Conversion of IVP into integral equations

In the present lecture, we discuss the conversion of an initial value problem into a Volterra integral equation of the second kind.

[erickdanielperez]

Very nice video, thanks for your excellent subject. I have a question: In ordinary differential equations (ODE's) and in partial differential equations (PDE'S) there is a uniqueness theorem that guarantees with a geometric argument, the analytical existence of at least one solution to an ODE or PDE. In ordinary integral equations (IOE'S) and in partial integral equations (IPE'S), is there or is there not something similar theorem, that proves the existence of at least one solution?

[فاطمةالضاحي-نخ]

Please, can you answer me if we can form or get fredholm integral from initial value problem? because I need the answer, thank you.

[MuhammadInaamSufi]

Sir can you put a proof of Leibniz rule of differentiation under integral sign?

[gausiyaali]

thank you sir.. please solve some more examples.

[ra-hulu]

If you're teaching on screen then teach on screen
If you're teaching on board then completely teach on board
Why this nonsense of switching back and forth
It's very annoying and proper content doesn't get passed to us

[marykashmari]

Uncle Urdu ya hindi main baat kr lya kren. Zada acha smj aye ga