Course Overview
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Course Synopsis
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This course contains many tools to solve different type of differential equations like, First-Order Differential Equations, Second Order Differential Equations, Applications of Linear and Nonlinear differential equations. While the aim of second segment to emphasize on system of Linear equations, vector spaces, determinants and their properties.
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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 non-homogenous equations are explained and solved.
- Construct the applications of second order differential equations and different vibration models.
- To master the techniques for solving systems of linear equations.
- Introduce matrix algebra as a generalization of single-variable algebra of high school.
- Build on the background in Euclidean space and formalize it with vector space theory.
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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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Quiz1
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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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16
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Homogeneous Linear Equations with Constant Coefficients
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Assignment
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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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20
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Variation of Parameters
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21
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Introduction and Overview of Linear Algebra
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22
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Introduction to Matrices.
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Mid Term
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23
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System Of Linear Equations.
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24
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Row reduction and Echelon Form of a Matrix
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27
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Solution Set of Linear Equations
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Quiz2
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29
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Linear Transformations
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30
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The Matrix of Linear Transformations
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33
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Characterization of Invertible Matrices
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34
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Partitioning of a Matrix.
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Quiz3
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36
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Iterative Solution of Linear Systems
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37
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Introduction to Determinants
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38
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Properties of Determinants
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39
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Cramer's rule, Volume and Linear Transformations
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Quiz4
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41
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Null Spaces,Column Spaces and Linear Transformations
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42
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Bases for a vector Space
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44
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Dimension of a Vector Space
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Final Term
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