Numerical methods for mathematics, science, and engineering

Numerical methods for mathematics, science, and engineering

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Détails bibliographiques
Auteur principal : Mathews John H. (Auteur)
Format : Livre
Langue : anglais
Titre complet : Numerical methods for mathematics, science, and engineering / John H. Mathews
Édition : 2nd edition
Publié : Englewood Cliffs : Prentice Hall , cop. 1992
Description matérielle : 1 vol. (X-646 p.)
Sujets :
Analyse numérique > Problèmes et exercices
Analyse numérique
  • 1. Preliminaries
  • 1.1 Review of calculus
  • 1.2 Binary numbers
  • 1.3 Error analysis
  • 2. The solution of nonlinear equations f(x)=0
  • 2.1 Iteration for solving x=g(x)
  • 2.2 Bracketing methods for locating a root
  • 2.3 Initial approximations and convergence criteria
  • 2.4 Newton-Raphson and Secant methods
  • 2.5 Aitken's process and Steffensen's and Muller's methods (optional)
  • 2.6 Iteration for nonlinear systems
  • 2.7 Newton's method for systems
  • 3. The oslution of linear systems AX=B
  • 3.1 Introduction to vectors and matrices
  • 3.2 Properties of vectors and matrices
  • 3.3 Upper-triangular linear systems
  • 3.4 Gaussian elimination and pivoting
  • 3.5 Matrix inversion
  • 3.6 Triangular factorization
  • 3.7 Iterative methods for linear systems
  • 4. Interpolation and polynomial approximation
  • 4.1 Taylor series and calculation of functions
  • 4.2 Introduction to interpolation
  • 4.3 Lagrange approximation
  • 4.4 Newton polynomials
  • 4.5 Chebyshev polynomials (optional)
  • 4.6 Padé approximations
  • 5. Curve fitting
  • 5.1 Least-squares line
  • 5.2 Curve fitting
  • 5.3 Interpolation by spline functions
  • 5.4 Fourier series and trigonometric polynomials
  • 6. Numerical differentiation
  • 6.1 Approximating the derivative
  • 6.2 Numerical differentiation formulas
  • 7. Numerical integration
  • 7.1 Introduction to quadrature
  • 7.2 Composite trapzoidal and Simpson's rule
  • 7.3 Recursive rules and Romberg integration
  • 7.4 Adaptive quadrature
  • 7.5 Gauss-Legendre integration (optional)
  • 8. Numerical optimization
  • 8.1 Minimization of a function
  • 9. Solution of differential equations
  • 9.1 Introduction to differential equations
  • 9.2 Euler's method
  • 9.3 Heun's method
  • 9.4 Taylor series method
  • 9.5 Runge-Kutta methods
  • 9.6 Predictor-corrector methods
  • 9.7 Systems of differential equations
  • 9.8 Boundary value problems
  • 9.9 Finite-difference method
  • 10. SOlution of partial differential equations
  • 10.1 Hyperbolic equations
  • 10.2 Parabolic equations
  • 10.3 Elliptic equations
  • 11. Eigenvalues and Eigenvectors
  • 11.1 Homogeneous systems : the Eignevalue problem
  • 11.2 The power method
  • 11.3 Jacobi's method
  • 11.4 Eigenvalues of symmetric matrices