Applied Mathematics for Science and Engineering
(Sprache: Englisch)
Based on a decade's worth of the authors lecture notes detailing the topic of applied mathematics for scientists and engineers. The flow of the chapters is smooth and moves from one mathematical method to the next sustaining reader interest and easing the application of the techniques.
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Based on a decade's worth of the authors lecture notes detailing the topic of applied mathematics for scientists and engineers. The flow of the chapters is smooth and moves from one mathematical method to the next sustaining reader interest and easing the application of the techniques.
Klappentext zu „Applied Mathematics for Science and Engineering “
Prepare students for success in using applied mathematics for engineering practice and post-graduate studies* moves from one mathematical method to the next sustaining reader interest and easing the application of the techniques
* Uses different examples from chemical, civil, mechanical and various other engineering fields
* Based on a decade's worth of the authors lecture notes detailing the topic of applied mathematics for scientists and engineers
* Concisely writing with numerous examples provided including historical perspectives as well as a solutions manual for academic adopters
Inhaltsverzeichnis zu „Applied Mathematics for Science and Engineering “
Preface viii1 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
... mehr
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
5 Analytic Solution of Ordinary Differential Equations 65
An Introductory Example 65
First-Order Ordinary Differential Equations 66
Nonlinear First-Order Ordinary Differential Equations 67
Solutions with Elliptic Integrals and Elliptic Functions 69
Higher-Order Linear ODEs with Constant Coefficients 71
Use of the Laplace Transform for Solution of ODEs 73
Higher-Order Equations with Variable Coefficients 75
Bessel's Equation and Bessel Functions 76
Power Series Solutions of Ordinary Differential Equations 78
Regular Perturbation 80
Linearization 81
Conclusion 83
Problems 84
References 88
6 Numerical Solution of Ordinary Differential Equations 89
An Illustrative Example 89
The Euler Method 90
Modified Euler Method 91
Runge-Kutta Methods 91
Simultaneous Ordinary Differential Equations 94
Some Potential Difficulties Illustrated 94
Limitations of Fixed Step-Size Algorithms 95
Richardson Extrapolation 97
Multistep Methods 98
Split Boundary Conditions 98
Finite-Difference Methods 100
Stiff Differential Equations 100
Backward Differentiation Formula (BDF) Methods
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
5 Analytic Solution of Ordinary Differential Equations 65
An Introductory Example 65
First-Order Ordinary Differential Equations 66
Nonlinear First-Order Ordinary Differential Equations 67
Solutions with Elliptic Integrals and Elliptic Functions 69
Higher-Order Linear ODEs with Constant Coefficients 71
Use of the Laplace Transform for Solution of ODEs 73
Higher-Order Equations with Variable Coefficients 75
Bessel's Equation and Bessel Functions 76
Power Series Solutions of Ordinary Differential Equations 78
Regular Perturbation 80
Linearization 81
Conclusion 83
Problems 84
References 88
6 Numerical Solution of Ordinary Differential Equations 89
An Illustrative Example 89
The Euler Method 90
Modified Euler Method 91
Runge-Kutta Methods 91
Simultaneous Ordinary Differential Equations 94
Some Potential Difficulties Illustrated 94
Limitations of Fixed Step-Size Algorithms 95
Richardson Extrapolation 97
Multistep Methods 98
Split Boundary Conditions 98
Finite-Difference Methods 100
Stiff Differential Equations 100
Backward Differentiation Formula (BDF) Methods
... weniger
Autoren-Porträt von Larry A. Glasgow
Larry A. Glasgow is Professor of Chemical Engineering at Kansas State University. He has taught many of the core courses in chemical engineering with particular emphasis upon transport phenomena, engineering mathematics, and process analysis. Dr. Glasgow's work in the classroom and his enthusiasm for teaching have been recognized many times with teaching awards. Glasgow is also the author of Transport Phenomena: An Introduction to Advanced Topics (Wiley, 2010).
Bibliographische Angaben
- Autor: Larry A. Glasgow
- 2014, 1. Auflage, 256 Seiten, Maße: 22,1 x 28,6 cm, Gebunden, Englisch
- Verlag: Wiley & Sons
- ISBN-10: 1118749928
- ISBN-13: 9781118749920
- Erscheinungsdatum: 29.08.2014
Sprache:
Englisch
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