diffyqs - Notes on Diffy Qs Differential Equations for...

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Unformatted text preview: Notes on Diffy Qs Differential Equations for Engineers by Jiˇrí Lebl October 24, 2011 2 Typeset in L A T E X. Copyright c 2008–2011 Jiˇrí Lebl This work is licensed under the Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License. To view a copy of this license, visit http://creativecommons.org/ licenses/by-nc-sa/3.0/us/ or send a letter to Creative Commons, 171 Second Street, Suite 300, San Francisco, California, 94105, USA. You can use, print, duplicate, share these notes as much as you want. You can base your own notes on these and reuse parts if you keep the license the same. If you plan to use these commercially (sell them for more than just duplicating cost), then you need to contact me and we will work something out. If you are printing a course pack for your students, then it is fine if the duplication service is charging a fee for printing and selling the printed copy. I consider that duplicating cost. During the writing of these notes, the author was in part supported by NSF grant DMS-0900885. See http://www.jirka.org/diffyqs/ for more information (including contact information). Contents Introduction 5 0.1 Notes about these notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 0.2 Introduction to di ff erential equations . . . . . . . . . . . . . . . . . . . . . . . . . 7 1 First order ODEs 13 1.1 Integrals as solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.2 Slope fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.3 Separable equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.4 Linear equations and the integrating factor . . . . . . . . . . . . . . . . . . . . . . 27 1.5 Substitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 1.6 Autonomous equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1.7 Numerical methods: Euler’s method . . . . . . . . . . . . . . . . . . . . . . . . . 42 2 Higher order linear ODEs 47 2.1 Second order linear ODEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.2 Constant coe ffi cient second order linear ODEs . . . . . . . . . . . . . . . . . . . . 51 2.3 Higher order linear ODEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.4 Mechanical vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 2.5 Nonhomogeneous equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 2.6 Forced oscillations and resonance . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3 Systems of ODEs 85 3.1 Introduction to systems of ODEs . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 3.2 Matrices and linear systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 3.3 Linear systems of ODEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 3.4 Eigenvalue method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
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This note was uploaded on 03/19/2012 for the course AEROSPACE mae260 taught by Professor Park,seung-o&han-limchoi during the Spring '12 term at Korea Advanced Institute of Science and Technology.

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diffyqs - Notes on Diffy Qs Differential Equations for...

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