The Newman lectures on mathematics
著者
書誌事項
The Newman lectures on mathematics
Pan Stanford Publishing, c2018
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
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.
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