Derivation of the 1D Wave Equation

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. This video focuses on the derivation of the governing PDE only, other videos in this series discuss how to solve this PDE. Additional videos in this series: -Introduction to Partial Differential Equations (https://youtu.be/THjaxvPBGOU) -Standing Waves Demonstration (https://youtu.be/42WBuhVJ7sA) -Derivation of the 1D Wave Equation (https://youtu.be/IAut5Y-Ns7g) -Solving the 1D Wave Equation (https://youtu.be/lMRnTd8yLeY) -Heat Transfer Demonstration (https://youtu.be/FsLFZT44l48) -Derivation of the Heat Equation (https://youtu.be/ixsRJPlO_rc) -Solving the 1D Heat Equation (https://youtu.be/I3jiMhVGmcg) -Derivation and Solution of Laplace’s Equation (https://youtu.be/GCESkCyZt4g) -Derivation of the 2D Wave Equation (https://youtu.be/KAS7JBztw8E) -Solving the 2D Wave Equation (https://youtu.be/Whp6jolTu34) -Numerically Solving Partial Differential Equations (https://youtu.be/ZSNl5crAvsw) Associated videos on software tools relevant to PDEs include: -Creating Movies and Animations in Mathematica (https://youtu.be/S03e6dwM100) -Creating Movies and Animations in Matlab (https://youtu.be/3I1_5M7Okqo) You can see all the videos related to partial differential equations at https://www.youtube.com/playlist?list=PLxdnSsBqCrrFvek-n1MKhFaDARSdKWPnx