The Newman Lectures on Mathematics

ISBN-13: 9789814774253 / Angielski / Twarda / 2018 / 206 str.

USA) Berkeley John (University of California Newman; B Vincent (Lawrence Berkeley National Laboratory Battaglia

Opis

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. The simplicity of the presentation instils confidence in the readers that they can solve any problem they come across either analytically or computationally.

Spis treści

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.