separation of variables Method to solve heat equation
We shall Apply separation of variables Method to solve heat equation
what are inverse Laplace transform examples
what are inverse Laplace transform examples Q (i) \[L^{-1}\left[\frac{4}{s-3}\right]\] (ii)\[f(s) =\frac{5}{(s+1)^4}\] (iii) \[f(s)=\frac{s+4}{s^2+8s+37}\] (iv) \[\frac{1}{s}-\frac{2}{s^2}\ +\frac{4}{s-3}+\frac{5}{{(s-3)}^4}\] Answer : (i) First Shifting Theorem States thatIf \[L\left[f\left(t\right)\right]=\ F\left(s\right)\] Then \[ L\left[e^{\alpha t}f\left(t\right)\right]=\…
How to find roots of x^3-3x^2-16x+48=0 if the sum of two of its roots being equal to zero ?
How to find roots of x^3-3x^2-16x+48=0 if the sum of two of its roots being equal to zero ? Answer : To find roots of x^3-3x^2-16x+48=0 if the sum of…
How to prove that Every square matrix can be expressed
Question : Prove that Every square matrix can be expressed as a sum of a symmetric and a skew symmetric matrix uniquely Answer : Here We shall show step by…
How to express a square matrix as a sum of symmetric and a skew symmetric matrix?
How do you express following square matrix as a sum of symmetric and a skew symmetric matrix? A=[8 3 2;-1 0 6;4 2 5] Answer : We shall express following…
how to find solution of pde 3d^2z/dx^2+2d^2z/dxdy-5d^2z/dy^2=0
Question : Find the solution of pde 3d^2z/dx^2+2d^2z/dxdy-5d^2z/dy^2=0 Solution : Given PDE [3\frac{\partial^2z}{\partial x^2}+2\frac{\partial^2z}{\partial x\partial y}-5\frac{\partial^2z}{\partial y^2}=0 ] Is a Homogeneous Linear PDE with constant coefficients. To solve such equations…
how to Find the sum of the series 1+2+2^2+2^3+…..+2^n
Find the sum of the series 1+2+2^2+2^3+…..+2^n Answer : To Find 1+2+2^2+2^3+…..+2^n We know that any series of the from [a+ar+ar^2+ar^3+\ldots\ldots+ar^{n-1}] is called Geometric Progression. Where a is the first…
Q. If A is a 3 by 3 non-singular matrix such that AA^T = A^TA and B = A^(-1)AT,then BB^T is
Question : If A is a 3 by 3 non-singular matrix such that AA^T = A^TA and B = A^(-1)AT,then BB^T is (A)I+B (B) I (c) A+B …
Three coplanar forces acting on a particle are in equilibrium
Question : Three coplanar forces acting on a particle are in equilibrium. The angle between the first and thesecond is 60 degree and that between the second and the third…
what are examples of cyclic groups with two generators ?
Question : What are examples of cyclic groups with two generators ? Answer : We know that a Cyclic Group G is generated by a single element in G. That…