What is ds in ds2 = dx2 - cdt2 • Physics Forums
May 5, 2019 · So I'm just looking at: (assume, as they do, the motion is only in x) ds2 = dx2 - dt2 The German word for distance is Strecke. So German mathematicians will often use S or s for Strecke, …
Why is the second derivative notation written as d^2y/dx^2?
May 4, 2009 · The notation for the second derivative, d²y/dx², is a shorthand that simplifies the expression of repeated differentiation. It avoids potential confusion that could arise from writing d²y/d …
Heat equation - separation of variables • Physics Forums
Jul 24, 2010 · The discussion focuses on solving the heat equation using separation of variables with specified boundary and initial conditions. The solution derived is u (x,t) = B.e^ (-L^2t).sin (Lx), where …
Leibniz Notation Explained: dy/dx, d2y/dx2, d/dx - Physics Forums
Nov 11, 2013 · I never really understood leibniz notation. I know that dy/dx means differential of y with respect to x, but what do the 'd's mean? How come the second-order differential is d2y/dx2? What …
Solving Du/dt=A*d^2u/dx^2 w/ Boundary Conditions
Jan 29, 2013 · du/dt = A*d^2u/dx^2 Where u=u(x,t) and A is a constant. The boundary conditions are: u=f(x) when t=0 u=0 when x=0, independent of t u=V when x=L, independent of t, where V and L are …
How to integrate d2x/dt2 with respect to x? • Physics Forums
Sep 8, 2019 · Here, m is the mass on the spring, k is the spring constant, x is the extension of the spring, and t is time. My problem is about figuring out how equation (3-1) becomes equation (3-2)? I …
Implicit differentiation find dy/dx and d2y/dx2 - Physics Forums
Oct 11, 2009 · Your dy/dx is correct. I didn't work out the second derivative, but as long as you took the derivative of dy/dx using the quotient rule and implicit differentiation, replacing dy/dx in that …
Is (d^2/dx^2) a Hermitian Operator? - Physics Forums
Oct 15, 2006 · Hi, I'm doing a Quantum mechanics and one of my question is to determine if \frac {d^2} {dx^2} (a second derivative wrt to x) is a Hermitian Operator or not...
Parametric equation confusion of d2y/dx2 • Physics Forums
Apr 1, 2012 · x=t2 and y=t3-3t, find dy/dx and d2y/dx2 I understand how to get to dy/dx but an confused on how to get to d2y/dx2 can someone please explain in depth, I know the formula is (d/dt …
How to Add Metres & Seconds for Equal ds2: Einstein's Theory
May 4, 2023 · Reading this PDF from Professor Richard Conn Henry, I am confused by the multiplication by c on page 2. Einstein's claim is that dx2 + dy2 + dz2 − dt2 = ds2 = dx′ 2 + dy′ 2 + dz′ …