We know about vectors, and we know about functions, so we are ready to learn about vector fields. These are like functions that take in coordinates and give back vectors, so there will be a vector associated with every single point in the field. There are two things we must be able to do with vector fields as well, which involve the del operator and either the dot product or the cross product with the vector field. These give us the divergence and the curl of the vector field, respectively. Let's learn all about these operations now. Script by Howard Whittle Watch the whole Mathematics playlist: http://bit.ly/ProfDaveMath Classical Physics Tutorials: http://bit.ly/ProfDavePhysics1 Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2 General Chemistry Tutorials: http://bit.ly/ProfDaveGenChem Organic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChem Biochemistry Tutorials: http://bit.ly/ProfDaveBiochem Biology Tutorials: http://bit.ly/ProfDaveBio EMAIL► ProfessorDaveExplains@gmail.com PATREON► http://patreon.com/ProfessorDaveExplains Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience! Amazon: https://amzn.to/2HtNpVH Bookshop: https://bit.ly/39cKADM Barnes and Noble: https://bit.ly/3pUjmrn Book Depository: http://bit.ly/3aOVDlT