10 Questions
What is the basis of mathematical formulation?
Existing laws or experiments if laws are not available
What is mathematical modelling?
Approximation of objects with geometrical objects
In the context of the vibrating string equation, what does 'y' represent?
Elements of arc of string
What does 'dx/dt' represent in the context of the vibrating string equation?
Derivative of x with respect to time
What is the purpose of Fourier analysis in the context of the heat flow problem?
To analyze complex periodic patterns as a sum of simple sine and cosine waves
In the context of vibrating string equations, what does the boundary condition 'displacement is bounded' imply?
The displacement of the string at any instant is limited to a finite real number
What is the definition of heat flux?
Heat per unit area per unit time
What does a negative value of heat flux indicate in the context of thermal conductivity?
Heat flows from lower temperature to higher temperature
What does a limit case where ∆𝑛 approaches 0 and ∆𝑢 approaches 0 imply for heat flux?
The heat flux becomes infinite
What is a Partial Differential Equation (PDE) by definition?
An equation containing unknown functions of two or more variables and total derivatives w.r.to these variables
Learn about mathematical modelling and mathematical formulation in the context of mathematical physics with this lecture handout for MTH647 at Virtual University of Pakistan. The lecture covers the approximation of objects with geometrical objects and the derivation of equations corresponding to physical phenomena.
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