MA8251 Important questions ENGINEERING MATHEMATICS 2

MA8251 Important questions ENGINEERING MATHEMATICS 2 Regulation 2017 Anna University free download. ENGINEERING MATHEMATICS 2 MA8251 Important questions pdf free download.

Sample MA8251 Important questions ENGINEERING MATHEMATICS 2:

If the sum of 2 eigen values and the trace of a 3×3 matrix are equal , find
the value of |?|
State Cayley-Hamilton theorem.
Prove that sum of eigen values of a matrix is equal to its trace. (MA8251 Important questions ENGINEERING MATHEMATICS 2)
Find the matrix corresponding to the quadratic form 2xy+2yz+2zx.
What is the nature of the quadratic form x2+y2+z2 in 4 variables?
Reduce the quadratic form 8×2+7y2+3z2-12xy+4xz-8yz into canonical
form by orthogonal reduction and find its nature.
State Gauss Divergence theorem (MA8251 Important questions ENGINEERING MATHEMATICS 2)
State Stokes theorem.
State Greens theorem
Give the unit normal vector to the surface ??? = ? at (2, 1, 1).
Give the unit normal vector to the surface ?? + ?? + ?? = ? at (1,1,1).
Define conformal mapping.
Show that an analytic function in a region R with constant
imaginary part is constant. (MA8251 Important questions ENGINEERING MATHEMATICS 2)
If f(z) is an analytic function whose real part is constant, Point
out f(z) is a constant function.
Explain that a bilinear transformation has at most 2 fixed
points.
Examine whether the function ??? can be real part of analytic
function. (MA8251 Important questions ENGINEERING MATHEMATICS 2)
Formulate the image of |? + ?| = ? under the map ? = ?/?.
Show that the transformation maps, in general, circles and
straight lines into circles and straight lines. Point out the circles
and straight lines are transformed into straight lines and circles
respectively. (MA8251 Important questions ENGINEERING MATHEMATICS 2)
State the sufficient conditions for the existence of Laplace
transform.
State first and second shifting theorem.
State and prove change of scale property.
Apply initial and final value theorem for the verification of the
function f(t) = 1+ e-t (sint + cost). (MA8251 Important questions ENGINEERING MATHEMATICS 2)