Topic

 

Differential Equation

In mathematics, a differential equation is an equation that relates one or more functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly.

Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy.

from Differential equation - Wikipedia

This topic includes the following resources and journeys:

 

 

Derivation of the 1D Wave Equation

Christopher Lum
26 min
Beginner
Video
Theory

In this video, we derive the 1D wave equation. This partial differential equation (PDE) applies to scenarios such as the vibrations of a continuous string. ...

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Derivation of the 2D Wave Equation

Christopher Lum
27 min
Beginner
Video
Theory

In this video we derive the 2D wave equation. This partial differential equation governs the motion of waves in a plane and is applicable for thin vibrating...

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Heat Transfer Demonstration

Christopher Lum
63 min
Beginner
Video
Theory

In this video we demonstrate heat transfer through a metal bar. By heating one side of the bar we can impose a non-uniform temperature distribution across t...

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Solving the 2D Wave Equation

Christopher Lum
73 min
Beginner
Video
Theory

In this video, we solve the 2D wave equation. We utilize two successive separation of variables to solve this partial differential equation. Topics discuss...

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Solving the 1D Wave Equation

Christopher Lum
118 min
Beginner
Video
Theory

In this video, we solve the 1D wave equation. We utilize the separation of variables method to solve this 2nd order, linear, homogeneous, partial differenti...

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Derivation of the Heat Equation

Christopher Lum
31 min
Beginner
Video
Theory

In this video, we derive the heat equation. This partial differential equation (PDE) applies to scenarios such as the transfer of heat in a uniform, homogen...

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Solving the 1D Heat Equation

Christopher Lum
47 min
Beginner
Video
Theory

In this video we simplify the general heat equation to look at only a single spatial variable, thereby obtaining the 1D heat equation. We solving the result...

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Standing Waves Demonstration

Christopher Lum
44 min
Beginner
Video
Theory

In this video we demonstrate standing waves. We show how the system can be excited by oscillating at specific frequencies to generating standing waves. The...

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