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Partial Differential Equations - Lecture 8 Notes
- College aantekeningen • 9 pagina's • 2019
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The aim of this course unit is to enable a student to:
1.	Demonstrate an understanding of methods used to solve partial differential equations and their engineering areas of application,
2.	Apply mathematical skills from partial differentiation to solve problems that require partial differentiation methods,
3.	Appreciate the role of partial differentiation in solving problems that are related to science and engineering.

At the end of this course unit, the student should be able to:
1.	Apply par...
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Partial Differential Equations - Lecture 7 Notes
- College aantekeningen • 4 pagina's • 2019
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Ook in voordeelbundel
-
- $4.53
- + meer info
The aim of this course unit is to enable a student to:
1.	Demonstrate an understanding of methods used to solve partial differential equations and their engineering areas of application,
2.	Apply mathematical skills from partial differentiation to solve problems that require partial differentiation methods,
3.	Appreciate the role of partial differentiation in solving problems that are related to science and engineering.

At the end of this course unit, the student should be able to:
1.	Apply par...
-
1. First order ordinary differential equations
- College aantekeningen • 3 pagina's • 2019
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Looking at the steps to Modelling Ordinary Differential Equations and the different types of forms: first order ODEs in explicit form, implicit form. How to solve Separable ODEs using a Chauvet Cave example. Lastly looking at the Concepts of a particular solution and a general solution.
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32. More partial differential equations
- College aantekeningen • 5 pagina's • 2019
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Frobenius ODEs, and looking at special cases. Using the indicial equation to find what type of solution the Frobenius ODEs. Edge Waves redux finding a power series solution.
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28. PDEs and waves & Series solutions of ODEs create special functions
- College aantekeningen • 7 pagina's • 2019
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Series Solution and how they can be found. Modelling of shallow water and finding solutions. Variation of Parameters and an example. Variation of parameters general solution and deriving it. Power Series method and using is to solve ODEs creating a recurrence relationship.
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23. PDEs and waves
- College aantekeningen • 4 pagina's • 2019
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Linearising wave equation for a water column. Using separation of variables to create a general solution to the wave equation.
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20. Representing periodic functions by Fourier series
- College aantekeningen • 3 pagina's • 2019
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Theorem for Fourier series, the fourier series and the integrals to solve the coefficients. Forced oscillation example and graphing of solution. Generalising Fourier series to an Arbitrary period and derivation.
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16. Partial differential equations
- College aantekeningen • 4 pagina's • 2019
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Partial Differential Equations and its definition and properties. Some important PDEs are given and an example given of how to solve one. It goes through how to make a well-posed PDE question and the modelling framework. An example is given of modelling car traffic going through the steps of the modelling framework.
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11. Second and higher order ODEs
- College aantekeningen • 5 pagina's • 2019
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General solution for two nonhomogeneous ODE example. How to use matlab to check your solutions. Modelling free and forced oscillations theory and finding the solutions to an undamped system. Example of a harmonic oscillator and looking at the different types of damped systems.
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9. Second and higher order ODEs
- College aantekeningen • 5 pagina's • 2019
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Existence and completeness theorem and a general proof (not complete), Characteristic Equation derivation and the different types with an example. Theory of linear independent solutions and a basis, using Wronksian for linear independence and basis- partial proof. Complex roots theory and an example with a graph and matlab code. Multiple roots theory of the number of linearly independent solutions and an example.
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