An Introduction to Numerical Methods and Analysis

Detalles Bibliográficos
Autor principal: Epperson, James F.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2013.
Colección:New York Academy of Sciences Ser.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Intro
  • Half Title page
  • Title page
  • Copyright page
  • Dedication
  • Preface
  • Chapter 1: Introductory Concepts and Calculus Review
  • 1.1 Basic Tools of Calculus
  • 1.2 Error, Approximate Equality, and Asymptotic Order Notation
  • 1.3 A Primer on Computer Arithmetic
  • 1.4 A Word on Computer Languages and Software
  • 1.5 Simple Approximations
  • 1.6 Application: Approximating the Natural Logarithm
  • 1.7 A Brief History of Computing
  • 1.8 Literature Review
  • References
  • Chapter 2: A Survey of Simple Methods and Tools
  • 2.1 Horner's Rule and Nested Multiplication
  • 2.2 Difference Approximations to the Derivative
  • 2.3 Application: Euler's Method for Initial Value Problems
  • 2.4 Linear Interpolation
  • 2.5 Application-The Trapezoid Rule
  • 2.6 Solution of Tridiagonal Linear Systems
  • 2.7 Application: Simple Two-Point Boundary Value Problems
  • Chapter 3: Root-Finding
  • 3.1 The Bisection Method
  • 3.2 Newton's Method: Derivation and Examples
  • 3.3 How to Stop Newton's Method
  • 3.4 Application: Division Using Newton's Method
  • 3.5 The Newton Error Formula
  • 3.6 Newton's Method: Theory and Convergence
  • 3.7 Application: Computation of the Square Root
  • 3.8 The Secant Method: Derivation and Examples
  • 3.9 Fixed-Point Iteration
  • 3.10 Roots of Polynomials, Part 1
  • 3.11 Special Topics in Root-Finding Methods
  • 3.12 Very High-Order Methods and the Efficiency Index
  • 3.13 Literature and Software Discussion
  • References
  • Chapter 4: Interpolation and Approximation
  • 4.1 Lagrange Interpolation
  • 4.2 Newton Interpolation and Divided Differences
  • 4.3 Interpolation Error
  • 4.4 Application: Muller's Method and Inverse Quadratic Interpolation
  • 4.5 Application: More Approximations to the Derivative
  • 4.6 Hermite Interpolation
  • 4.7 Piecewise Polynomial Interpolation
  • 4.8 An Introduction to Splines
  • 4.9 Application: Solution of Boundary Value Problems
  • 4.10 Tension Splines
  • 4.11 Least Squares Concepts in Approximation
  • 4.12 Advanced Topics in Interpolation Error
  • 4.13 Literature and Software Discussion
  • References
  • Chapter 5: Numerical Integration
  • 5.1 A Review of the Definite Integral
  • 5.2 Improving the Trapezoid Rule
  • 5.3 Simpson's Rule and Degree of Precision
  • 5.4 The Midpoint Rule
  • 5.5 Application: Stirling's Formula
  • 5.6 Gaussian Quadrature
  • 5.7 Extrapolation Methods
  • 5.8 Special Topics in Numerical Integration
  • 5.9 Literature and Software Discussion
  • References
  • Chapter 6: Numerical Methods for Ordinary Differential Equations
  • 6.1 The Initial Value Problem: Background
  • 6.2 Euler's Method
  • 6.3 Analysis of Euler's Method
  • 6.4 Variants of Euler's Method
  • 6.5 Single-Step Methods: Runge-Kutta
  • 6.6 Multistep Methods
  • 6.7 Stability Issues
  • 6.8 Application to Systems of Equations
  • 6.9 Adaptive Solvers
  • 6.10 Boundary Value Problems
  • 6.11 Literature and Software Discussion
  • References

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