Oxford Calculus: Separable Solutions to PDEs

University of Oxford mathematician Dr Tom Crawford explains how to solve PDEs using the method of "separable solutions". Links to worksheets and app download below. Test yourself with some exercises on separable solutions with this FREE worksheet in Maple Learn: https://learn.maplesoft.com/doc/i72vej3p2d/trm-separable-solutions Investigate separable solutions to the Heat Equation with this FREE worksheet in Maple Learn: https://learn.maplesoft.com/d/PQOSOULGKPFHEREGBKJSJRHRKPCPJPHLGRCIFSHOOKFUERPPEGLUDILQNTLIAUJUBTJMLGKPMJJRHMJFIHKJKNLIKOLHNKFNONKU Check your working using the Maple Calculator App – available for free on Google Play and the App Store. Android: https://play.google.com/store/apps/details?id=com.maplesoft.companion&hl=en Apple: https://apps.apple.com/us/app/maple-companion/id1466659419 The technique of solving PDEs using separable solutions is introduced and then used to solve two examples. In both cases the technique of "separation of variables" is required. Other videos in the Oxford Calculus series can be found here: https://www.youtube.com/playlist?list=PLMCRxGutHqflZoTY8JCm1GRzCdGXvZ3_S Finding critical points for functions of several variables: https://youtu.be/Leomuu82-u8 Classifying critical points using the method of the discriminant: https://www.youtube.com/watch?v=5M_ts8Q2LEM Partial differentiation explained: https://youtu.be/RVwcBGzQcT8 Second order linear differential equations: https://youtu.be/F54yhRB9qDI Integrating factors explained: https://www.youtube.com/watch?v=ftqKuOfOX3E Solving simple PDEs: https://youtu.be/uztjxrGY6Jw Jacobians explained: https://www.youtube.com/watch?v=YqMelRryG8U Separation of variables integration technique explained: https://youtu.be/zk41c0vs9XQ Solving homogeneous first order differential equations: https://youtu.be/uqvqjbAcbL8 Taylor’s Theorem explained with examples and derivation: https://www.youtube.com/watch?v=DULzJmUHN5g Heat Equation derivation: https://youtu.be/rz3cdzZXQms Find out more about the Maple Calculator App and Maple Learn on the Maplesoft YouTube channel: https://www.youtube.com/channel/UCq2MmZQ8-kqEVAnmL2GSMsQ Produced by Dr Tom Crawford at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: https://www.seh.ox.ac.uk/people/tom-crawford For more maths content check out Tom's website https://tomrocksmaths.com/ You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths. https://www.facebook.com/tomrocksmaths/ https://twitter.com/tomrocksmaths https://www.instagram.com/tomrocksmaths/ Get your Tom Rocks Maths merchandise here: https://beautifulequations.net/collections/tom-rocks-maths