2nd Edition
Computer Methods for Engineering with MATLAB® Applications
Introduction
Introductory Remarks
Numerical Solutions
Importance of Analytical Results
Physical Considerations
Application of Computer Methods to Engineering Problems
Outline and Scope of the Book
Basic Considerations in Computer Methods
Introduction
Computational Procedure
Numerical Errors and Accuracy
Iterative Convergence
Numerical Parameters
A Review of MATLAB Programming
Introduction
MATLAB Environment
Ordinary Differential Equations
Input/Output
Script m-Files
Function m-Files
Plotting
Taylor Series and Numerical Differentiation
Introduction
The Taylor Series
Direct Approximation of Derivatives
Taylor-Series Approach and Accuracy
Polynomial Representation
Partial Derivatives
Roots of Equations
Introduction
Search Method for Real Roots
Bisection Method
Regula Falsi and Secant Methods
Newton–Raphson Method and Modified Newton’s Method
Successive Substitution Method
Other Methods
Numerical Solutions of Simultaneous Algebraic Equations
Introduction
Gaussian Elimination
Gauss–Jordan Elimination
Compact Methods
Numerical Solution of Linear Systems by Matrix Inversion
Iterative Methods
Homogeneous Linear Equations
Solution of Simultaneous Nonlinear Equations
Numerical Curve Fitting and Interpolation
Introduction
Exact Fit and Interpolation
Lagrange Interpolation
Newton’s Divided-Difference Interpolating Polynomial
Numerical Interpolation with Splines
Method of Least Squares for a Best Fit
Function of Two or More Independent Variables
Numerical Integration
Introduction
Rectangular and Trapezoidal Rules for Integration
Simpson’s Rules for Numerical Integration
Higher-Accuracy Methods
Integration with Segments of Unequal Width
Numerical Integration of Improper Integrals
Numerical Solution of Ordinary Differential Equations
Introduction
Euler’s Method
Improvements in Euler’s Method
Runge–Kutta Methods
Multistep Methods
Predictor–Corrector Methods
Boundary-Value Problems
Numerical Solution of Partial Differential Equations
Introduction
Parabolic PDEs
Elliptic PDEs
Hyperbolic PDEs
Appendix A: Some Common Commands in MATLAB
Appendix B: Computer Programs in MATLAB
Appendix C: Computer Programs in FORTRAN
References
Index
A Summary and Problems appear at the end of each chapter.
Biography
Yogesh Jaluria is a Board of Governors Professor in the Mechanical and Aerospace Engineering Department at Rutgers University. He has contributed to more than 450 technical articles and received numerous honors, including the Kern Award from AIChE, the Max Jakob Memorial Award from ASME and AIChE, and the Robert Henry Thurston Lecture Award, Freeman Scholar Award, Worcester Reed Warner Medal, and Heat Transfer Memorial Award, all from ASME.
