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Engineering Analysis Interactive Methods and Programs with MATLAB - Y. C. Pao
© 2001 by CRC Press LLC



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Preface and Acknowledgments
Writing textbooks on topics in the field of
Computer Aided Engineering
(CAE)
indeed has been a very satisfying experience. First, I had the pleasure of being a
coauthor with Prof. Thomas C. Smith of the book
Introduction to Digital Computer
Plotting
by Gordon & Breach in 1973. The book
Elements of Computer-Aided
Design and Manufacturing, CAD/CAM
, was published in 1982 by John Wiley &
Sons. The book
A First Course in Finite Element Analysis
published by Allyn &
Bacon followed in 1986, and
Engineering Drafting and Solid Modeling with Silver-
Screen,
published by CRC Press, appeared in 1993.
Having taught the subjects of computer methods for engineering analysis since
1966, I finally have the courage to organize this textbook out of a large volume of
classroom notes collected over the past 31 years.
The rapid growth of computer technology is difficult for any one to keep pace,
and to make revision of textbooks in the CAE field. However, the computational
methods developed by the pioneers, such as Euler, Gauss, Lagrange, Newton, and
Runge, continue to serve us incredibly effective. These computational algorithms
remain classic, only are now executed with modern computer technology..........

Contents
1 Matrix Algebra and Solution of Matrix Equations
1.1 Introduction
1.2 Manipulation of Matrices
1.3 Solution of Matrix Equation
1.4 Program Gauss — Gaussian Elimination Method
1.5 Matrix Inversion, Determinant, and Program MatxInvD
1.6 Problems
1.7 Reference
2 Exact, Least-Squares, and Spline Curve-Fits
2.1 Introduction
2.2 Exact Curve Fit
2.3 Program LeastSq1 — Linear Least-Squares Curve-Fit
2.4 Program LeastSqG — Generalized Least-Squares Curve-Fit
2.5 Program CubeSpln — Curve Fitting with Cubic Spline
2.6 Problems
2.7 Reference
3 Roots of Polynomial and Transcendental Equations
3.1 Introduction
3.2 Iterative Methods and Program Roots
3.3 Program NewRaphG — Generalized Newton-Raphson
Iterative Method
3.4 Program Bairstow — Bairstow Method for Finding
Polynomial Roots
3.5 Problems
3.6 References
4 Finite Differences, Interpolation, and Numerical Differentiation
4.1 Introduction
4.2 Finite Differences and Program DiffTabl — Constructing
Difference Table
4.3 Program LagrangI — Applications of Lagrangian
Interpolation Formula
4.4 Problems
4.5. Reference
5 Numerical Integration and Program Volume
5.1 Introduction
5.2 Program NuIntGra — Numerical Integration by Application of the
Trapezoidal and Simpson Rules
5.3 Program Volume — Numerical Solution of Double Integral
5.4 Problems
5.5 References
6 Ordinary Differential Equations — Initial and Boundary
Value Problems
6.1 Introduction
6.2 Program RungeKut — Application of Runge-Kutta Method
for Solving InitialValue Problems
6.3 Program OdeBvpRK — Application of Runge-Kutta Method
for Solving Boundary Value Problems
6.4 Program OdeBvpFD — Application of Finite-Difference Method
for Solving Boundary-Value Problems
6.5 Problems
6.6 References
7 Eigenvalue and Eigenvector Problems
7.1 Introduction
7.2 Programs EigenODE.Stb and EigenODE.Vib — for Solving
Stability and Vibration Problems
7.3 Program CharacEq — Derivation of Characteristic Equation
of a Specified Square Matrix
7.4 Program EigenVec — Solving Eigenvector by Gaussian
Elimination Method
7.5 Program EigenvIt — Iterative Solution of Eigenvalue
and Eigenvector
7.6 Problems
7.7 References
8 Partial Differential Equations
8.1 Introduction
8.2 Program ParabPDE — Numerical Solution of Parabolic Partial
Differential Equations
8.3 Program Relaxatn — Solving Elliptical Partial Differential
Equations by Relaxation Method
8.4 Program WavePDE — Numerical Solution of Wave Problems
Governed by Hyperbolic Partial Differential Equations
8.5 Problems
8.6 References

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