How to solve the wave equation (PDE)

[timl]

cant believe that i can understand how to solve this in 10min easily which i've spent like 3 hours on lec note and had no clue with. u r a great teacher!

[lightspd]

Dr. Tisdell, thank you very much for all of the top notch content. You explain things very clearly and I always find myself coming back to these videos for refresher.

[TheToggleguy]

Cheers Chris you've really helped me

[khaledfarghly]

thanks so much Dr. Chris, hope I can got some solved examples :)

[Peter_]

I like the way he says "partial", it sounds very soothing for some reason.

[Adkorane]

Thanks Dr Chris, you Always make the problem so easy!

[mennaabrham]

The wave PDE: 𝑢𝑡𝑡 = 𝑐2𝑢𝑥𝑥
represents the steady state temperature on a rectangular surface of length “L” and open top. The initial and boundary conditions are:
𝑢(0, 𝑡) = 𝑢(𝐿, 𝑡) = 0, 𝑢(𝑥, 0) = 𝑠𝑖𝑛 3𝜋𝑥, 𝑢𝑡(𝑥.0) = 4𝑠𝑖𝑛7𝜋𝑥
2. Solve, using finite difference method (numerically), the same problem (use central difference for the partial derivative on boundaries ), 𝐿 = 3, taking ∆𝑥 = 0.2 and ∆𝑦 = 0.1.
Evaluate only the first 3 lines above the boundary conditions. Write your answers in a tabular form.

[bistromathematics]

at 5:40 min should it be (-2c del/del eta)(2c del/del tzi)u ? are signs reversed ? although doesn't matter in the end

[gregmcn]

At 9 min onwards, where has dz come from? Should it be ds?

[bansishah]

at 10:47, why is u(x, t) = f(s) + g(s) ? and, why is A+B=0 ? we aren't working with f(x) and g(x) are we ?

[Sacklar]

Hi, thanks for the series on PDEs mate! Think I might actually pass now haha...

At around 3:15 shouldn't the penultimate sentence be "where j(x) = v(x, 0) ..." instead of u(x, 0)?

[gregmcn]

Hi can anyone explain the steps at 5.50 where tzi and eta are introduced?

[dusmantnaik]

sir kindly give the fundamental solution of wave operator

[valoraz]

A lecture without actually explaining anything