Enhanced descriptions from Syndetics:

Although most realistic process engineering models require numerical solution, it is important for chemical engineering students to have an understanding of the gross tendencies of the particular model they are using. This understanding most naturally arises from deriving analytical solutions of a modified version of the problem being considered. Analytical models also allow for easier process optimizations.

Emphasizing these analytical methods, Applied Mathematical Methods for Chemical Engineers introduces several techniques essential to solving real problems. The author's presentation shows students how to translate a problem from prose to mathematical symbolism and allows them to inductively build on previous experience.

Designed for senior undergraduates and first-year graduates, the text provides detailed examples that allow students to experience how to actually use the methods presented. It contains an entire chapter of fully worked examples involving traditional mass, heat, and momentum applications along with cutting edge technologies, such as membrane separation and chemical vapor deposition. Another chapter acquaints readers with selected numerical methods and available software packages.

Favoring clear, practical exposition over strict mathematical rigor, Applied Mathematical Methods for Chemical Engineers removes the mathematics phobia that often exists among chemical engineering students. It allows them to learn by example the techniques they will need to solve problems in practice.

Table of contents provided by Syndetics

• Chapter 1 Differential Equations
• 1.1 Introduction (p. 1)
• 1.2 Ordinary Differential Equations (p. 2)
• References (p. 4)
• Chapter 2 First Order Ordinary Differential Equations
• 2.1 Linear Equations (p. 5)
• 2.2 Additional Information on Linear Equations (p. 14)
• 2.3 Nonlinear Equations (p. 18)
• 2.3.1 Separable Equations (p. 19)
• 2.3.2 Exact Equations (p. 21)
• 2.3.3 Homogeneous Equations (p. 23)
• 2.4 Problem Setup (p. 23)
• 2.5 Problems (p. 30)
• References (p. 33)
• Chapter 3 Linear Second Order Ordinary Differential Equations
• 3.1 Introduction (p. 35)
• 3.2 Fundamental Solutions of the Homogeneous Equation (p. 38)
• 3.3 Homogeneous Equations with Constant Coefficients (p. 40)
• 3.4 Nonhomogeneous Equations (p. 45)
• 3.4.1 Method of Variation of Parameters (p. 53)
• 3.5 Variable Coefficient Problems (p. 57)
• 3.5.1 Series Solutions Near a Regular Singular Point (p. 59)
• 3.6 Alternative Methods (p. 65)
• 3.6.1 Initial Value Problems (p. 69)
• 3.6.2 Some Useful Properties of Laplace Transforms (p. 75)
• 3.6.3 Inverting the Laplace Transform (p. 78)
• 3.6.4 Taylor Series Solution of Initial Value Problems (p. 84)
• 3.7 Applications of Second Order Differential Equations (p. 87)
• 3.8 Problems (p. 115)
• References (p. 120)
• Chapter 4 Sturm-Liouville Problems
• 4.1 Introduction (p. 123)
• 4.2 Classification of Sturm-Liouville Problems (p. 124)
• 4.2.1 Properties of the Eigenvalues and Eigenfunctions of a Sturm-Liouville Problem (p. 133)
• 4.3 Eigenfunction Expansion (p. 137)
• 4.4 Problems (p. 139)
• References (p. 141)
• Chapter 5 Fourier Series and Integrals
• 5.1 Introduction (p. 143)
• 5.2 Fourier Coefficients (p. 146)
• 5.3 Arbitrary Interval (p. 151)
• 5.4 Cosine and Sine Series (p. 153)
• 5.5 Convergence of Fourier Series (p. 158)
• 5.6 Fourier Integrals (p. 166)
• 5.7 Problems (p. 176)
• References (p. 176)
• Chapter 6 Partial Differential Equations
• 6.1 Introduction (p. 177)
• 6.2 Separation of Variables (p. 179)
• 6.2.1 Boundary Conditions (p. 183)
• 6.3 The Nonhomogeneous Problem and Eigenfunction Expansion (p. 211)
• 6.4 Laplace Transform Methods (p. 221)
• 6.5 Combination of Variables (p. 229)
• 6.6 Fourier Integral Methods (p. 237)
• 6.7 Regular Perturbation Approaches (p. 241)
• 6.8 Problems (p. 257)
• References (p. 260)
• Chapter 7 Applications of Partial Differential Equations in Chemical Engineering
• 7.0 Introduction (p. 263)
• 7.1 Heat Transfer (p. 263)
• 7.2 Mass Transfer (p. 281)
• 7.3 Comparison Between Heat and Mass Transfer Results (p. 293)
• 7.4 Simultaneous Diffusion and Convection (p. 296)
• 7.5 Simultaneous Diffusion and Chemical Reaction (p. 302)
• 7.6 Simultaneous Diffusion, Convection, and Chemical Reaction (p. 315)
• 7.7 Viscous Flow (p. 330)
• 7.8 Problems (p. 342)
• References (p. 350)
• Chapter 8 Dimensional Analysis and Scaling of Boundary Value Problems
• 8.1 Introduction (p. 353)
• 8.2 A Classical Approach to Dimensional Analysis (p. 355)
• 8.3 Finding the [pi]s (p. 357)
• 8.4 Scaling Boundary Value Problems (p. 364)
• 8.5 Problems (p. 376)
• References (p. 378)
• Chapter 9 Selected Numerical Methods and Available Software Packages
• 9.1 Introduction and Philosophy (p. 379)
• 9.2 Solution of Nonlinear Algebraic Equations (p. 379)
• 9.2.1 The Newton-Raphson Method (p. 385)
• 9.2.2 The Modified Newton-Raphson Method (p. 386)
• 9.3 Solution of Simultaneous Linear Algebraic Equations (p. 388)
• 9.3.1 Error Estimate (p. 399)
• 9.4 Solution of Ordinary Differential Equations (p. 405)
• 9.4.1 Initial Value Problems (p. 405)
• 9.4.2 Boundary Value Problems (p. 413)
• 9.4.3 Systems of Ordinary Differential Equations (p. 418)
• 9.5 Solution of Partial Differential Equations (p. 420)
• 9.6 Chapter Summary (p. 423)
• 9.7 Problems (p. 424)
• References (p. 426)
• Appendix A Elementary Properties of Determinants and Matrices (p. 429)
• Index (p. 445)

Reviews provided by Syndetics

CHOICE Review

Loney (New Jersey Institute of Technology) directs his book specifically toward upper-division undergraduate and beginning graduate engineering students, with examples illustrating some basic chemical engineering principles. Chapters 1-6 cover techniques for the solution of first- and second-order ordinary differential equations, Sturm-Liouville problems, Fourier series, and partial differential equations. Chapter 7 illustrates applications to some problems in chemical engineering, mostly involving the diffusion equation for heat or mass. Chapter 8 summarizes dimensional analysis and scaling of boundary value problems, and chapter 9 presents an overview of the use of various software packages for numerical solution of algebraic and differential equations. Numerous examples are included in each chapter, as well as a list of selected references and some exercises for the student. The first three chapters treating ordinary differential equations are particularly useful, interesting, and well done. Remaining chapters are largely repetitions of material from classical references. Since the book's focus is on analytical methods, the material on numerical methods is quite concise and condensed. A useful text or resource for upper-division undergraduate and graduate engineering mathematics students. R. Darby; Texas A&M University

Author notes provided by Syndetics

Norman W. Loney is an Associate Professor of Chemical Engineering at New Jersey Institute of Technology