L5.pdf - MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 –Éléments de machines UNIVERSITY GINA CODY SCHOOL OF ENGINEERING

L5.pdf - MECH ENGR 6501 213 Advanced – Applied ODE’s...

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Unformatted text preview: MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines UNIVERSITY - GINA CODY SCHOOL OF ENGINEERING CliquezCONCORDIA pour modifier le style du titre AND COMPUTER SCIENCE ENGR 213/1: APPLIED ORDINARY DIFFERENTIAL EQUATIONS (ODE’s) Lecture 5 Non-linear models (Population dynamics, logistic equation, chemical, reaction, leaking tank) Local: FG C080 SGW, Tue. and Thu. 10:20 am – 12:45 pm Instructor: Sam Eskandarian, Ph.D. PEng (Ontario) Introduction Lecture 5 - 1 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre References ● PowerPoint slides on the course site (Moodle). ● Textbook: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. ● E. Kreyszig, Advanced Engineering Mathematics, 9th Edition, Wiley, 2006. ● Other reference materials will be given in course presentations. AE Tutor: Nima Farhang AF Tutor: Mehrshad Moghadamazad AG Tutor: Omid Aghababaei AH Tutor: Maziar Sargordi Sam Eskandarian Introduction Lecture 5 - 2 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines CliquezContact pour modifier style du titre info & le Recalls ● Office: EV3.276 Tel: 3462 Email: [email protected] Office hours: Every Tue. and Thu. from 2:00 pm – 3:00 pm ● Recalls: - Lecture 5 on Moodle - Quiz 2: Sections 2.4, 2.5, 1.3 and 2.7 - Midterm 1 on next Tuesday (May 28th) on lecture materials from L1 to L4. Introduction Lecture 5 - 3 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier style du titre Course contentle(1/2) Lecture 01: 1.1 Definition and Terminology; problems: 1,3,5,6,8,10,11,13,14,21,23 1.2 Initial Value Problems; problems: 7,9,11,12,17,18 2.1 Solution curves without a solution; problems: 3, 4, 26, 27 Lecture 02: 2.2 Separable Equations; problems: 7,9,13,19,25,27 2.3 Linear Equations; problems: 7,9,23,27,31 2.4 Exact Equations, integrating factors; problems: 3,5,9,15,27,29,31 Lecture 03: 2.5 Solutions by Substitution (Bernoulli, homogeneous, linear substitution); problems: 5,7,9,13,17,19,21,25,27 Lecture 04: 1.3 Differential Equations as Mathematical Models; problems: 1,2,3,5,7,9,1013,15,16,19 2.7 Linear models (growth/decay, heating/cooling, circuits, mixtures); problems: 3,5,9,15,17,23,25,29,31 Lecture 05: 2.8 Non-linear models (Population dynamics, logistic equation, chemical, reaction, leaking tank); problems: 2,3,11,13,17 17.1 Complex numbers; problems: 1,3,7,11,15,25,27,29,31,35,39 Lecture 06: Midterm 1 (during tutorials) on material of Lectures 01-04 17.2 Powers and Roots; problems: 3,7,9,15,21,31,33,35 3.1 Theory of Linear Equations; problems: 1,9,23,27 Lecture 07: 3.3 Homogeneous Linear Equations with Constant Coefficients problems: 3,5,9,13,15,17,21 3.4 Undetermined Coefficients; problems: 1,3,7,11,15,19,23,31 =-_ Introduction Lecture 5 - 4 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le (1/2) style du titre Course calendar Introduction Lecture 5 - 6 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Nonlinear Models Nonlinear Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 5 - 7 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Nonlinear Models dp dF=flk ) K - . dp AT flofr fikto -_ O . . Nonlinear * - Poos - - Po Potato ⇒ { b- E [email protected] , - I Pur at . ac e-at-bctalnlpl-talnla-bpl-t.ec cent bp ✓ , In ⇒ f- I eat attac .ea4=P_ a- , 7 eat a , a- Petatop ) - = BP . .cat/=ac.eat Pfftbc bp Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. c Introduction Lecture 5 - 8 Introduction p Pathak bpoterbpoeat ⇒ t be f . to p→fz → dd¥= PL-bdafi-la-bpjddf-dffca-zt.pl o P = Ib → Inflection ÷! ;I÷⇒da¥ { ⇒ Pt . BLK Eb a= b- t - I F- k xp a . b- Lk ) a- - Po ) > cannot fzckd carry ⇒ " ° DI dt2 Pos Fb capacity . =L t po> a- 2b of s - curve i. Ex : project process :b - so . ✓ - t MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Nonlinear Models Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 5 - 9 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Nonlinear Models Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 5 - 11 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier Linear Models le style du titre Example 25 (1-3) - fthx kxctx - DX af - XLK = ⇒ dp ) - . =PLa-bp ) ⇒ KX ) - )=__ 149 ke b=k 10002 999 It XL infected students I . k . -100014 → = of r 1000k A- 1000k yet I percentage " t "bpII÷poFae Pco ) -4 . etoookt 41=50 took ⇒ ⇒ xct ) = = - 0.9906 LIFE - . agent XCG ) - - 226 students Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. infected . Introduction Lecture 5 - 12 Introduction FT kyflooo - - dy = Footy , Yeo ) =/ y) - k . , dt ⇒ tytfooy.dy-fkdt.tn/Yoooyfioookttc . y ⇒ c- Y I t ) YL4) 1000 = -50 at - - @ 100014 I . 1000k£ e - 999-1 eloookt . ⇒ k . MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Nonlinear Models Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 5 - 14 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Nonlinear Models Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 5 - 15 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier Linear Models le style du titre Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Example 26 (1-3) Introduction Lecture 5 - 16 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Nonlinear Models Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 5 - 19 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Selected problems Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 5 - 20 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Selected problems Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 5 - 21 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Complex numbers tf 4 aec > o , Real # - co Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. , complex # . Introduction Lecture 5 - 22 Introduction MECH ENGR 6501 213 Advanced Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Complex numbers Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. * Rec Z y= 2mA ) ) . Introduction Lecture 5 - 23 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Complex numbers TE Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. - I Introduction Lecture 5 - 24 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Complex numbers Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 5 - 25 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Complex numbers ( Zit as Zz = It - - (b) - 2122=213+8 = = 6+16 - - 12 i ) I t 41 ' ( -31-81 321 ' ' ) 2 6+45+321-2(-6-32)+46-12 i Example 27 (1-3) - 12 it = IZ - ) i = -38+41 ' I Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 5 - 26 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Complex numbers Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 5 - 28 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Complex numbers on to Is . . IT 43¥ = = x = = II Example 28 (1-3) 842ai-zi.to#-iozfi= = complex L Et Es i Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. = - If - Fs i ) # Introduction Lecture 5 - 30 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Complex numbers Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 5 - 32 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Complex numbers Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Example 29 (1-3) Introduction Lecture 5 - 33 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Complex numbers Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 5 - 34 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Selected problems Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 5 - 35 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Questions Introduction Lecture 5 - 36 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Questions Introduction Lecture 5 - 36 Introduction ...
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