Tom Rocks Maths | Oxford Calculus: Separation of Variables Integration Technique Explained with Examples @TomRocksMaths | Uploaded 2 years ago | Updated 1 hour ago
University of Oxford mathematician Dr Tom Crawford explains how to use the method of separation of variables to solve first order separable differential equations.
Test yourself with some exercises on the separation of variables technique for solving differential equations with this FREE worksheet in Maple Learn: learn.maplesoft.com/doc/eb9iozpfsn/trm-separation-of-variables-worksheet
The separation of variables technique is introduced for a general first order separable differential equation, and then used to solve two problems with fully worked example solutions. The first example requires manipulation of a fraction, and the second a substitution and the use of some trigonometric identities. In both cases the solution is checked by calculating derivatives, with the second one requiring implicit differentiation due to the solution being given implicitly.
Check your working using the Maple Calculator App – available for free on Google Play and the App Store.
Android: play.google.com/store/apps/details?id=com.maplesoft.companion&hl=en
Apple: apps.apple.com/us/app/maple-companion/id1466659419
Other videos in the Oxford Calculus series can be found here: youtube.com/playlist?list=PLMCRxGutHqflZoTY8JCm1GRzCdGXvZ3_S
Finding critical points for functions of several variables: youtu.be/Leomuu82-u8
Classifying critical points using the method of the discriminant: youtube.com/watch?v=5M_ts8Q2LEM
Partial differentiation explained: youtu.be/RVwcBGzQcT8
Second order linear differential equations: youtu.be/F54yhRB9qDI
Integrating factors explained: youtube.com/watch?v=ftqKuOfOX3E
Solving simple PDEs: youtu.be/uztjxrGY6Jw
Jacobians explained: youtube.com/watch?v=YqMelRryG8U
Find out more about the Maple Calculator App and Maple Learn on the Maplesoft YouTube channel: 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: seh.ox.ac.uk/people/tom-crawford
For more maths content check out Tom's website tomrocksmaths.com
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
facebook.com/tomrocksmaths
twitter.com/tomrocksmaths
instagram.com/tomrocksmaths
Get your Tom Rocks Maths merchandise here:
beautifulequations.net/collections/tom-rocks-maths
University of Oxford mathematician Dr Tom Crawford explains how to use the method of separation of variables to solve first order separable differential equations.
Test yourself with some exercises on the separation of variables technique for solving differential equations with this FREE worksheet in Maple Learn: learn.maplesoft.com/doc/eb9iozpfsn/trm-separation-of-variables-worksheet
The separation of variables technique is introduced for a general first order separable differential equation, and then used to solve two problems with fully worked example solutions. The first example requires manipulation of a fraction, and the second a substitution and the use of some trigonometric identities. In both cases the solution is checked by calculating derivatives, with the second one requiring implicit differentiation due to the solution being given implicitly.
Check your working using the Maple Calculator App – available for free on Google Play and the App Store.
Android: play.google.com/store/apps/details?id=com.maplesoft.companion&hl=en
Apple: apps.apple.com/us/app/maple-companion/id1466659419
Other videos in the Oxford Calculus series can be found here: youtube.com/playlist?list=PLMCRxGutHqflZoTY8JCm1GRzCdGXvZ3_S
Finding critical points for functions of several variables: youtu.be/Leomuu82-u8
Classifying critical points using the method of the discriminant: youtube.com/watch?v=5M_ts8Q2LEM
Partial differentiation explained: youtu.be/RVwcBGzQcT8
Second order linear differential equations: youtu.be/F54yhRB9qDI
Integrating factors explained: youtube.com/watch?v=ftqKuOfOX3E
Solving simple PDEs: youtu.be/uztjxrGY6Jw
Jacobians explained: youtube.com/watch?v=YqMelRryG8U
Find out more about the Maple Calculator App and Maple Learn on the Maplesoft YouTube channel: 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: seh.ox.ac.uk/people/tom-crawford
For more maths content check out Tom's website tomrocksmaths.com
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
facebook.com/tomrocksmaths
twitter.com/tomrocksmaths
instagram.com/tomrocksmaths
Get your Tom Rocks Maths merchandise here:
beautifulequations.net/collections/tom-rocks-maths
