Course Overview
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Course Synopsis
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This course we focused on ordinary differential equations. We describe the main ideas to solve first and second order differential equations and systems of linear equations. We discussed the applications of these differential equations. We use power series methods to solve variable coefficients second order linear equations. We also provided a brief introduction to the eigenvalue problems.
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Course Learning Outcomes
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At the end of the course you should be able to
- Apply the concept of Fist Order Differential Equations.
- Deduce the applications of first order differential equations.
- Conclude differential equations of orders with methods of their solutions and homogenous and nonhomogenous equations are explained and solved.
- Construct the applications of second order differential equations and different vibration models.
- Evaluate the differential equations of higher orders with variable coefficients and methods of their solutions including solution in series. Also Bessels equation and Legendres equation are introduced and solved.
- Compute the concept of systems of linear differential equations and different methods of solutions is provided.
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Course Calendar
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4
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Homogeneous Differential Equations
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5
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Exact Differential Equations
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6
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Integrating Factor Technique
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7
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First Order Linear Equation
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Assignment 1
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10
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Applications of First Order Differential Equations
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12
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Applications of Non Linear Equations
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13
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Higher Order Linear Differential Equations
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14
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Solutions of Higher Order Linear Equations
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15
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Construction of a Second Solution
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Quiz 1
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16
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Homogeneous Linear Equations with Constant Coefficients
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17
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Method of Undetermined Coefficients ( Superposition Approach)
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18
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Method of Undetermined Coefficients (Annihilator Operator Approach)_1
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19
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Method of Undetermined Coefficients (Annihilator Operator Approach)_2
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Quiz 2
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20
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Variation of Parameters
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21
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Variation of Parameters for Higher-Order Equations
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22
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Applications of Second Order Differential Equations
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Mid Term Examination
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25
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Forced Motion-Examples
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26
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Differential Equations with Variable Coefficients
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27
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Cauchy-Euler Equation: Alternative Method of Solution
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28
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Power Series: An Introduction
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29
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Power Series: An Introduction Examples
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Assignment 2
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30
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Solution about Ordinary points
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31
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Solution about Singular Points
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32
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Solution about Singular Points (other cases)
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33
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Bessel's Differential Equation
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34
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Legendre's Differential Equation
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Quiz 3
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35
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Systems of Linear Differential Equations
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36
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Systems of Linear Differential Equations (Continued)
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37
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System of Linear First Order Equation
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38
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Introduction to Matrices
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39
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The Eigenvalue Problem
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Quiz 4
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40
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Matrices and Systems of Linear First-Order Equations
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41
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Matrices and Systems of Linear First-Order Equations (Continued)
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42
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Homogeneous Linear Systems
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43
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Linear and Repeated Eignevalues
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44
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Non-Homogeneous System
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45
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Revision of the course
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Final Term Examination
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