Introduction to the Method of Multiple Scales
by Per Jakobsen
Publisher: arXiv 2014
Number of pages: 65
These lecture notes give an introduction to perturbation method with main focus on the method of multiple scales as it applies to pulse propagation in nonlinear optics. The lecture notes are aimed at students that have little or no background in perturbation methods.
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by Sigurdur Freyr Hafstein
In this monograph we develop an algorithm for constructing Lyapunov functions for arbitrary switched dynamical systems, possessing a uniformly asymptotically stable equilibrium. We give examples of Lyapunov functions constructed by our method.
by D. M. Causon, C. G. Mingham - BookBoon
This book presents finite difference methods for solving partial differential equations (PDEs) and also general concepts like stability, boundary conditions etc. The book is intended for undergraduates who know Calculus and introductory programming.
by G.B. Folland - Tata Institute of Fundamental Research
The purpose of this course was to introduce students to the applications of Fourier analysis -- by which I mean the study of convolution operators as well as the Fourier transform itself -- to partial differential equations.
by Ganesh Prasad - Patna University
The reason for my choosing the partial differential equations as the subject for these lectures is my wish to inspire in my audience a love for Mathematics. I give a brief historical account of the application of Mathematics to natural phenomena.