Types of Integrals of a PDE: Complete, Particular, General, Singular Integrals. Lect. # 6.

B. Sc. Second year Mathematics.
Partial Differential Equations: Types of Integrals of a PDE:
Complete Integral, Particular Integral, General Integral, Singular Integral.

Links to the handwritten notes:

1. Linear Partial Differential Equations of order one
2. Nonlinear Partial Differential Equations of order one
Pages 1 to 24
Pages 25 to 35
Pages 33 and 36

[sukhan]

Very very thanks sir to explain in such an easy and understandable manner ❤

[rohanverma]

Sir, I was trying to understand the difference between all these integrals for the last 2-3 days. It was very helpful that you clearly demarcated what each integral referred to. Thank you.

[MrAAMNNITAllahabad]

Sir in 12:08 what is the reason behind putting d(phi)/d(a) = 0

I mean... I understand we need to eliminate a and b. But how we know that eliminating them (using the above method) will give the envelope surface?? Please, let me know.

And thank you for the tutorials, sir.

[universallawismyname]

sir i have a silly doubt plz ans
potential energy = U = xy - yz -xz^2
force = f = - (∂ U/∂x) icap - (∂U/∂y) jcap - (∂U/∂z) kcap
force = f = (z^2-y) i + (z-x) j + (2xy+y) k
i know how to do partial differentiation but not partial integration
how do i integrate this force to again get the same above potential energy ???
plz ans