Course Overview
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Course Synopsis
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This is an advanced course in Differential Equations, solutions of some differential equations and their applications. MTH701 contains many interactive differential equations tools and covers the entire differential equations course, First-Order Differential Equations, Second Order Differential Equations, Linear and Nonlinear differential equations and their Applications, Series Solutions, Partial Differential Equations, Adomian decomposition method: its applications and convergence.
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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 homogeneous and non-homogeneous equations are explained and solved.
- Construct the applications of second order differential equations.
- Evaluate the differential equations of higher orders with variable coefficients and methods of their solutions, including solution in series. Also Bessel’s equation and Legendre’s equation are introduced and solved.
- Compute the concept of systems of linear differential equations and different methods of solutions is provided.
- Evaluate the Partial Differential Equations, their order, linearity and non-linearity.
- Use of Adomian decomposition method and deduce its applications.
- Apply Adomian method for higher-order ordinary differential equations.
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Course Calendar
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1
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Introduction to Differential Equations
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2
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Higher Order Linear Differential Equations
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3
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Solutions of Higher Order Linear Equations
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4
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Construction of a Second Solution
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5
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Homogeneous Linear Equations with Constant Coefficients
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6
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Method of Undetermined Coefficients-Superposition Approach
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7
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Undetermined Coefficient: Annihilator Operator Approach
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8
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Undetermined Coefficients: Annihilator Operator Approach
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9
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Variation of Parameters
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10
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Variation of Parameters Method for Higher-Order Equations
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11
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Applications of Second Order Differential Equation
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12
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Differential Equations with Variable Coefficients
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13
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Cauchy-Euler Equation: Alternative Method of Solution
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14
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Power Series: An Introduction
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15
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Power Series: An Introduction Part 2
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16
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Solution about Ordinary Points
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17
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Solution about Singular Points
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18
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Solutions about Singular Points
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19
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Bessel’s Differential Equation
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20
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Legendre’s Differential Equation
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21
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Systems of Linear Differential Equations
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22
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Systems of Linear Differential Equations Part 2
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23
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Systems of Linear First-Order Equation
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24
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Introduction to Matrices
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25
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The Eigenvalue problem
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26
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Matrices and Systems of Linear First-Order Equations
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27
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Matrices and Systems of Linear 1st-Order Equations (Continued)
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28
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Homogeneous Linear Systems
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29
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Real and Repeated Eigenvalues
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30
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Non-Homogeneous System
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31
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Basic Concepts of Partial Differential Equations
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32
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Adomian Decomposition Method
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33
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Applications of Adomian Decomposition Method
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34
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Convergence of Adomian Decomposition Method
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35
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Adomian Method for Higher-Order Ordinary Differential Equations
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