Applied Mathematics for Science and Engineering

Detalles Bibliográficos
Autor principal: Glasgow, Larry A.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2014.
Colección:New York Academy of Sciences Ser.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Title page
  • Copyright page
  • Contents
  • Preface
  • 1: Problem Formulation and Model Development
  • Introduction
  • Algebraic Equations from Vapor-Liquid Equilibria (VLE)
  • Macroscopic Balances: Lumped-Parameter Models
  • Force Balances: Newton's Second Law of Motion
  • Distributed Parameter Models: Microscopic Balances
  • Using the Equations of Change Directly
  • A Contrast: Deterministic Models and Stochastic Processes
  • Empiricisms and Data Interpretation
  • Conclusion
  • Problems
  • References
  • 2: Algebraic Equations
  • Introduction
  • Elementary Methods
  • Newton-Raphson (Newton's Method of Tangents)
  • Regula Falsi (False Position Method)
  • Dichotomous Search
  • Golden Section Search
  • Simultaneous Linear Algebraic Equations
  • Crout's (or Cholesky's) Method
  • Matrix Inversion
  • Iterative Methods of Solution
  • Simultaneous Nonlinear Algebraic Equations
  • Pattern Search for Solution of Nonlinear Algebraic Equations
  • Algebraic Equations with Constraints
  • Conclusion
  • Problems
  • References
  • 3: Vectors and Tensors
  • Introduction
  • Manipulation of Vectors
  • Force Equilibrium
  • Equating Moments
  • Projectile Motion
  • Dot and Cross Products
  • Differentiation of Vectors
  • Gradient, Divergence, and Curl
  • Green's Theorem
  • Stokes' Theorem
  • Conclusion
  • Problems
  • References
  • 4: Numerical Quadrature
  • Introduction
  • Trapezoid Rule
  • Simpson's Rule
  • Newton-Cotes Formulae
  • Roundoff and Truncation Errors
  • Romberg Integration
  • Adaptive Integration Schemes
  • Simpson's Rule
  • Gaussian Quadrature and the Gauss-Kronrod Procedure
  • Integrating Discrete Data
  • Multiple Integrals (Cubature)
  • Monte Carlo Methods
  • Conclusion
  • Problems
  • References
  • 5: Analytic Solution of Ordinary Differential Equations
  • An Introductory Example
  • First-Order Ordinary Differential Equations
  • Nonlinear First-Order Ordinary Differential Equations
  • Solutions with Elliptic Integrals and Elliptic Functions
  • Higher-Order Linear ODEs with Constant Coefficients
  • Use of the Laplace Transform for Solution of ODEs
  • Higher-Order Equations with Variable Coefficients
  • Bessel's Equation and Bessel Functions
  • Power Series Solutions of Ordinary Differential Equations
  • Regular Perturbation
  • Linearization
  • Conclusion
  • Problems
  • References
  • 6: Numerical Solution of Ordinary Differential Equations
  • An Illustrative Example
  • The Euler Method
  • Modified Euler Method
  • Runge-Kutta Methods
  • Simultaneous Ordinary Differential Equations
  • Some Potential Difficulties Illustrated
  • Limitations of Fixed Step-Size Algorithms
  • Richardson Extrapolation
  • Multistep Methods
  • Split Boundary Conditions
  • Finite-Difference Methods
  • Stiff Differential Equations
  • Backward Differentiation Formula (BDF) Methods
  • Bulirsch-Stoer Method
  • Phase Space
  • Summary
  • Problems
  • References

Ejemplares similares