Larry A. Glasgow

Math for Science and Engineeri

• Gebundenes Buch

Produktbeschreibung

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

Produktdetails

• Verlag: Wiley & Sons
• Artikelnr. des Verlages: 1W118749920
• 1. Auflage
• Seitenzahl: 258
• Erscheinungstermin: 29. August 2014
• Englisch
• Abmessung: 286mm x 221mm x 19mm
• Gewicht: 920g
• ISBN-13: 9781118749920
• ISBN-10: 1118749928
• Artikelnr.: 41244784

Autorenporträt

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).

Inhaltsangabe

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 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 101 Bulirsch-Stoer Method 102 Phase Space 103 Summary 105 Problems
106 References 109 7 Analytic Solution of Partial Differential Equations
111 Introduction 111 Classification of Partial Differential Equations and
Boundary Conditions 111 Fourier Series 112 A Preview of the Utility of
Fourier Series 114 The Product Method (Separation of Variables) 116
Parabolic Equations 116 Elliptic Equations 122 Application to Hyperbolic
Equations 127 The Schrödinger Equation 128 Applications of the Laplace
Transform 131 Approximate Solution Techniques 133 Galerkin MWR Applied to a
PDE 134 The Rayleigh-Ritz Method 135 Collocation 137 Orthogonal Collocation
for Partial Differential Equations 138 The Cauchy-Riemann Equations
Conformal Mapping and Solutions for the Laplace Equation 139 Conclusion 142
Problems 143 References 146 8 Numerical Solution of Partial Differential
Equations 147 Introduction 147 Finite-Difference Approximations for
Derivatives 148 Boundaries with Specified Flux 149 Elliptic Partial
Differential Equations 149 An Iterative Numerical Procedure: Gauss-Seidel
151 Improving the Rate of Convergence with Successive Over-Relaxation (SOR)
152 Parabolic Partial Differential Equations 154 An Elementary Explicit
Numerical Procedure 154 The Crank-Nicolson Method 155 Alternating-Direction
Implicit (ADI) Method 157 Three Spatial Dimensions 158 Hyperbolic Partial
Differential Equations 158 The Method of Characteristics 160 The Leapfrog
Method 161 Elementary Problems with Convective Transport 162 A Numerical
Procedure for Two-Dimensional Viscous Flow Problems 165 MacCormack's Method
170 Adaptive Grids 171 Conclusion 173 Problems 176 References 183 9
Integro-Differential Equations 184 Introduction 184 An Example of
Three-Mode Control 185 Population Problems with Hereditary Infl uences 186
An Elementary Solution Strategy 187 VIM: The Variational Iteration Method
188 Integro-Differential Equations and the Spread of Infectious Disease 192
Examples Drawn from Population Balances 194 Particle Size in Coagulating
Systems 198 Application of the Population Balance to a Continuous
Crystallizer 199 Conclusion 201 Problems 201 References 204 10 Time-Series
Data and the Fourier Transform 206 Introduction 206 A Nineteenth-Century
Idea 207 The Autocorrelation Coeffi cient 208 A Fourier Transform Pair 209
The Fast Fourier Transform 210 Aliasing and Leakage 213 Smoothing Data by
Filtering 216 Modulation (Beats) 218 Some Familiar Examples 219 Turbulent
Flow in a Deflected Air Jet 219 Bubbles and the Gas-Liquid Interface 220
Shock and Vibration Events in Transportation 222 Conclusion and Some Final
Thoughts 223 Problems 224 References 227 11 An Introduction to the Calculus
of Variations and the Finite-Element Method 229 Some Preliminaries 229
Notation for the Calculus of Variations 230 Brachistochrone Problem 231
Other Examples 232 Minimum Surface Area 232 Systems of Particles 232
Vibrating String 233 Laplace's Equation 234 Boundary-Value Problems 234 A
Contemporary COV Analysis of an Old Structural Problem 236 Flexing of a Rod
of Small Cross Section 236 The Optimal Column Shape 237 Systems with
Surface Tension 238 The Connection between COV and the Finite-Element
Method (FEM) 238 Conclusion 241 Problems 242 References 243 Index 245