Engineering Analysis-Y.C.Pao<br><br><br>Contents<br>1 Matrix Algebra and Solution of Matrix Equations....................................... 1<br>1.1 Introduction.................................................................................................!<br>1.2 Manipulation of Matrices ...........................................................................2<br>1.3 Solution of Matrix Equation.....................................................................25<br>1.4 Program Gauss - Gaussian Elimination Method ...................................30<br>1.5 Matrix Inversion, Determinant, and Program MatxInvD.........................41<br>1.6 Problems....................................................................................................54<br>1.7 Reference...................................................................................................63<br>2 Exact, Least-Squares, and Spline Curve-Fits...............................................65<br>2.1 Introduction...............................................................................................65<br>2.2 Exact Curve Fit.........................................................................................65<br>2.3 Program LeastSql - Linear Least-Squares Curve-Fit............................71<br>2.4 Program LeastSqG - Generalized Least-Squares Curve-Fit..................70<br>2.5 Program CubeSpln - Curve Fitting with Cubic Spline .........................88<br>2.6 Problems.................................................................................................. 100<br>2.7 Reference................................................................................................. 105<br>3 Roots of Polynomial and Transcendental Equations................................. 107<br>3.1 Introduction.............................................................................................107<br>3.2 Iterative Methods and Program Roots.................................................... 108<br>3.3 Program NewRaphG - Generalized Newton-Raphson<br>Iterative Method......................................................................................118<br>3.4 Program Bairstow - Bairstow Method for Finding<br>Polynomial Roots....................................................................................127<br>3.5 Problems..................................................................................................136<br>3.6 References............................................................................................... 141<br>4 Finite Differences, Interpolation, and Numerical Differentiation............143<br>4.1 Introduction............................................................................................. 143<br>4.2 Finite Differences and Program DiffTabl - Constructing<br>Difference Table......................................................................................144<br>4.3 Program LagrangI - Applications of Lagrangian<br>Interpolation Formula.............................................................................161<br>4.4 Problems..................................................................................................168<br>4.5. Reference................................................................................................. 170<br>5 Numerical Integration and Program Volume............................................. 171<br>5.1 Introduction............................................................................................. 171<br>5.2 Program NuIntGra - Numerical Integration by Application of the<br>Trapezoidal and Simpson Rules............................................................. 174<br> <br>5.3 Program Volume - Numerical Solution of Double Integral................ 186<br>5.4 Problems..................................................................................................197<br>5.5 References...............................................................................................200<br>6 Ordinary Differential Equations - Initial and Boundary<br>Value Problems...............................................................................................201<br>6.1 Introduction.............................................................................................201<br>6.2 Program RungeKut - Application of Runge-Kutta Method<br>for Solving InitialValue Problems..........................................................202<br>6.3 Program OdeBvpRK - Application of Runge-Kutta Method<br>for Solving Boundary Value Problems...................................................223<br>6.4 Program OdeBvpFD - Application of Finite-Difference Method<br>for Solving Boundary-Value Problems...................................................234<br>6.5 Problems..................................................................................................247<br>6.6 References...............................................................................................256<br>7 Eigenvalue and Eigenvector Problems ........................................................257<br>7.1 Introduction.............................................................................................257<br>7.2 Programs EigenODE.Stb and EigenODE.Vib - for Solving<br>Stability and Vibration Problems............................................................260<br>7.3 Program CharacEq - Derivation of Characteristic Equation<br>of a Specified Square Matrix..................................................................267<br>7.4 Program EigenVec - Solving Eigenvector by Gaussian<br>Elimination Method................................................................................275<br>7.5 Program Eigenvlt - Iterative Solution of Eigenvalue<br>and Eigenvector.......................................................................................285<br>7.6 Problems..................................................................................................294<br>7.7 References...............................................................................................300<br>8 Partial Differential Equations ......................................................................301<br>8.1 Introduction.............................................................................................301<br>8.2 Program ParabPDE - Numerical Solution of Parabolic Partial<br>Differential Equations.............................................................................302<br>8.3 Program Relaxatn - Solving Elliptical Partial Differential<br>Equations by Relaxation Method............................................................311<br>8.4 Program WavePDE - Numerical Solution of Wave Problems<br>Governed by Hyperbolic Partial Differential Equations........................332<br>8.5 Problems..................................................................................................342<br>8.6 References............................................................................................... 347<br>General Index.......................................................................................................349<br>FORTRAN Commands and Programs Index..................................................353<br>QuickBASIC Commands and Programs Index ...............................................355<br>MATLAB Commands and Programs Index..................................................... 357<br>Mathematica Commands and Programs Index...............................................359<br>