ii
5 Linear System Equations 43
5.1 Linear System Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.2 Sparse Linear System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.3 Tridiagonal System Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.4 Band Diagonal System Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
6 Ordinary Differential Equations 61
6.1 First Order ODE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
6.2 Second Order ODE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.2.1 Analysis of second order ODE . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.2.2 Using a second order ODE function . . . . . . . . . . . . . . . . . . . . . 70
7 Integration 73
7.1 Single Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
7.2 Double-Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
8 Curve Fitting and Interpolations 81
8.1 Polynomial Curve Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
8.2 One-Dimensional Polynomial Interpolation . . . . . . . . . . . . . . . . . . . . . 87
8.3 Two-Dimensional Polynomial Interpolation for Grid Points . . . . . . . . . . . . 88
9 Roots of Equations 97
9.1 Roots of Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
98
9.2 The Root of a Nonlinear-Equation . . . . . . . . . . . . . . . . . . . . . . . . . . 101
10 Fast Fourier Transform 103
10.1 One-Dimensional Fast Fourier Transform . . . . . . . . . . . . . . . . . . . . . . 105
10.2 Two-Dimensional Fast Fourier Transform . . . . . . . . . . . . . . . . . . . . . . 109
11 Eigenvalues and Eigenvectors 113
11.1 Eigenvalues and Eigenvectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Part II:
Calling MATLAB Workspace in C
#
Functions
Using MATLAB functions in C
#
Windows Form Applications 119
12
Calling MATLAB Workspace in C
#
Functions 121
12.1 Calling MATLAB Workspace with Input/Output as a Scalar . . . . . . . . . . . 121
