# Search for tag: "example"

#### Exercise sheet ODE 1: Question 1 worked example

Worked solution for Question 1 from Exercise sheet ODE 1 from EM2A

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#### Hyperbolic PDE Analytical methods Example 3: Laplace transform method example 9.16

Step by step solution of the wave equation with the Laplace transform method for example 9.16 from the textbook

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#### Hyperbolic PDE Analytical methods Example 2: Separation of variables example 9.14

Step by step solution of both cases from example 9.14. This example uses the method of separation of variables on the wave equation.

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#### Hyperbolic PDE Analytical methods Example 1: Characteristics example 9.13

Step by step solution of example 9.13 which covers a wave equation problem solved by the method of characteristics.

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#### Parabolic PDE Analytical methods Example 5: Radially symmetric heat conduction

Step by step solution of the radially symmetric heat conduction or diffusion problem from example 9.24

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#### Parabolic PDE Analytical methods Example 4: Laplace transform method example 9.23

Step by step solution of example 9.23 with the Laplace transform method

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#### Parabolic PDE Analytical methods Example 3: Separated solution example 9.22

Step by step solution of the heat conduction or diffusion equation example 9.22 from the textbook

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#### Parabolic PDE Analytical methods Example 2: Separated solution example 9.21

Step by step solution for example 9.21 from the textbook.

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#### Parabolic PDE Analytical methods Example 1: Separated solution example 9.20

Step by step solution for example 9.20 from the textbook.

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#### Elliptic PDE Analytical methods Example 5: Cylindrical coordinates

Step by step example solving the Laplace equation on a circle where the upper half of the circle is held at a high temperature while the lower half is held at a low temperature.

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#### Elliptic PDE Analytical methods Example 4: Poisson's equation

Example video for Poisson's equation

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#### Elliptic PDE Analytical methods Example 3: Separated solution with Fourier series

This video show how we can use the method of separation of variables together with the Fourier series to find the solution of the Laplace equation. A brief recap of the Fourier series is given at the…

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#### Elliptic PDE Analytical methods Example 2: Separation of variables

Example video showing how to use the method of separation of variables to calculate the solution to the Laplace equation.

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#### Elliptic PDE Analytical methods Example 1: Laplace equation solutions

The video gives three solutions to the Laplace equation and demonstrates how we can show that these equations are solutions to the Laplace equation.

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#### Fourier series Week 3 Example 2: Harmonic oscillator

Video discussing the harmonic oscillator. We use the Fourier series of a periodic forcing to find the particular solution of the differential equation describing the harmonic oscillator.

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#### Fourier series Week 3 Example 1: Fourier series by differentiation or integration

Three examples showing the use of differentiation and integration to find Fourier series.

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