User David Lingard

8 votes

1 answer

319 views

Weak derivative under the integral sign

asked Aug 5, 2019 at 23:19

6 votes

1 answer

149 views

Limit $\lim\limits_{x\to\infty}\int\limits_0^\pi\cos\left(x\sin\theta \right)d\theta=0$

asked Dec 2, 2019 at 0:22

4 votes

1 answer

289 views

Steady states of $u_t= u_{xx}+\pi^2u$

asked Aug 14, 2019 at 18:44

4 votes

2 answers

121 views

Roots of $f(x)=x^3-x^2-2x+1$

asked Feb 26, 2018 at 0:46

3 votes

1 answer

72 views

$\displaystyle \sup_{t\in \mathbb{R}}\left(\sin(\sqrt 2 \ t)+\sin(t)\right)=2$

asked Feb 17, 2020 at 5:00

3 votes

2 answers

109 views

Why does the ODE $xy''+y'+xy=0$ require only one initial condition?

asked Dec 25, 2020 at 13:06

3 votes

1 answer

178 views

Nonnegativity of solution of $u_t=\Delta u+u$

asked Jul 31, 2019 at 18:56

2 votes

1 answer

711 views

The solution of the heat equation $u_t=\alpha u_{xx}$ is continuous on time $[0,\infty)$

asked Dec 27, 2020 at 18:03

2 votes

1 answer

115 views

The operator $Sf=f(1)$ defined on $L^1[0,1]$

asked Sep 30, 2021 at 12:49

2 votes

1 answer

58 views

Mean value theorem $e^{f(t)}-e^{g(t)}=e^{h(t)}(f(t)-g(t)).$

asked May 2, 2020 at 4:57

2 votes

1 answer

327 views

Existence theorem for the SIR epidemic differential equations

asked May 4, 2020 at 20:16

2 votes

5 answers

317 views

Show that the sequence $\sum\limits_{k=1}^n\cos\left(\frac kn\right)^{2n^2/k}$ converges

asked May 6, 2018 at 0:52

2 votes

2 answers

3k views

Limit of cumulative distribution functions is a cumulative distribution function

asked May 28, 2018 at 2:41

2 votes

4 answers

680 views

If derivative goes to $0$, does the function have a limit?

asked Dec 28, 2018 at 22:58

1 vote

1 answer

112 views

How many steady state solutions does $u_t=d\Delta u+au-bu^2$ possess?

asked Aug 13, 2019 at 10:14

1 vote

5 answers

96 views

Asymptotic behavior of the sequence $u_n=\int_0^1\frac{e^{-t}}{t+\frac{1}{n}}dt$

asked Apr 10, 2018 at 16:47

1 vote

0 answers

64 views

Exponential decay of solution in $L^p$ with $p>2$

asked Jul 28, 2019 at 19:35

1 vote

1 answer

78 views

Asymptotic behavior of the geometric sequence $U_{n+1}=QU_n$ in a probability problem

asked Mar 13, 2018 at 14:04

1 vote

0 answers

98 views

Perron-Frobenius Theorem and probability

asked Mar 14, 2018 at 14:13

1 vote

2 answers

132 views

How can we prove that $\lim_{x\to0^+} \sum_{n=1}^\infty e^{-n^2x}=\infty$? [closed]

asked Dec 21, 2020 at 20:13

1 vote

2 answers

75 views

Sequence of subspaces $Ker(\lambda I-A)^k$ stationary at algebraic multiplicity?

asked Dec 4, 2021 at 0:33

1 vote

1 answer

567 views

Hermitian matrix having repeated eigenvalues

asked Mar 2, 2022 at 13:54

1 vote

1 answer

136 views

Asymptotic behavior of $u_t= u_{xx}+au$

asked Aug 15, 2019 at 10:24

1 vote

2 answers

461 views

Book for Mathematics applied to engineering

asked Sep 16, 2019 at 13:56

1 vote

1 answer

149 views

Laplace transform: $\mathcal{L}(f')=s\mathcal{L}(f)-f(0)$ for weak derivatives

asked Jan 6, 2020 at 1:16

1 vote

0 answers

99 views

Gamma function and factorial [duplicate]

asked Sep 27, 2019 at 23:21

1 vote

4 answers

162 views

Solve $0.9^n+0.8^n \leq 0.1$

asked Oct 9, 2019 at 22:46

0 votes

1 answer

2k views

Fourier series of $f(x)=x$

asked Sep 21, 2019 at 23:58

0 votes

1 answer

87 views

Proof of $\sum_{n=1}^\infty \frac{\cos \ n}{n}=-\frac{\ln\left(2-2 \cos(1)\right)}{2} $

asked Sep 24, 2019 at 22:42

0 votes

0 answers

63 views

Book dealing with PDEs of the form $u_t=\Delta u+f(t,u)$

asked May 27, 2021 at 17:21

Stack Exchange Network

36 Questions

Weak derivative under the integral sign

Limit $\lim\limits_{x\to\infty}\int\limits_0^\pi\cos\left(x\sin\theta \right)d\theta=0$

Steady states of $u_t= u_{xx}+\pi^2u$

Roots of $f(x)=x^3-x^2-2x+1$

$\displaystyle \sup_{t\in \mathbb{R}}\left(\sin(\sqrt 2 \ t)+\sin(t)\right)=2$

Why does the ODE $xy''+y'+xy=0$ require only one initial condition?

Nonnegativity of solution of $u_t=\Delta u+u$

The solution of the heat equation $u_t=\alpha u_{xx}$ is continuous on time $[0,\infty)$

The operator $Sf=f(1)$ defined on $L^1[0,1]$

Mean value theorem $e^{f(t)}-e^{g(t)}=e^{h(t)}(f(t)-g(t)).$

Existence theorem for the SIR epidemic differential equations

Show that the sequence $\sum\limits_{k=1}^n\cos\left(\frac kn\right)^{2n^2/k}$ converges

Limit of cumulative distribution functions is a cumulative distribution function

If derivative goes to $0$, does the function have a limit?

How many steady state solutions does $u_t=d\Delta u+au-bu^2$ possess?

Asymptotic behavior of the sequence $u_n=\int_0^1\frac{e^{-t}}{t+\frac{1}{n}}dt$

Exponential decay of solution in $L^p$ with $p>2$

Asymptotic behavior of the geometric sequence $U_{n+1}=QU_n$ in a probability problem

Perron-Frobenius Theorem and probability

How can we prove that $\lim_{x\to0^+} \sum_{n=1}^\infty e^{-n^2x}=\infty$? [closed]

Sequence of subspaces $Ker(\lambda I-A)^k$ stationary at algebraic multiplicity?

Hermitian matrix having repeated eigenvalues

Asymptotic behavior of $u_t= u_{xx}+au$

Book for Mathematics applied to engineering

Laplace transform: $\mathcal{L}(f')=s\mathcal{L}(f)-f(0)$ for weak derivatives

Gamma function and factorial [duplicate]

Solve $0.9^n+0.8^n \leq 0.1$

Fourier series of $f(x)=x$

Proof of $\sum_{n=1}^\infty \frac{\cos \ n}{n}=-\frac{\ln\left(2-2 \cos(1)\right)}{2} $

Book dealing with PDEs of the form $u_t=\Delta u+f(t,u)$