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Curves, Parameterizations, and the Arclength Parameterization

WELCOME TO THE START OF VECTOR CALCULUS. Full playlist here: ►VECTOR CALCULUS (Calc IV)    • Calculus IV: Vector Calculus (Line In...   In this video we give an overview of one of the foundational concepts: curves. We will contrast the idea of a curve and path, talk about different parameterizations, the tangent vector, arclength, arclength parameterizations and contrast when to use the arclength parameter versus a time parameter. A lot of these topics are covered in more depth back in my Calc III: Multivariable Calculus playlist, so check out that below as well. 0:00 Curves 1:00 Parameterizations 3:10 Tangent Vector 4:25 Arclength 7:23 Arclength vs Time Parameter THE MULTIVARIABLE PLAYLIST: ►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus ...   OTHER COURSE PLAYLISTS: ►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Log...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   ►CALCULUS I:    • Calculus I (Limits, Derivative, Integ...   ► CALCULUS II:    • Calculus II (Integration Methods, Ser...   ►DIFFERENTIAL EQUATIONS:    • How to solve ODEs with infinite serie...   OTHER PLAYLISTS: ► Learning Math Series    • 5 Tips To Make Math Practice Problems...   ►Cool Math Series:    • Cool Math Series   BECOME A MEMBER: ►Join:    / @drtrefor   MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett SOCIALS: ►Twitter (math based):   / treforbazett   ►Instagram (photography based):   / treforphotography