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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.

From  Daniel Friedrich on March 1st, 2021 0 likes 62 plays 0  

Hyperbolic PDE Analytical methods Part 6: Separation of variables

This video introduces the method of separation of variables or separated solutions for the wave equation.

From  Daniel Friedrich on March 1st, 2021 0 likes 65 plays 0  

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.

From  Daniel Friedrich on March 1st, 2021 0 likes 73 plays 0  

Hyperbolic PDE Analytical methods Part 5: Formal classification of PDEs

Derive and discuss the formal classification for second order partial differential equations

From  Daniel Friedrich on February 22nd, 2021 0 likes 72 plays 0  

Hyperbolic PDE Analytical methods Part 4: Method of characteristics

Introduce the method of characteristics for hyperbolic PDEs

From  Daniel Friedrich on February 22nd, 2021 0 likes 89 plays 0  

Hyperbolic PDE Analytical methods Part 3: D'Alembert solution

This video derives the d'Alembert solution for the hyperbolic wave equation.

From  Daniel Friedrich on February 16th, 2021 0 likes 86 plays 0  

Hyperbolic PDE Analytical methods Part 2: Vibrating string and linear advection

This video shows that two expressions are solutions to the wave equation for two different conditions: 1) the fundamental mode of the vibrating string and 2) the linear advection problem.

From  Daniel Friedrich on February 16th, 2021 0 likes 76 plays 0  

Hyperbolic PDE Analytical methods Part 1: Introduction

Introduction to the hyperbolic wave equation and derivation of the 1D wave equation.

From  Daniel Friedrich on February 16th, 2021 0 likes 83 plays 0  

Parabolic PDE Analytical methods ConcepTest solutions

Video with the solutions to the ConcepTests for the Analytical methods for Parabolic PDE part

From  Daniel Friedrich on February 16th, 2021 0 likes 29 plays 0  

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

From  Daniel Friedrich on February 16th, 2021 0 likes 59 plays 0  

Parabolic PDE Analytical methods Part 6: Spherical coordinates

This video discusses the heat conduction or diffusion equation in spherical coordinates. It also introduces the scaled temperature for radially symmetric heat conduction or diffusion problems.

From  Daniel Friedrich on February 16th, 2021 0 likes 68 plays 0  

Elliptic PDE Analytical methods ConcepTest solutions

Video with the solutions to the ConcepTests for the Analytical methods for Elliptic PDE part

From  Daniel Friedrich on February 16th, 2021 0 likes 11 plays 0  

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

From  Daniel Friedrich on February 6th, 2021 0 likes 87 plays 0  

Laplace transform Week 1 Part 5: Frequency shift property

This video introduces the frequency shift property of the Laplace transform.

From  Daniel Friedrich on September 3rd, 2020 0 likes 376 plays 0  

Laplace transform Week 1 Part 3: Convergence region

In this video we introduce the concept of exponential order and define the region of convergence of the Laplace transform.

From  Daniel Friedrich on September 3rd, 2020 0 likes 464 plays 0  

Laplace transform Week 1 Example 1: Direct calculation of the Laplace transform

In this example video, we calculate the Laplace transform of the ramp, sine and cosine functions, and the hyperbolic sine and cosine functions directly from the Laplace transform definition.

From  Daniel Friedrich on September 3rd, 2020 0 likes 482 plays 0