Find the solution of each of the following initial-value problems.

MATH 2010 - Multivariable Calculus & Matrix Algebra Professor Herron - Rensselaer Polytechnic Institute Week 6 (2/29/16 - 3/4/16) Important : These notes are in no way intended to replace attendance in lecture. For best results in this course, it is imperative that you attend lecture and take your own detailed notes. Please keep in mind that these notes are written speci▯cally with Professor Herron’ s sections in mind, and no one else’ s. Many of the examples done in class had corresponding graphics. For simplicity, I will not be including said graphics in these notes, but they should be easily found on the course page on LMS or elsewhere online. Gradient Vector Fields The gradient of f is de▯ned as: rf = hf ;f x. y