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78 votes

5 answers

132k views

What exactly is Laplace transform?

asked Aug 10, 2012 at 21:07

11 votes

4 answers

13k views

Given two subspaces $U,W$ of vector space $V$, how to show that $\dim(U)+\dim(W)=\dim(U+W)+\dim(U\cap W)$

asked Jan 29, 2013 at 19:06

11 votes

2 answers

2k views

how to prove $\displaystyle \frac{\sin (2n+1)\theta}{\sin \theta} = .... $

asked Feb 21, 2013 at 14:54

8 votes

2 answers

377 views

How to evaluate $ \int_0^\infty {1 \over x^x}dx$ in terms of summation of series?

asked Aug 20, 2012 at 17:02

7 votes

0 answers

192 views

How to evaluate $\int_0^\infty {x \over 1 + x^5} \;dx $? [duplicate]

asked Sep 1, 2012 at 5:44

6 votes

2 answers

360 views

how to show that $\lim_{z \to 0}z^z$ does not exist?

asked Jan 28, 2013 at 9:21

6 votes

3 answers

24k views

building transformation matrix from spherical to cartesian coordinate system

asked Jun 23, 2012 at 22:25

6 votes

2 answers

3k views

condition for roots of quartic equation to be purely imaginary

asked Feb 27, 2013 at 15:14

6 votes

7 answers

4k views

How to show that linear map is invertible?

asked Jan 29, 2013 at 21:38

4 votes

1 answer

4k views

how to show a scalar product defined by trace of matrices is non-degenerate

asked Jan 31, 2013 at 13:58

4 votes

3 answers

367 views

Find $ \lim_{n \to \infty } z_n $ if $z_{n+1} = \frac{1}{2} \left( z_n + \frac{1}{z_n} \right) $ [closed]

asked Mar 17, 2013 at 18:11

4 votes

3 answers

666 views

proving $\csc^2 \left( \frac{\pi}{7}\right)+\csc^2 \left( \frac{2\pi}{7}\right)+\csc^2 \left( \frac{4\pi}{7}\right)=8$

asked Feb 20, 2013 at 17:19

4 votes

4 answers

290 views

condition for two complex number $a$ and $b$ to be $|a+b| = |a| + |b|$

asked Dec 20, 2012 at 19:52

4 votes

5 answers

2k views

Does $i^i$ and $i^{1\over e}$ have more than one root in $[0, 2 \pi]$

asked Sep 1, 2012 at 17:13

4 votes

2 answers

563 views

Integrate: $\int \frac{dx}{x \sqrt{(x+a) ^2- b^2}}$ [duplicate]

asked Jun 5, 2013 at 15:33

4 votes

2 answers

363 views

Asymptotic expansion of a function $\frac{4}{\sqrt \pi} \int_0^\infty \frac{x^2}{1 + z^{-1} e^{x^2}}dx$

asked Aug 24, 2013 at 7:19

3 votes

2 answers

1k views

How to evaluate $ \int_{-\infty}^\infty {e^{ax} \over 1 +e^x } \; dx $ [duplicate]

asked Sep 5, 2012 at 16:11

3 votes

4 answers

263 views

How to show that $\sum\limits_{n=1}^\infty \exp(i\,nz)$ converges?

asked Aug 25, 2012 at 21:45

3 votes

4 answers

21k views

How to find the laplace transform of $ |\sin (t)| $?

asked Aug 30, 2012 at 4:18

3 votes

2 answers

226 views

what is the easiest way to represent $ \sqrt{1 + x} $ in series

asked Aug 8, 2012 at 13:43

3 votes

1 answer

2k views

How to show $\sum x^n (1-x)$ does not converge uniformly on $[0,1]$

asked Feb 2, 2013 at 23:24

2 votes

1 answer

6k views

what is dimension of orthogonal complement of a subspace of a vector space.

asked Jan 31, 2013 at 14:56

2 votes

1 answer

1k views

the product of diagonals of a regular polygon

asked Feb 21, 2013 at 15:46

2 votes

5 answers

17k views

how to change polar coordinate into cartesian coordinate using transformation matrix

asked Jun 24, 2012 at 11:48

2 votes

2 answers

236 views

Evaluating $\sum_{k=1}^n k^x$ [duplicate]

asked Aug 31, 2012 at 3:20

2 votes

4 answers

4k views

Evaluate the integral $\int_0^{2 \pi} {\cos^2 \theta \over a + b \cos \theta}\; d\theta$

asked Sep 1, 2012 at 8:09

2 votes

2 answers

63 views

expressing $\sum_{k=0}^\infty \sum_{m=0}^k a_k a_m t^{m+k}$ as power series of $t$, $\sum_{n=0}^{\infty}a_n t^n $

asked Sep 1, 2013 at 16:12

2 votes

1 answer

2k views

expression for Remainder in Taylor theorem for complex variables

asked Apr 15, 2013 at 19:58

2 votes

3 answers

208 views

showing $1 + z + z^2 + \dots $ uniformly converges to $\frac{1}{1-z}$ for $|z| < 1$

asked Apr 27, 2013 at 16:59

2 votes

1 answer

109 views

calculate the roots of $z = 1 + z^{1/2}$ using Lagrange expansion

asked May 7, 2013 at 8:50

Stack Exchange Network

55 Questions

What exactly is Laplace transform?

Given two subspaces $U,W$ of vector space $V$, how to show that $\dim(U)+\dim(W)=\dim(U+W)+\dim(U\cap W)$

how to prove $\displaystyle \frac{\sin (2n+1)\theta}{\sin \theta} = .... $

How to evaluate $ \int_0^\infty {1 \over x^x}dx$ in terms of summation of series?

How to evaluate $\int_0^\infty {x \over 1 + x^5} \;dx $? [duplicate]

how to show that $\lim_{z \to 0}z^z$ does not exist?

building transformation matrix from spherical to cartesian coordinate system

condition for roots of quartic equation to be purely imaginary

How to show that linear map is invertible?

how to show a scalar product defined by trace of matrices is non-degenerate

Find $ \lim_{n \to \infty } z_n $ if $z_{n+1} = \frac{1}{2} \left( z_n + \frac{1}{z_n} \right) $ [closed]

proving $\csc^2 \left( \frac{\pi}{7}\right)+\csc^2 \left( \frac{2\pi}{7}\right)+\csc^2 \left( \frac{4\pi}{7}\right)=8$

condition for two complex number $a$ and $b$ to be $|a+b| = |a| + |b|$

Does $i^i$ and $i^{1\over e}$ have more than one root in $[0, 2 \pi]$

Integrate: $\int \frac{dx}{x \sqrt{(x+a) ^2- b^2}}$ [duplicate]

Asymptotic expansion of a function $\frac{4}{\sqrt \pi} \int_0^\infty \frac{x^2}{1 + z^{-1} e^{x^2}}dx$

How to evaluate $ \int_{-\infty}^\infty {e^{ax} \over 1 +e^x } \; dx $ [duplicate]

How to show that $\sum\limits_{n=1}^\infty \exp(i\,nz)$ converges?

How to find the laplace transform of $ |\sin (t)| $?

what is the easiest way to represent $ \sqrt{1 + x} $ in series

How to show $\sum x^n (1-x)$ does not converge uniformly on $[0,1]$

what is dimension of orthogonal complement of a subspace of a vector space.

the product of diagonals of a regular polygon

how to change polar coordinate into cartesian coordinate using transformation matrix

Evaluating $\sum_{k=1}^n k^x$ [duplicate]

Evaluate the integral $\int_0^{2 \pi} {\cos^2 \theta \over a + b \cos \theta}\; d\theta$

expressing $\sum_{k=0}^\infty \sum_{m=0}^k a_k a_m t^{m+k}$ as power series of $t$, $\sum_{n=0}^{\infty}a_n t^n $

expression for Remainder in Taylor theorem for complex variables

showing $1 + z + z^2 + \dots $ uniformly converges to $\frac{1}{1-z}$ for $|z| < 1$

calculate the roots of $z = 1 + z^{1/2}$ using Lagrange expansion