Notes on Diffy Qs - jirka.org

1 Notes on Diffy QsDifferential equations for Engineersby Ji r LeblFebruary 22, 2018(version )2 Typeset in 2008 2018 Ji r LeblThis work is dual licensed under the Creative Commons Attribution-Noncommercial-Share International License and the Creative Commons Attribution-Share Alike InternationalLicense. To view a copy of these licenses, send a letterto Creative Commons PO Box 1866, Mountain View, CA 94042, can use, print, duplicate, share this book as much as you want. You can base your own noteson it and reuse parts if you keep the license the same. You can assume the license is either theCC-BY-NC-SA or CC-BY-SA, whichever is compatible with what you wish to do, your derivativeworks must use at least one of the the writing of these Notes , the author was in part supported by NSF grant DMS-0900885and date is the main identifier of version.

2 The major version/edition number is raised only if therehave been substantial changes. Edition number started at 5, that is, version , as it was not kepttrack of more information (including contact information). about these .. to differential .. of differential .. 131 First order as .. equations and the integrating .. methods: Euler s .. 542 Higher order linear order linear .. coefficient second order linear .. order linear .. oscillations and .. 953 Systems of to systems of .. and linear .. systems of .. dimensional systems and their vector.

3 Order systems and .. 1544 Fourier series and value .. trigonometric .. on the Fourier .. and cosine .. of Fourier .. , separation of variables, and the heat .. dimensional wave .. Alembert solution of the wave .. state temperature and the .. Dirichlet problem in the circle and the Poisson .. 2375 Eigenvalue .. of eigenfunction .. periodic .. 2596 The Laplace Laplace .. of derivatives and .. delta and impulse .. 2877 Power series .. solutions of linear second order .. points and the method of .. 3108 Nonlinear , critical points, and.

4 And classification of isolated critical .. of nonlinear .. 345 Further to Selected Notes about these notesThis book originated from my class Notes for Math 286 at theUniversity of Illinois at Fall 2008 and Spring 2009. It is a first course on differential equations for this book, I also taught Math 285 at UIUC, Math 20D atUCSD., and Math 4233 these courses are taught with Edwards and Penney,Differential equations and BoundaryValue Problems: Computing and Modeling[EP.], or Boyce and DiPrima sElementary DifferentialEquations and Boundary Value Problems[BD.], and this book aims to be more or less a drop-inreplacement. Other books I used as sources of information and inspiration are Ince s classic(and inexpensive)Ordinary Differential equations [I.]

5 ], Stanley Farlow sDifferential Equationsand Their Applications[F.], now available from Dover, Berg and McGregor sElementary PartialDifferential equations [BM.], and William Trench s free bookElementary Differential Equationswith Boundary Value Problems[T.]. See theFurther at the end of the organization of this book to some degree requires chapters be done in order. Later chapterscan be dropped. The dependence of the material covered is are some references in material fromchapter 3.(some linear algebra),but these references are not absolutely essential and can be skimmed over, sochapter safelybe dropped, while still covering The textbook was originally made for two typesof courses.

6 Either at 4 hours a week for a semester (Math 286 at UIUC):56 INTRODUCTIONI ntroduction.,chapter 1.,chapter 2.,chapter 3.,chapter 4.(w/o ),chapter 5.( ).For a shorter version (3 hours a week) of the above course, skip The secondtype of the course at 3 hours a week (Math 285 at UIUC) was:Introduction.,chapter 1.,chapter 2.,chapter 4.(w/o ), (and maybechapter 5.,6., or7.).The complete book can be covered at a reasonably fast pace at approximately 75 lectures, notaccounting for exams, review, or time spent in computer lab. A two quarter course can be easily runwith the material, and if one does not rush, a two semester course. For example:Semester 1:Introduction.

7 ,chapter 1.,chapter 2.,chapter 6.,chapter 7., (and perhaps bits of4.).Semester 2:Chapter 3.,chapter 8.,chapter 4.,chapter chapter on Laplace transform (chapter 6.), the chapter on Sturm-Liouville (chapter 5.), thechapter on power series (chapter 7.), and the chapter on nonlinear systems (chapter 8.), are more orless interchangeable time-wise. Ifchapter covered it may be best to place it right afterchapter time is short, the first two sections ofchapter a reasonable self-contained taught the UIUC courses using the IODE software ( ).IODE is a free software package that works with Matlab (proprietary) or Octave (free software).Unfortunately IODE is not kept up to date at this point, and may have trouble running on newerversions of Matlab.

8 The graphs in the book were made with the Genius software ( ). I used Genius in class to show these (and other) book is available Check there for any possibleupdates or errata. The LATEX source is also available for possible modification and :Firstly, I would like to acknowledge Rick Laugesen. I used his handwrittenclass Notes the first time I taught Math 286. My organization of this book through chapter 5, and thechoice of material covered, is heavily influenced by his Notes . Many examples and computationsare taken from his Notes . I am also heavily indebted to Rick for all the advice he has given me,not just on teaching Math 286. For spotting errors and other suggestions, I would also like toacknowledge (in no particular order): John P.

9 D Angelo, Sean Raleigh, Jessica Robinson, MichaelAngelini, Leonardo Gomes, JeffWinegar, Ian Simon, Thomas Wicklund, Eliot Brenner, SeanRobinson, Jannett Susberry, Dana Al-Quadi, Cesar Alvarez, Cem Bagdatlioglu, Nathan Wong,Alison Shive, Shawn White, Wing Yip Ho, Joanne Shin, Gladys Cruz, Jonathan Gomez, JanelleLouie, Navid Froutan, Grace Victorine, Paul Pearson, Jared Teague, Ziad Adwan, Martin Weilandt,S nmez Sahuto glu, Pete Peterson, Thomas Gresham, Prentiss Hyde, Jai Welch, Simon Tse, AndrewBrowning, James Choi, Dusty Grundmeier, John Marriott, Jim Kruidenier, Barry Conrad, WesleySnider, Colton Koop, Sarah Morse, Erik Boczko, Asif Shakeel, Chris Peterson, Nicholas Hu, PaulSeeburger, Jonathan McCormick, and probably others I have forgotten.

10 Finally I would like toacknowledge NSF grants DMS-0900885 and INTRODUCTION TO DIFFERENTIAL Introduction to differential equationsNote: more than 1 lecture, in [EP.], chapter 1 in [BD.] Differential equationsThe laws of physics are generally written down as differential equations . Therefore, all of scienceand engineering use differential equations to some degree. Understanding differential equations isessential to understanding almost anything you will study in your science and engineering can think of mathematics as the language of science, and differential equations are one ofthe most important parts of this language as far as science and engineering are concerned.