Condensation 8. Interpolation 8.1. Introduction 8.2. Interpolating Polynomials for Even Intervals 8.3. Difference Operators and Difference Tables 8.4. Differences and Interpolating Polynomials 8.5. Interpolating Polynomials for Uneven Intervals 8.6. Interpolation Errors 8.7. Inverse Interpolation 8.8. Cubic Splines 9. Curve Fitting 9.1. Introduction 9.2. Introduction to the Method of Least Squares 9.3. What Type of Function to Fit 9.4. Linear Regression 9.5. Linearization 9.6. Nonlinear Regression 9.7. Multiple Regression 9.8. Orthogonal Polynomials for Equal Intervals 9.9. Goodness of Functional Approximations 10. Numerical Differentiation 10.1. Introduction 10.2. Review of Taylor Series 10.3. Numerical Differentiation of FunctionsAl-Khafaji, Amir W. is the author of 'Numerical Methods in Engrg.practice' with ISBN 9780030017575 and ISBN 0030017572.