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13.Proof the uniqueness of the solution, if exists, to the equation below: u_{tt}-a^2(u_{xx}+u_{yy})=f(x,y,t),\ (x,y,t)\in\mathbb{\Omega\times R^+}\\u|_{t=0}=\varphi(x,y),\ u_t|_{t=0}=\psi(x,y)\\\frac{\partial u}{\partial n}{\bigg|}_{\partial\Ome...
The mantra for popular-science books is to minimize the use of equations. In The Theoretical Minimum: What You Need to Know to Start Doing Physics, authors Leonard Susskind and George Hrabovsky have taken the opposite approach by producing a physics book for the educated general public that ...
Thus, if in the process of solving an equation we resort to steps—such as squaring—that may introduce extraneous roots, then the solutions of the transformed equation must be verified by substitution in the original equation. We know most about equations for which the functions fk are ...
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Forum:Introductory Physics Homework Help M Understanding Force Equations: Solving for Weight, Normal, and Pulling Forces Hello everyone, I have a physics test coming up and am working on the Pre-test however I have run into a problem and cannot find the proper equations anywhere to solve this...
1.) To begin deriving the first kinematic equation, we should first consider the definition of acceleration.a=ΔvΔt 2.) We know Δv=v−v0 , and when we plug that in, we get a=v−v0Δt 3.) If we solve for v, the equation becomes v=v0+aΔt 4.) We can denote th...
Inphysics,equations of motionareequationsthat describe the behavior of a system (e.g., the motion of a particle under an influence of aforce) as a function of time. Sometimes the term refers to thedifferential equationsthat the system satisfies (e.g.,Newton's second laworEuler–Lagrange equ...
Fluid mechanics, science concerned with the response of fluids to forces exerted upon them. It is a branch of classical physics with applications of great importance in hydraulic and aeronautical engineering, chemical engineering, meteorology, and zoolog