Description
Prof. Newman is considered one of the great chemical engineers of his time. His reputation derives from his mastery of all phases of the subject matter, his clarity of thought, and his ability to reduce complex problems to their essential core elements. He is a member of the National Academy of Engineering, Washington, DC, USA, and has won numerous national awards including every award offered by the Electrochemical Society, USA. His motto, as known by his colleagues, is "do it right the first time." He has been teaching undergraduate and graduate core subject courses at the University of California, Berkeley (UC Berkeley), USA, since joining the faculty in 1966. His method is to write out, in long form, everything he expects to convey to his class on a subject on any given day. He has maintained and updated his lecture notes from notepad to computer throughout his career. This book is an exact reproduction of those notes.
This book shows a clean and concise way on how to use different analytical techniques to solve equations of multiple forms that one is likely to encounter in most engineering fields, especially chemical engineering. It provides the framework for formulating and solving problems in mass transport, fluid dynamics, reaction kinetics, and thermodynamics through ordinary and partial differential equations. It includes topics such as Laplace transforms, Legendre’s equation, vector calculus, Fourier transforms, similarity transforms, coordinate transforms, conformal mapping, variational calculus, superposition integrals, and hyperbolic equations. The simplicity of the presentation instils confidence in the readers that they can solve any problem they come across either analytically or computationally.
Table of Contents
Introduction and Philosophical Remarks
Differentiation of Integrals
Linear, First-Order Differential Equations
Linear Systems
Linearization of Nonlinear Problems
Reduction of Order
Linear, Second-Order Differential Equations
Euler’s Equation and Equations with Constant Coefficients
Series Solutions and Singular Points
Legendre’s Equation and Special Functions
The Laplace Transformation
Strum–Liouville Systems and Orthogonal Functions
Numerical Methods for Ordinary Differential Equations
Vector Calculus
Classification and Examples of Partial Differential Equations
Steady Heat Conduction in a Rectangle
Coordinate Transformations
A Disk Electrode in an Insulating Plane
Suspension of Charged Drops
Transient Temperature Distribution in a Slab
Inversion of Laplace Transforms by the Method of Residues
Similarity Transformations
Superposition Integrals and Integral Equations
Decomposition of Complicated Problems by Superposition
Migration in Rapid Double-Layer Charging
