ISE Numerical Methods for Engineers

<p>Part 1 - Modeling, Computers, and Error Analysis</p><p>1) Mathematical Modeling and Engineering Problem Solving</p><p>2) Programming and Software</p><p>3) Approximations and Round-Off Errors</p><p>4) Truncation Errors and the Taylor Series</p><p>Part 2 - Roots of Equations</p><p>5) Bracketing Methods</p><p>6) Open Methods</p><p>7) Roots of Polynomials</p><p>8) Case Studies: Roots of Equations</p><p>Part 3 - Linear Algebraic Equations</p><p>9) Gauss Elimination</p><p>10) LU Decomposition and Matrix Inversion</p><p>11) Special Matrices and Gauss-Seidel</p><p>12) Case Studies: Linear Algebraic Equations</p><p>Part 4 - Optimization</p><p>13) One-Dimensional Unconstrained Optimization</p><p>14) Multidimensional Unconstrained Optimization</p><p>15) Constrained Optimization</p><p>16) Case Studies: Optimization</p><p>Part 5 - Curve Fitting</p><p>17) Least-Squares Regression</p><p>18) Interpolation</p><p>19) Fourier Approximation</p><p>20) Case Studies: Curve Fitting</p><p>Part 6 - Numerical Differentiation and Integration</p><p>21) Newton-Cotes Integration Formulas</p><p>22) Integration of Equations</p><p>23) Numerical Differentiation</p><p>24) Case Studies: Numerical Integration and Differentiation</p><p>Part 7 - Ordinary Differential Equations</p><p>25) Runge-Kutta Methods</p><p>26) Stiffness and Multistep Methods</p><p>27) Boundary-Value and Eigenvalue Problems</p><p>28) Case Studies: Ordinary Differential Equations</p><p>Part 8 - Partial Differential Equations</p><p>29) Finite Difference: Elliptic Equations</p><p>30) Finite Difference: Parabolic Equations</p><p>31) Finite-Element Method</p><p>32) Case Studies: Partial Differential Equations</p><p>Appendix A - The Fourier Series</p><p>Appendix B - Getting Started with Matlab</p><p>Appendix C - Getting Starte dwith Mathcad</p><p>Bibliography</p><p>Index</p>