My Math Forum Difference between vector differentiation and parametric differentiation

 Calculus Calculus Math Forum

 March 9th, 2015, 12:08 AM #1 Senior Member     Joined: Feb 2014 From: Louisiana Posts: 156 Thanks: 6 Math Focus: algebra and the calculus Difference between vector differentiation and parametric differentiation This might seem like a naive question to ask, but a full explanation of why these two concepts are different would be welcome. I am confused because parametric equations are $\displaystyle y = 8t^2$ and $\displaystyle x = 5t$, but at the same time, these two equations can describe the $\displaystyle x$ and $\displaystyle y$ components of a vector. Parametric differentiation is defined as $\displaystyle \frac{\mathrm{d} y}{\mathrm{d} x} = \frac{\frac{\mathrm{d} y}{\mathrm{d} t}}{\frac{\mathrm{d} x}{\mathrm{d} t}}$, while vector differentiation is defined as $\displaystyle \frac{\mathrm{d} \vec{r}}{\mathrm{d} t} = \left \langle \frac{\mathrm{d} x}{\mathrm{d} t}, \frac{\mathrm{d} y}{\mathrm{d} t} \right \rangle$
 March 9th, 2015, 05:50 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,598 Thanks: 2583 Math Focus: Mainly analysis and algebra Note the "denominators" of your differential operators on the left hand side. The first relates how$y$ varies with $x$ along the path of a "particle" (independently of time), the second shows how the position of that "particle" changes with time (i.e. it's velocity).

,

### difference between vector differentiation and differentiation

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post hatchelhoff Calculus 4 September 27th, 2013 08:28 AM frnick Calculus 10 July 19th, 2013 12:51 PM wulfgarpro Calculus 6 May 24th, 2010 05:31 AM wulfgarpro Algebra 6 May 11th, 2010 08:57 PM mikeportnoy Calculus 2 May 2nd, 2010 08:03 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top