عنوان

Numerical mathematics :

0805325301

9780805325300

Numerical mathematics :

[Book]

theory and computer applications /

Carl-Erik Fröberg.

Menlo Park, Calif. :

Benjamin/Cummings Pub. Co.,

1985.

xi, 436 pages :

illustrations ;

25 cm

Revised edition of: Introduction to numerical analysis. 2nd ed. 1969.

Includes bibliographical references (pages 424-426) and index.

I. Mathematical introduction. 1. Numerical computation. Representation of numbers -- The origin and growth of errors -- Numerical cancellation -- Algorithms and complexity -- Use of computers. 2. Vectors and matrices. Vectors -- Matrices -- Eigenvalues and eigenvectors -- Matrix norms -- Matrix functions -- Localization of eigenvalues -- Normal forms -- Rectangular matrices. 3. Series expansions. Power series -- Generating functions -- Asymptotic series -- Fourier series -- Bernoulli numbers and Bernoulli polynomials -- Continued fractions. 4. Orthoganal functions. General concepts -- Polynomials: orthoganal; Legendre; Laguerre; Hermite; Chebyshev. 5. Linear operations. General properties -- Special operators -- Representation with differences -- Factorials and stirling numbers. 6. Difference equations. General concepts -- Linear, homogeneous difference equations -- Differences of elementary functions.

Partial difference equations. 7. Special functions. Analytic functions and complex integration -- The gamma function -- The beta function -- Some functions defined defined by definite integrals -- The Riemann zeta function -- Bessel functions -- Spherical harmonics. 8. Laplace transformation. Basic theory -- Laplace transforms of some special functions. 9. Calculus of variations. II. Equations. Gaussian elimination -- Error analysis -- Overdetermined systems of equations -- Iterative methods -- Gradient methods. 11. Nonlinear equations and systems of equations. Equations in one variable -- Horner's scheme -- Interpolation methods for real roots -- Fixed-point methods -- Laguerre's method -- Systems of nonlinear equations -- Minimization methods. 12. Algebraic eigenvalue problems. Iteravive methods -- Transformation methods. 13. Linear programming. The simplex method -- The transportation problem.

Quadratic, integer, and dynamic programming. III. Approximation. 14. Interpolation. Polynomial interpolation -- Devided differences -- Interpolation by use of differences -- Extrapolation -- Special features. 15. Function representation and curve fitting. Least-squares polynomial approximation -- Trigonometric interpolation -- The fast Fourier transform -- Approximation with: trigonometric functions; exponential functions; Chebyshev polynomials -- Spline approximation -- Rational approximations. 16. The Monte Carlo method. Random numbers -- Random walks -- Computation of definite integrals -- Simulation. IV. Integration and summation. 17. Numerical integration. General rules -- Methods based on equidistant node points -- Formulas of Gauss type -- Multiple integrals. 18. Summation. Sums of factorials and powers -- Euler-McLaurin's summation formula -- Stirling's formula -- Euler's transformation and alternating series.

Summation by use of Riemann's zeta function. V. Differential and integral equations. 19. Ordinary differential equations. Existeence of solutions -- Euler's method -- Taylor series expansion -- Runge-Kutta (RK) methods -- Stiff differential equations -- Multi-step methods -- Cowell-Numerov's method -- Systems of firts-order linear differential equations -- Boundary value problems -- Eigenvalue problems. 20. Partial differential equations. Classification -- Hyperbolic equations -- Parabolic equations -- Elliptic equations -- The finite element method (FEM) -- Eigenvalue problems. 2. Integral equations. Classification -- Fredholm's inhomogeneous equation of the second kind -- ... homogeneous ... -- Fredholm's equation of the first kind -- Volterra's equations -- Numerical treatment of integral equations -- Connections between differential and integral equations.

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Numerical mathematics.

Numerical analysis-- Data processing.

Numerical analysis.

Analyse numérique-- Informatique.

Analyse numérique.

Analyse numérique-- Logiciels.

Analyse numérique.

Analysis

Numerical analysis-- Data processing.

Numerical analysis.

Numerische Mathematik

512.97

519.6

Fröberg, Carl Erik.

Fröberg, Carl Erik.

20200822132045.0

[Book]

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