Thanks for the explanation. I am having trouble understanding the cartesian equations. When you change the right hand side of the equation, it changes x-intercept or y-intercept. But the line is still a vector. How does that affect the solution? The same thing applies to my lack of...
Note there are m equations and n unknowns and m > n.
Lets take an example of a 2D system. Suppose we have 3 equations. So we have 2 unknowns and 3 equations. Now since they all lie in x-y plane, one of those lines can be expressed as a linear combination of the other two and hence can be...
Hi,
I have a confusion regarding solving an overdetermined system of equations. Consider M equations and N unknowns. If M > N, then the system is overdetermined. Now since when expressed in matrix form, the column rank is N (in other words N degrees of freedom), the N equations must be linear...
eehhh.. how did you get that result? I've been trying to find the nth term for so many hours with no success. If you expand \sqrt{1+t} about t=0, how can you just substitute t for x^2 since that would change the differentiation of each term and effects of that additional 2x will compound as we...
Hi,
We need a generic expression of a taylor series nth term to find out the radius of convergence of the series. However, there are series where I don't think it is even possible to find a generic term. How do we find the radius of convergence in such cases?
e.g. sqrt (1 - x^2)
There...
Hi,
I've using numerical integration method (Simpson rule) to evaluate a definite integral in the interval [a,b]. I was wondering what is the ideal way to approximate the integral in the boundary [a,b) or (a,b] or (a,b) when for example, the function inside the integral does not exist at that...
Hi,
As per Clariut's theorem, if the derivatives of a function up to the high order are continuous at (a,b), then we can apply mixed derivatives. I am looking at
http://en.wikipedia.org/wiki/Symmetry_of_second_derivatives
and I cannot understand in the example for non-symmetry, why the...
Hi,
This may sound lame but I am not able to get the definition of uniform continuous functions past my head.
by definition:
A function f with domain D is called uniformly continuous on the domain D if for any eta > 0 there exists a delta > 0 such that: if s, t D and | s - t | < delta...