Đang chuẩn bị liên kết để tải về tài liệu:
A textbook of Computer Based Numerical and Statiscal Techniques part 2

A textbook of Computer Based Numerical and Statiscal Techniques part 2. By joining statistical analysis with computer-based numerical methods, this book bridges the gap between theory and practice with software-based examples, flow charts, and applications. Designed for engineering students as well as practicing engineers and scientists, the book has numerous examples with in-text solutions. | CONTENTS 5.4.2. Relation Between Divided Differences and Ordinary Differences 247 5.5 Newton s Divided Difference Formula 247 Problem Set 5.3 258 5.6. Hermite s Interpolation Formula 259 Problem Set 5.4 261 5.7. Some Related Terms 269 5.7.1 Some Remarkable Points about Chosen Different Interpolation Formulae 269 5.7.2 Approximation of Function 270 5.7.3 Spline Interpolation 285 5.7.4 Cubic Spline Interpolation for Equally and Unequally Spaced Values 286 Problem Set 5.5 291 6. Numerical Differentiation and Integration 294-331 6.1 Introduction 294 6.2 Numerical Differentiation 294 6.2.1 Derivation Using Newton s Forward Interpolation Formula 295 6.2.2 Derivatives Using Newton s Backward Difference Formula 296 6.2.3 Derivatives Using Stirling s Formula 298 6.2.4 Derivative Using Newton s Divided Difference Formula 298 Problem Set 6.1 313 6.3 Numerical Integration 315 6.4 General Quadrature Formula 315 6.5 Trapezoidal Rule 316 6.6 Simpson s One-Third Rule 316 6.7 Simpson s Three-Eight Rule 317 6.8 Boole s Rule 317 6.9 Weddle s Rule 318 6.10 Euler-Maclaurin s Formula 327 Problem Set 6.2 330 7. Numerical Solution of Ordinary Differential Equation 332-372 7.1 Introduction 332 7.2 Taylor s Method 332 7.3 Picard s Method of Successive Approximations 336 7.4 Euler s Method 342 7.5 Euler s Modified Method 343 Problem Set 7.1 351 7.6 Runge-Kutta Method 352 7.7 Milne s Predictor-Corrector Method 361 Predictor-Corrector Methods 361 Milne s Method 361 CONTENTS 7.8 Automatic Error Monitoring 369 Convergence of a Method 370 7.9 Stability in the Solution of Ordinary Differential Equation 370 Problem Set 7.2 372 8. Solution of Simultaneous Linear Equation 8.1 Introduction 373 8.2 Gauss-Elimination Method 373 8.3 Gauss-Elimination with Pivoting Method 375 8.4 Ill-Conditioned System of Equations 376 8.5 Iterative Refinement of the Solution by Gauss Elimination Method 376 8.6 Iterative Method for Solution of Simultaneous Linear Equation 377 8.6.1 Jacobi s Method or Gauss-Jacobi Method .