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[资源] ★★★★★★2014书籍超级帖七七五《应用数学科学与工程》

书名 APPLIED MATHEMATICS FOR
SCIENCE AND ENGINEERING
作者LARRY A. GLASGOW
Department of Chemical Engineering
页数255
出版社wiley
ISBN 978-1-118-74992-0 (hardback)
Preface viii
1 Problem Formulation and Model
Development 1
Introduction, 1
Algebraic Equations from Vapor–Liquid Equilibria
(VLE), 3
Macroscopic Balances: Lumped-Parameter Models, 4
Force Balances: Newton’s Second Law of Motion, 6
Distributed Parameter Models: Microscopic
Balances, 6
Using the Equations of Change Directly, 8
A Contrast: Deterministic Models and Stochastic
Processes, 10
Empiricisms and Data Interpretation, 10
Conclusion, 12
Problems, 13
References, 14
2 Algebraic Equations 15
Introduction, 15
Elementary Methods, 16
Newton–Raphson (Newton’s Method of
Tangents), 16
Regula Falsi (False Position Method), 18
Dichotomous Search, 19
Golden Section Search, 20
Simultaneous Linear Algebraic Equations, 20
Crout’s (or Cholesky’s) Method, 21
Matrix Inversion, 23
Iterative Methods of Solution, 23
Simultaneous Nonlinear Algebraic Equations, 24
Pattern Search for Solution of Nonlinear
Algebraic Equations, 26
Sequential Simplex and the Rosenbrock
Method, 26
An Example of a Pattern Search Application, 28
Algebraic Equations with Constraints, 28
Conclusion, 29
Problems, 30
References, 32
3 Vectors and Tensors 34
Introduction, 34
Manipulation of Vectors, 35
Force Equilibrium, 37
Equating Moments, 37
Projectile Motion, 38
Dot and Cross Products, 39
Differentiation of Vectors, 40
Gradient, Divergence, and Curl, 40
Green’s Theorem, 42
Stokes’ Theorem, 43
Conclusion, 44
Problems, 44
References, 46
4 Numerical Quadrature 47
Introduction, 47
Trapezoid Rule, 47
Simpson’s Rule, 48
Newton–Cotes Formulae, 49
Roundoff and Truncation Errors, 50
Romberg Integration, 51
Adaptive Integration Schemes, 52
Simpson’s Rule, 52
Gaussian Quadrature and the Gauss–Kronrod
Procedure, 53
Integrating Discrete Data, 55
Multiple Integrals (Cubature), 57
Monte Carlo Methods, 59
Conclusion, 60
Problems, 62
References, 64
v

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2014-09-20 08:08:04, 13.83 M