Applied mathematical methods for chemical engineers / Norman W. Loney.

Format:

Book

Author/Creator:

Loney, Norman W.

Contributor:

Sabin W. Colton, Jr., Memorial Fund.

Language:

English

Subjects (All):

Chemical engineering--Mathematics.

Chemical engineering.

Physical Description:

447 pages : illustrations ; 25 cm

Place of Publication:

Boca Raton, Fla. ; London : CRC Press, 2001.

Contents:

Chapter 1 Differential Equations

1.2 Ordinary Differential Equations 2

Chapter 2 First Order Ordinary Differential Equations

2.1 Linear Equations 5

2.2 Additional Information on Linear Equations 14

2.3 Nonlinear Equations 18

2.3.1 Separable Equations 19

2.3.2 Exact Equations 21

2.3.3 Homogeneous Equations 23

2.4 Problem Setup 23

Chapter 3 Linear Second Order Ordinary Differential Equations

3.2 Fundamental Solutions of the Homogeneous Equation 38

3.3 Homogeneous Equations with Constant Coefficients 40

3.4 Nonhomogeneous Equations 45

3.4.1 Method of Variation of Parameters 53

3.5 Variable Coefficient Problems 57

3.5.1 Series Solutions Near a Regular Singular Point 59

3.6 Alternative Methods 65

3.6.1 Initial Value Problems 69

3.6.2 Some Useful Properties of Laplace Transforms 75

3.6.3 Inverting the Laplace Transform 78

3.6.4 Taylor Series Solution of Initial Value Problems 84

3.7 Applications of Second Order Differential Equations 87

Chapter 4 Sturm-Liouville Problems

4.2 Classification of Sturm-Liouville Problems 124

4.2.1 Properties of the Eigenvalues and Eigenfunctions of a Sturm-Liouville Problem 133

4.3 Eigenfunction Expansion 137

Chapter 5 Fourier Series and Integrals

5.2 Fourier Coefficients 146

5.3 Arbitrary Interval 151

5.4 Cosine and Sine Series 153

5.5 Convergence of Fourier Series 158

5.6 Fourier Integrals 166

Chapter 6 Partial Differential Equations

6.2 Separation of Variables 179

6.2.1 Boundary Conditions 183

6.3 The Nonhomogeneous Problem and Eigenfunction Expansion 211

6.4 Laplace Transform Methods 221

6.5 Combination of Variables 229

6.6 Fourier Integral Methods 237

6.7 Regular Perturbation Approaches 241

Chapter 7 Applications of Partial Differential Equations in Chemical Engineering

7.1 Heat Transfer 263

7.2 Mass Transfer 281

7.3 Comparison Between Heat and Mass Transfer Results 293

7.4 Simultaneous Diffusion and Convection 296

7.5 Simultaneous Diffusion and Chemical Reaction 302

7.6 Simultaneous Diffusion, Convection, and Chemical Reaction 315

7.7 Viscous Flow 330

Chapter 8 Dimensional Analysis and Scaling of Boundary Value Problems

8.2 A Classical Approach to Dimensional Analysis 355

8.3 Finding the [pi]s 357

8.4 Scaling Boundary Value Problems 364

Chapter 9 Selected Numerical Methods and Available Software Packages

9.1 Introduction and Philosophy 379

9.2 Solution of Nonlinear Algebraic Equations 379

9.2.1 The Newton-Raphson Method 385

9.2.2 The Modified Newton-Raphson Method 386

9.3 Solution of Simultaneous Linear Algebraic Equations 388

9.3.1 Error Estimate 399

9.4 Solution of Ordinary Differential Equations 405

9.4.1 Initial Value Problems 405

9.4.2 Boundary Value Problems 413

9.4.3 Systems of Ordinary Differential Equations 418

9.5 Solution of Partial Differential Equations 420

Appendix A Elementary Properties of Determinants and Matrices 429.

Notes:

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Sabin W. Colton, Jr., Memorial Fund.

ISBN:

0849308909

OCLC:

44425481