[영문] CONTENTS
Chapter 1: Introduction = 1
FORTRAN ―the Computer Language of Science = 2
Getting Started = 3
Running the Program = 5
A Numerical Example = 8
Code Fragments = 11
A Brief Guide to Good Programming = 13
Debugging and Testing = 19
A Cautionary Note = 20
Elementary Computer Graphics = 21
And in Living Color! = 26
Classic Curves = 27
Monster Curves = 29
The Mandelbrot Set = 33
References = 39
Chapter 2: Functions and Roots = 41
Finding the Roots of a Function = 41
Mr. Taylor's Series = 51
The Newton-Raphson Method = 54
Fools Rush In... = 58
Rates of Convergence = 60
Exhaustive Searching = 66
Look, Ma, No Derivatives! = 67
Accelerating the Rate of Convergence = 71
A Little Quantum Mechanics Problem = 74
Computing Strategy = 79
References = 85
Chapter 3: Interpolation and Approximation = 86
Lagrange Interpolation = 86
The Airy Pattern = 89
Hermite Interpolation = 93
Cubic Splines = 95
Tridiagonal Linear Systems = 99
Cubic Spline Interpolation = 103
Approximation of Derivatives = 108
Richardson Extrapolation = 113
Curve Fitting by Least Squares = 117
Gaussian Elimination = 119
General Least Squares Fitting = 131
Least Squares and Orthogonal Polynomials = 134
Nonlinear Least Squares = 138
References = 148
Chapter 4: Numerical Integration = 149
Anaxagoras of Clazomenae = 149
Primitive Integration Formulas = 150
Composite Formulas = 152
Errors... and Corrections = 153
Romberg Integration = 155
Diffraction at a Knife's Edge = 157
A Change of Variables = 157
The "Simple" Pendulum = 160
Improper Integrals = 164
The Mathematical Magic of Gauss = 169
Orthogonal Polynomials = 171
Gaussian Integration = 173
Composite Rules = 180
Gauss-Laguerre Quadrature = 180
Multidimensional Numerical Integration = 183
Other Integration Domains = 186
A Little Physics Problem = 188
More on Orthogonal Polynomials = 189
Monte Carlo Integration = 191
Monte Carlo Simulations = 200
References = 206
Chapter 5: Ordinary Differential Equations = 207
Euler Methods = 208
Constants of the Motion = 212
Runge-Kutta Methods = 215
Adaptive Step Sizes = 218
Runge-Kutta-Fehlberg = 219
Second Order Differential Equations = 226
The Van der Pol Oscillator = 230
Phase Space = 231
The Finite Amplitude Pendulum = 233
The Animated Pendulum = 234
Another Little Quantum Mechanics Problem = 236
Several Dependent Variables = 241
Shoot the Moon = 242
Finite Differences = 245
SOR = 250
Discretisation Error = 250
A Vibrating String = 254
Eigenvalues via Finite Differences = 257
The Power Method = 260
Eigenvectors = 262
Finite Elements = 265
An Eigenvalue Problem = 271
References = 278
Chapter 6: Fourier Analysis = 280
The Fourier Series = 280
The Fourier Transform = 284
Properties of the Fourier Transform = 286
Convolution and Correlation = 294
Ranging = 304
The Discrete Fourier Transform = 309
The Fast Fourier Transform = 312
Life in the Fast Lane = 316
Spectrum Analysis = 319
The Duffing Oscillator = 324
Computerized Tomography = 325
References = 338
Chapter 7: Partial Differential Equations = 340
Classes of Partial Differential Equations = 340
The Vibrating String... Again! = 342
Finite Difference Equations = 344
The Steady-State Heat Equation = 354
Isotherms = 358
Irregular Physical Boundaries = 359
Neumann Boundary Conditions = 361
A Magnetic Problem = 364
Boundary Conditions = 366
The Finite Difference Equations = 367
Another Comment on Strategy = 370
Are We There Yet? = 374
Spectral Methods = 374
The Pseudo-Spectral Method = 377
A Sample Problem = 385
The Potential Step = 388
The Well = 391
The Barrier = 394
And There's More... = 394
References = 394
Appendix A: Software Installation = 396
Installing the Software = 396
The FL Command = 398
AUTOEXEC.BAT = 400
README.DOC = 401
Appendix B: Using FCCP.lib = 402
Library User's Guide = 403
Appendix C: Library Internals = 407
Library Technical Reference = 407
Index = 421
Chapter 1: Introduction = 1
FORTRAN ―the Computer Language of Science = 2
Getting Started = 3
Running the Program = 5
A Numerical Example = 8
Code Fragments = 11
A Brief Guide to Good Programming = 13
Debugging and Testing = 19
A Cautionary Note = 20
Elementary Computer Graphics = 21
And in Living Color! = 26
Classic Curves = 27
Monster Curves = 29
The Mandelbrot Set = 33
References = 39
Chapter 2: Functions and Roots = 41
Finding the Roots of a Function = 41
Mr. Taylor's Series = 51
The Newton-Raphson Method = 54
Fools Rush In... = 58
Rates of Convergence = 60
Exhaustive Searching = 66
Look, Ma, No Derivatives! = 67
Accelerating the Rate of Convergence = 71
A Little Quantum Mechanics Problem = 74
Computing Strategy = 79
References = 85
Chapter 3: Interpolation and Approximation = 86
Lagrange Interpolation = 86
The Airy Pattern = 89
Hermite Interpolation = 93
Cubic Splines = 95
Tridiagonal Linear Systems = 99
Cubic Spline Interpolation = 103
Approximation of Derivatives = 108
Richardson Extrapolation = 113
Curve Fitting by Least Squares = 117
Gaussian Elimination = 119
General Least Squares Fitting = 131
Least Squares and Orthogonal Polynomials = 134
Nonlinear Least Squares = 138
References = 148
Chapter 4: Numerical Integration = 149
Anaxagoras of Clazomenae = 149
Primitive Integration Formulas = 150
Composite Formulas = 152
Errors... and Corrections = 153
Romberg Integration = 155
Diffraction at a Knife's Edge = 157
A Change of Variables = 157
The "Simple" Pendulum = 160
Improper Integrals = 164
The Mathematical Magic of Gauss = 169
Orthogonal Polynomials = 171
Gaussian Integration = 173
Composite Rules = 180
Gauss-Laguerre Quadrature = 180
Multidimensional Numerical Integration = 183
Other Integration Domains = 186
A Little Physics Problem = 188
More on Orthogonal Polynomials = 189
Monte Carlo Integration = 191
Monte Carlo Simulations = 200
References = 206
Chapter 5: Ordinary Differential Equations = 207
Euler Methods = 208
Constants of the Motion = 212
Runge-Kutta Methods = 215
Adaptive Step Sizes = 218
Runge-Kutta-Fehlberg = 219
Second Order Differential Equations = 226
The Van der Pol Oscillator = 230
Phase Space = 231
The Finite Amplitude Pendulum = 233
The Animated Pendulum = 234
Another Little Quantum Mechanics Problem = 236
Several Dependent Variables = 241
Shoot the Moon = 242
Finite Differences = 245
SOR = 250
Discretisation Error = 250
A Vibrating String = 254
Eigenvalues via Finite Differences = 257
The Power Method = 260
Eigenvectors = 262
Finite Elements = 265
An Eigenvalue Problem = 271
References = 278
Chapter 6: Fourier Analysis = 280
The Fourier Series = 280
The Fourier Transform = 284
Properties of the Fourier Transform = 286
Convolution and Correlation = 294
Ranging = 304
The Discrete Fourier Transform = 309
The Fast Fourier Transform = 312
Life in the Fast Lane = 316
Spectrum Analysis = 319
The Duffing Oscillator = 324
Computerized Tomography = 325
References = 338
Chapter 7: Partial Differential Equations = 340
Classes of Partial Differential Equations = 340
The Vibrating String... Again! = 342
Finite Difference Equations = 344
The Steady-State Heat Equation = 354
Isotherms = 358
Irregular Physical Boundaries = 359
Neumann Boundary Conditions = 361
A Magnetic Problem = 364
Boundary Conditions = 366
The Finite Difference Equations = 367
Another Comment on Strategy = 370
Are We There Yet? = 374
Spectral Methods = 374
The Pseudo-Spectral Method = 377
A Sample Problem = 385
The Potential Step = 388
The Well = 391
The Barrier = 394
And There's More... = 394
References = 394
Appendix A: Software Installation = 396
Installing the Software = 396
The FL Command = 398
AUTOEXEC.BAT = 400
README.DOC = 401
Appendix B: Using FCCP.lib = 402
Library User's Guide = 403
Appendix C: Library Internals = 407
Library Technical Reference = 407
Index = 421