Vectors, Vector Fields, and Gradients | Multivariable Calculus

In this video, we introduce the idea of a vector in detail with several examples. Then, we demonstrate the utility of vectors in defining vector-valued functions and vector fields. Finally, we wrap it up by showing why vectors and a vector fields are so fundamental to multivariable calculus: by moving towards gradients! Hope you enjoy! Chapters: 0:00 Intro 1:07 What is Vector? 5:21 Vector-Valued Functions 8:14 Vector Fields 9:45 Vector Fields in Multivariable Calculus 10:58 Input Spaces 14:56 Gradients 18:58 Exercises Subscribe for more: https://www.youtube.com/@FoolishChemist?sub_confirmation=1 https://www.instagram.com/foolish.chemist/ https://www.tiktok.com/@foolishchemist #maths #calculus #multivariable #multivariablecalculus #perspective #some