Problem Solving in Engineering - Glasgow, Larry A.

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Résumé :

Preface xiii?

About the Companion Website xv?

1 Problem Formulation, Models, and Solution Strategies 1?

1.1 Introduction 1?

1.1.1 Rationale for Modeling and Some Unwanted Complications 5?

1.2 Algebraic Equations: Force Resolution and Vapor-Liquid Equilibria (VLE) 6?

1.3 Macroscopic Balances-Lumped-Parameter Models 8?

1.3.1 Recognizing When a Model Suggests Potential Hazards 10?

1.4 Force Balances-Newton's Second Law of Motion 10?

1.5 Distributed Parameter Models-Microscopic Balances 11?

1.5.1 Fluid Flow and Heat Transfer Combined 14?

1.6 Using the Equations of Change Directly 14?

1.7 Discretizing a Problem that is Continuous in Time or Space 16?

1.8 A Contrast: Deterministic Models and Stochastic Processes 19?

1.9 Problems with Integer-Valued Variables 20?

1.10 Empiricisms and Data Interpretation 25?

1.10.1 Energy Output of Candle Flame 25?

1.10.2 Correlations Developed from Experimental Data 26?

1.10.3 Frictional Resistance for Transitional Flow 27?

1.10.4 Speech Recognition 28?

1.11 Conclusion 29?

Problems 30?

References 35?

2 Algebraic Equations 37?

2.1 Introduction 37?

2.1.1 An Interpolation Example 38?

2.2 Elementary Methods 39?

2.2.1 Newton-Raphson (Newton's Method of Tangents) 39?

2.2.2 Regula Falsi (False Position Method) 42?

2.2.3 Dichotomous Search 44?

2.2.4 Golden Section Search 46?

2.3 Simultaneous Linear Algebraic Equations 47?

2.3.1 Crout's (or Cholesky's) Method 48?

2.3.2 Matrix Inversion 50?

2.3.3 Iterative Methods of Solution 52?

2.4 Simultaneous Nonlinear Algebraic Equations 54?

2.4.1 Successive Substitution 54?

2.4.2 Newton's Method 55?

2.4.3 An Example Problem with Simultaneous Nonlinear Algebraic Equations 56?

2.4.4 Pattern Search for Solution of Nonlinear Algebraic Equations, Sequential Simplex, and the Rosenbrock Method 57?

2.4.5 An Example of a Pattern Search Application: Ship Hull Design 59?

2.5 Algebraic Equations with Constraints 61?

2.5.1 Further Practice with the Lagrange Multiplier 62?

2.6 Conclusion 62?

Problems 63?

References 76?

3 Vectors and Tensors 77?

3.1 Introduction 77?

3.2 Elementary Operations 78?

3.2.1 An Illustration 80?

3.3 Review of Some Basic Mechanics 81?

3.3.1 Force Equilibrium 81?

3.3.2 Frictional Force 82?

3.3.3 Equating Moments 83?

3.3.4 Calculation of Centroids 84?

3.3.5 Projectile Motion 85?

3.4 Other Important Vector Operations 86?

3.4.1 Dot and Cross-Products 86?

3.4.2 Coriolis Effect 87?

3.4.3 Differentiation of Vectors 87?

3.4.4 Gradient, Divergence, and Curl 88?

3.5 Green's Theorem 91?

3.5.1 The Divergence Theorem of Gauss 94?

3.6 Stokes' Theorem 96?

3.7 Conclusion 97?

Problems 98?

References 103?

4 Numerical Quadrature 105?

4.1 Introduction 105?

4.2 Trapezoid Rule 105?

4.3 Simpson's Rule 107?

4.4 Newton-Cotes Formulae 109?

4.5 Roundoff and Truncation Errors 109?

4.6 Romberg Integration 111?

4.7 Adaptive Integration Schemes 112?

4.7.1 Simpson's Rule 113?

4.8 Gaussian Quadrature and the Gauss-Kronrod Procedure 114?

4.9 Integrating Discrete Data 118?

4.10 Multiple Integrals (Cubature) 121?

4.11 Monte Carlo Methods 123?

4.12 Conclusion 126?

Problems 128?

References 136?