Numerical methods for mathematics john h mathews pdf merge
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Computer calculations are presented in the form of ta- tables and graphs whenever possible so that the resulting numerical approximations arc easier to visualize and interpret. Thus, there is a wide vari- variety of examples and problems that help to sharpen one's skill in both the theory and practice of numerical analysis. Students of various backgrounds should find numerical methods quite interesting and useful, and this is kept in mind throughout the book. In short, the book contains enough material so instructors will be able to select topics appropriate to their needs. The text has enough material fitted modularly for either a single-tern} course or a year sequence. It is assumed that the reader is familiar with calculus and has taken a struc- structured programming course. Preface This book provides a fundamental introduction to numerical analysis suitable for un dctgraduate students in mathematics, computer science, physical sciences, and engi- engineering. The Eigenvalue Problem 556 Power Method 568 Jacobi's Method 58/ Eigenvalues of Sy mmetric Matrices 594 Appendix: An Introduction to MATLAB Some Suggested References for Reports Bibliography and References 619 Answers to Selected Exercises 631 Index 655 608 616
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Polynomials 220 4.5 Chebyshev Polynomials (Optional) 230 4.6 Pade Approximations 245 Curve Fitting 252 5.1 Least-squares Line 253 5.2 Curve Fitting 26J 5.3 I interpolation by Spline Functions 279 5 4 Fourier Series and Trigonometric Polynomial 297 Numerical Differentiation 310 6.1 Approximating The Derivative 311 6.2 Numerical Differentiation Formulas 329 Numerical Integration 342 7.1 Introduction to Quadrature 343 7.2 Composite Trapezoidal and Simpson's Rule 354 7.3 Recursive Rules and Romberg Integration 368 7.4 Adaptive Quadrature 382 7.5 Gauss-Legendre Integration (Optional) 389 8 S.I 9.1 9.2 9.3 9.4 9.5 96 9.7 9.8 9.9 10 10.1 10.2 10 3 11 ILL 11.2 11.3 11,4 Numerical Optimization Minimization of г Function 400 399 Solution of Differential Equations 426 Introduction to Differential Equations 427 Euler's Method 433 Heun's Method 443 Tay lor Series Method 4 51 Runge-Kutta Methods 458 Predictor-Corrector Methods 474 Systems of Differentia' Equations 487 Boundary Value Problems 497 Finite-difference Method 505 Solution of Partial Differential Equations 514 Hyperboiic Equations 516' Parabolic Equations 526 Elliptic Hquations 538 Eigenvalues and Eigenvectors 555 Homogeneous Systems". ] Review of Calculus 1.2 Binary Numbers 13 '.3 Error Analysis 24 2.1 2.2 2.3 2.4 2.5 The Solution of Nonlinear Equations fix) = 0 40 Iteration for Solving jc = g(x) 41 Bracketing Methods for Locating a Root 5] Initial Approx imation and Convergence Criteria 62 Newton-Raphson and Secant Methods 70 Aitken's Process and Steffcnsen s and Muller's Methods (Optional) 90 The Solution of Linear Systems AX = В 101 3.1 Introduction :o Vectors and Matrices 101Ĭontents 3.2 3.3 14 3.5 3.6 3.7 Contents Properties of Vectors and Matrices 109 Upper-triangular Linear Systems 120 Gaussian elimination and Pivoting 125 Triangular Factorization 141 Iterative Methods for Linear Systems /56 Iteration for Nonlinear Systems: Seidel and Newton's Methods (Optional) 167 Interpolation and Polynomial Approximation 186 4.1 Taylor Series and Calculation of Functions 187 4.2 Introduction to Interpolation }99 4.3 Lagrange Approximation 206 4.4 Newior. Fink Northwest Missouri State Unwersit i-tegskoten i Vestfoki Sibtioteket - Borre Prentice Hall, Upper Saddle River, NJ 07458 Contents Preface vu Preliminaries J.
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Mathews California State University, Fullerton Kurds D. Numerical Methods Using MATLAB Third Edition ti CD О CD I Ш CD CD CD John H.