L1 ENGR213.pdf - MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 –Éléments de machines UNIVERSITY GINA CODY SCHOOL OF ENGINEERING

L1 ENGR213.pdf - MECH ENGR 6501 213 Advanced – Applied...

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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 1 Definition and Terminology Initial Value Problems; problems Solution curves without a solution Local: FG C080 SGW, Tue. and Thu. 10:15 am – 12:45 pm Instructor: Sam Eskandarian, Ph.D. PEng (Ontario) Introduction Lecture 1 - 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 1 - 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 9 – 10 am ● Recalls: - Who is your course instructor? - Course activities - Communications in ”Announcements Forum” - Course website and course outline on Moodle - Course content & calendar Introduction Lecture 1 - 3 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Breakdown of each course lecture ● Introduction and recalls – 10 to 15 min. - Course progress & questions - Video of the day ● 1st part – 10:30 to 11:30 am Example x ● Break (15 min.) ● 2nd part – 11:30 am to 12:45 pm (1-3) Introduction Lecture 1 - 4 Introduction 5 MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Course Objectives Introduction Lecture 1 - 5 Introduction 6 MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Course description COURSE Description This course introduces first year engineering students to the theory of ordinary differential equations (ODE’s) and their applications to mathematical models. The main topics include: Basics of general theory of differential equations; special types of first order equations (separable, linear, exact, homogeneous, Bernoulli); linear equations of higher order (homogeneous and non-homogeneous); Cauchy-Euler equations; non-linear equations of second order; systems of linear differential equations; linear and nonlinear mathematical models of first and second order. Introduction Lecture 1 - 6 Introduction 7 MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Course description If the student misses one mid-term test for any reason, including illness, then the final examination will count for 70% of the final grade. Since there is a 5% take-home projects bonus allocation, there will be no replacements of quizzes for any reason, including illness. Introduction Lecture 1 - 7 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 1 - 8 Introduction Lecture 05: 2.8 Non-linear models logistic equation, chemical, reaction, MECH ENGR 6501 213 – Advanced – Applieddynamics, ODE’s Materials MEC528 -(Population Éléments de machines 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 Lecture 08: 3.5 Variation of Parameters; problems: 1,13,15,23 3.6 Cauchy Euler Equations; problems: 5,7,11,23,45 Lecture 09: 3.7 Nonlinear Equations, Reduction of Order; problems: 3,7,9 3.8 Linear Models. Initial Value Problems (mass-spring systems, free motion) problems: 1,7,12,21 Lecture 10: 3.8 Linear Models. Initial Value Problems (driven motion and LRC-circuits) problems: 31,33,45,47,49 3.11 Non-linear models (telephone wires, rocket motion, pulled rope) problems Lecture 11: Midterm 2 (during tutorials) on material of Lectures 05-09 5.1.2 Power Series Solutions; problems: 17,21,27 10.1 Theory of Linear Systems; problems: 1,3,7,18 Lecture 12: 10.2 Homogeneous Linear Systems; problems: 1,3,7,9,21,31,35,37,48 10.4 Non-Homogeneous Linear Systems; problems: 1,3,7,17,30 Lecture 13: Review Cliquez pour modifier style du titre Course contentle(1/2) Introduction Lecture 1 - 9 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 1 - 10 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Evaluation Return Introduction Lecture 1 - 11 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Introduction Introduction Lecture 1 - 12 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Introduction Introduction Lecture 1 - 13 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Introduction ∑ Introduction Lecture 1 - 14 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Introduction Introduction Lecture 1 - 15 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier style du titre Definitions andleTerminology Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 1 - 16 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier style du titre Definitions andleTerminology Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 1 - 17 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier style du titre Definitions andleClassification Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 1 - 18 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier style du titre Definitions andleClassification Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Left : Right i Highest The order of derivative rest Introduction Lecture 1 - 19 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier style du titre Definitions andleClassification Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 1 - 20 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier style du titre Definitions andleClassification ✓ r Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 1 - 21 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier style du titre Definitions andleClassification constant Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 1 - 22 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier style du titre Definitions andleClassification Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 1 - 23 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier style du titre Definitions andleClassification Right - 0 Right = " X . ( Noy ) Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 1 - 24 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier style du titre Definitions andleClassification Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 1 - 25 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier style du titre Definitions andleClassification it Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 1 - 26 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier style du titre Definitions andleClassification Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 1 - 27 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Solution of an ODE Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 1 - 28 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Solution of an ODE Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 1 - 29 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Solution of an ODE Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 1 - 30 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Solution of an ODE y = 1/x is a solution of the linear first-order differential equation xy’ + y = 0. When we say y = 1/x is a solution of this DE, we mean it is a function defined on an interval I on which it is differentiable and satisfies the equation. Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 1 - 32 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Solution of an ODE Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 1 - 33 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Solution of an ODE Key lprove ) ? b- rn cos Acetyls ) DI d DX zxtzy.ME zy ⇒ . dat dy * = - = = - O 2X I Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 1 - 34 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Solution of an ODE Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 1 - 37 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquezofpour modifier le style du titre Solution an ODE Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 1 - 38 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Solution of an ODE Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 1 - 39 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Solution of an ODE Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 1 - 40 Introduction MECH ENGR 6501 213 Advanced – Applied ODE’s Materials MEC528 - –Éléments de machines Cliquez pour modifier le style du titre Solution of an ODE Ref.: Advanced Engineering Mathematics, by Dennis G. Zill, 6th Edition, Jones and Bartlett, 2016. Introduction Lecture 1 - 42 Introduction ...
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