What direction should you travel to increase your height on a mountain as fast as possible? What direction should you travel to keep your height constant (i.e. travel on a contour aka a level curve)? In this video we discuss the math of this problem, assuming we had some nice function describing the height of the mountain. The gradiant vector, whose components are the respective partial derivatives gives us the answer to the direction of maximal increase. Indeed, we saw previously how directional derivatives could be written in terms of the gradient vector. At the end we look at all of this with an actual topographical map full of contours. 0:00 The Mountain Problem 2:24 Deriving the Gradient Formula 6:07 Directional Derivatives 10:54 Topographical Maps **************************************************** COURSE PLAYLISTS: ►CALCULUS I:    • Calculus I (Limits, Derivative, Integ...   ► CALCULUS II:    • Calculus II (Integration Methods, Ser...   ►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus ...   ►DIFFERENTIAL EQUATIONS (Calc IV): https://www.youtube.com/watch?v=xeeM3TT4Zgg ►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Log...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   *************************************************** ► Want to learn math effectively? Check out my "Learning Math" Series: https://www.youtube.com/watch?v=LPH2lqis3D0 ►Want some cool math? Check out my "Cool Math" Series:    • Cool Math Series   **************************************************** ►Follow me on Twitter: http://twitter.com/treforbazett ***************************************************** This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria. BECOME A MEMBER: ►Join: null MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett