The Newman Lectures on Mathematics

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.

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.