Advanced Math

Question (Uniform Continuity): Show that 1/x is continuous on (0, ∞) but not uniformly continuous. Answer : Continuous function : A function f(x) is called continuous at a point p…

Example of classification of pde of second order Let a, b, c, d be four differentiable functions defined on R^2. Then the partial differential equation \[\left(a\left(x,y\right)\ \frac{\partial}{\partial x}+b\left(x,y\right)\ \frac{\partial}{\partial x}\right)\…

Reduction Of Order : Reduction of order is a method to find the general solution of a second-order linear ordinary differential equation. If one solution is given then Reduction of order method…

Question : Solve quasi linear pde x(y^2-z^2 )p+y(z^2-x^2 )q=z(x^2-y^2 ) Solution : Given quasi linear pde\[x\left(y^2-z^2\right)p+y\left(z^2-x^2\right)q=z\left(x^2-y^2\right)\]Comparing from standard equation of quasi linear pde P(x,y,z)p+Q(x,y,z)q=R(x,y,z) Where p, q are partial derivative…

Question : Which of the following can be the set of discontinuities of f ? Solution : Since a monotonic function f has limits right and left hand limits at every point on…

Question : If xn is a sequence of positive reals then yn=xn/(1+xn) is convergent or not convergent. Answer : Given xn is a sequence of positive reals and sequence \[y_n=\frac{x_n}{1+x_n}\]For…