Oxford Calculus: How to Solve the Heat Equation

University of Oxford mathematician Dr Tom Crawford explains how to solve the Heat Equation - one of the first PDEs encountered by undergraduate students. Links to worksheet and app download below. Accompanying Maple Learn worksheet with practice questions: https://learn.maplesoft.com/doc/yllfw9gbg7/trm-heat-equation-worksheet 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 here: 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 FULL DESCRIPTION OF CONTENT TO FOLLOW 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 Separable Solutions to PDEs: https://www.youtube.com/watch?v=hcm-CgHFbwI 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