1st Edition
The Newman Lectures on Mathematics
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.
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
Biography
John Newman is Charles W. Tobias Chair of Electrochemistry, Department of Chemical Engineering, University of California, Berkeley (UC Berkeley), USA. Before joining UC Berkeley, he was a senior scientist and principal investigator at the Energy Technologies Area (ETA), Lawrence Berkeley National Laboratory, Berkeley, California, USA. He received his BS degree from Northwestern University, Illinois, USA, and MS degree and PhD from UC Berkeley. He has been a recipient of the Onsager Professorship, 2002, of the Norwegian University of Science and Technology, Trondheim, Norway. His current research focus is on analysis and design of electrochemical systems, with batteries and fuel cells receiving the most attention. He is the author of over 300 technical publications, numerous plenary and invited lectures, and the book Electrochemical Systems.
Vincent Battaglia is a research scientist and group lead of Energy Storage and Distributed Resources Division of ETA. He received his BS degree in chemical engineering from Johns Hopkins University, Baltimore, USA, and his MS degree and PhD in chemical engineering from UC Berkeley. He joined Argonne National Laboratory, Washington, DC, as a postdoctoral fellow and was later appointed as a chemical engineer, then technical coordinator for DOC PNGV office and coordinator of DOE VTO Battery Research there. He specializes in electrochemical energy storage and conversion and has received the Pacesetter Award from Argonne National Laboratory, the DOE R&D Award, the 2013 R&D 100 Award, and the FMC Corporation external research collaboration award.
