| Autore |
Glasgow Larry A. <1950->
|
| Pubbl/distr/stampa |
Hoboken, New Jersey : , : Wiley, , 2014
|
| Descrizione fisica |
1 online resource (259 p.)
|
| Disciplina |
510
|
| Soggetto topico |
Engineering mathematics
Technology - Mathematical models
|
| Soggetto genere / forma |
Electronic books.
|
| ISBN |
1-118-75054-3
1-118-74976-6
|
| Formato |
Materiale a stampa  |
| Livello bibliografico |
Monografia |
| Lingua di pubblicazione |
eng
|
| Nota di contenuto |
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' TheoremConclusion; 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 FunctionsHigher-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 IllustratedLimitations 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; 7: Analytic Solution of Partial Differential Equations; Introduction; Classification of Partial Differential Equations and Boundary Conditions; Fourier Series; A Preview of the Utility of Fourier Series; The Product Method (Separation of Variables); Parabolic Equations
Elliptic Equations
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| Record Nr. | UNISA-996204357003316 |
Info
Applied mathematics for science and engineering / / Larry A. Glasgow
