Oxford Calculus: Gradient (Grad) and Divergence (Div) Explained

University of Oxford Mathematician Dr Tom Crawford explains the gradient vector (Grad) and the divergence (Div) for scalar and vector functions. Test yourself with this accompanying FREE worksheet in Maple Learn: https://learn.maplesoft.com/doc/ipube... Sign-up for Maple Learn Premium using the code TOMROCKSMATHS for a discounted subscription. Head to https://getlearn.maplesoft.com/ for more information. 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/de... Apple: https://apps.apple.com/us/app/maple-c... We begin with the formal definition of the gradient vector (Grad) and a visualisation of what it represents for a multivariable function. We then look at some examples with explicit calculation and 3D plots. The Divergence (Div) of a vector function is then introduced - both as an equation and via the physical interpretation of what it represents. We calculate the divergence for several vector fields and then show where the notation 'Grad Dot F' comes from with a derivation. Finally, the link between Grad, Div and the Laplacian is explored. Don’t forget to check out the other videos in the ‘Oxford Calculus’ series – all links below. Full playlist: Oxford Calculus Finding critical points for functions of several variables: Oxford Calculus: Finding Critical Points f... Classifying critical points using the method of the discriminant: Oxford Calculus: Classifying 2D Critical P... Partial differentiation explained: Oxford Calculus: Partial Differentiation E... Second order linear differential equations: Oxford Mathematics Open Day 2021: Differen... Integrating factors explained: Oxford Calculus: Integrating Factors Expla... Solving simple PDEs: Oxford Calculus: Solving Simple PDEs Jacobians explained: Oxford Calculus: Jacobians Explained Separation of variables integration technique explained: Oxford Calculus: Separation of Variables I... Solving homogeneous first order differential equations: Oxford Calculus: Solving Homogeneous First... Taylor’s Theorem explained with examples and derivation: Oxford Calculus: Taylor's Theorem Explaine... Heat Equation derivation: Oxford Calculus: Heat Equation Derivation Separable Solutions to PDEs: Oxford Calculus: Separable Solutions to PDEs How to solve the Heat Equation: Oxford Calculus: How to Solve the Heat Equ... Fourier Series Derivation: Oxford Calculus: Fourier Series Derivation Find out more about the Maple Calculator App and Maple Learn on the Maplesoft YouTube channel: @maplesoft 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-c... For more maths content check out Tom's website https://tomrocksmaths.com/ You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths. Facebook: tomrocksmaths Twitter: tomrocksmaths Instagram: tomrocksmaths Get your Tom Rocks Maths merchandise here: https://beautifulequations.net/collec...