User Nick The Dick

55 votes

7 answers

8k views

Why the real and imaginary parts of a complex analytic function are not independent?

complex-analysis

asked Oct 29, 2019 at 19:32

4 votes

1 answer

83 views

"Determine all functions $\Bbb{Z}\to\Bbb{Z}$ such that $f(2a)+2f(b)=f(f(a+b))$"

functions integers

asked Jun 30, 2021 at 16:06

3 votes

1 answer

43 views

Intuition for why we can apply complex analysis to solving 2D cases in applied science problems

complex-analysis applications

asked Jul 8, 2020 at 6:13

2 votes

2 answers

160 views

Why is the vector $(u_x, u_y, - 1)$ normal to the surface $u=u(x, y) $?

differential-geometry partial-differential-equations vector-analysis

asked Jun 18, 2020 at 12:37

2 votes

0 answers

28 views

Theorem weakening/strengthening confusion

logic

asked Nov 29, 2021 at 20:58

2 votes

2 answers

152 views

Derivative of $\log(r)$ with respect to $x$

complex-analysis derivatives coordinate-systems polar-coordinates implicit-differentiation

asked Jan 12, 2020 at 6:43

2 votes

1 answer

321 views

Help me understand a proof of Rouche's theorem

complex-analysis proof-explanation

asked Jan 5, 2020 at 3:16

1 vote

3 answers

3k views

Solving auxiliary equations in Charpit's method. Non-linear first-order ODE.

linear-algebra ordinary-differential-equations partial-differential-equations systems-of-equations

asked Jan 6, 2020 at 0:24

1 vote

0 answers

36 views

Solve $pq^2=ax+by$ - a nonlinear first-order pde

partial-differential-equations

asked Dec 26, 2019 at 22:48

1 vote

1 answer

169 views

Unclear first step in proof of the Schwarz Integral Formula.

complex-analysis

asked Feb 8, 2020 at 9:53

1 vote

1 answer

53 views

Finding the residue of $\frac{1}{ \sqrt{z^2+z+1}}$

complex-analysis

asked Nov 13, 2019 at 4:19

1 vote

1 answer

23 views

Proof that if a sequence of random variables converges weakly to a constant, then it converges to it in probability

probability-theory proof-verification

asked Dec 9, 2019 at 3:53

1 vote

1 answer

343 views

Defining stream function and velocity potential function

complex-analysis definition solution-verification fluid-dynamics

asked Jan 14, 2020 at 13:44

1 vote

0 answers

18 views

Confusion about posterior distribution dependence on priors in this example

statistics statistical-inference

asked Apr 1, 2020 at 22:18

1 vote

2 answers

720 views

Intuitive meaning of Neumann boundary condition

partial-differential-equations heat-equation

asked Apr 9, 2020 at 19:54

1 vote

1 answer

104 views

Surjectivity of operator $(\lambda I-A)x$, where A is a linear operator on a Hilbert space $X$, for non-real $\lambda$

functional-analysis hilbert-spaces spectral-theory

asked Apr 22, 2020 at 19:09

1 vote

1 answer

41 views

Fourier cosine series coefficients

fourier-series

asked Apr 26, 2020 at 20:39

1 vote

1 answer

221 views

How to compute confidence interval for variance with unknown mean from a normal $(a,\sigma ^2)$ sample?

statistics statistical-inference confidence-interval

asked May 15, 2020 at 11:30

0 votes

1 answer

27 views

Unsure of a proof shorcut in a simple chasing the angle problem

euclidean-geometry solution-verification

asked May 25, 2020 at 6:32

0 votes

0 answers

12 views

Numerical solution's evolution's dependance on timestep and the absolute time passed.

numerical-methods

asked Apr 28, 2020 at 19:51

0 votes

1 answer

34 views

Inverse operator in the space of infinite bounded sequences $l_2$

functional-analysis notation operator-theory

asked Apr 18, 2020 at 16:07

0 votes

0 answers

32 views

Understanding the proof of the Compactness principle

complex-analysis

asked Feb 6, 2020 at 18:53

0 votes

0 answers

23 views

Cumulative distribution function of sample average of size 4

probability statistics probability-distributions

asked Mar 31, 2020 at 11:13

0 votes

0 answers

17 views

Double integral over a paremeterised and a general surface

surface-integrals

asked Nov 12, 2021 at 11:49

0 votes

1 answer

63 views

Qualitative understanding of Fisher Information

statistics fisher-information

asked Jul 1, 2020 at 5:06

0 votes

0 answers

29 views

If space projects onto a sphere inside our eye, why do we see flat photographs as normal-looking?

differential-geometry

asked Sep 7, 2020 at 19:09

0 votes

2 answers

48 views

Confusion about how a dual space element is also a mapping.

functional-analysis dual-spaces

asked Sep 17, 2020 at 11:05

0 votes

0 answers

47 views

Proof of Chebyshev's inequality question

probability-theory

asked Dec 17, 2019 at 20:23

0 votes

2 answers

253 views

Reducing to the canonical form of a linear pde with constant coefficients in 4 dimensions

partial-differential-equations

asked Dec 21, 2019 at 10:55

0 votes

1 answer

60 views

Convert $-2xy+2zx-x^2$ into a sum of three squares of expressions of $x,y$ and $z$

linear-algebra

asked Dec 26, 2019 at 12:10

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41 Questions

Why the real and imaginary parts of a complex analytic function are not independent?

"Determine all functions $\Bbb{Z}\to\Bbb{Z}$ such that $f(2a)+2f(b)=f(f(a+b))$"

Intuition for why we can apply complex analysis to solving 2D cases in applied science problems

Why is the vector $(u_x, u_y, - 1)$ normal to the surface $u=u(x, y) $?

Theorem weakening/strengthening confusion

Derivative of $\log(r)$ with respect to $x$

Help me understand a proof of Rouche's theorem

Solving auxiliary equations in Charpit's method. Non-linear first-order ODE.

Solve $pq^2=ax+by$ - a nonlinear first-order pde

Unclear first step in proof of the Schwarz Integral Formula.

Finding the residue of $\frac{1}{ \sqrt{z^2+z+1}}$

Proof that if a sequence of random variables converges weakly to a constant, then it converges to it in probability

Defining stream function and velocity potential function

Confusion about posterior distribution dependence on priors in this example

Intuitive meaning of Neumann boundary condition

Surjectivity of operator $(\lambda I-A)x$, where A is a linear operator on a Hilbert space $X$, for non-real $\lambda$

Fourier cosine series coefficients

How to compute confidence interval for variance with unknown mean from a normal $(a,\sigma ^2)$ sample?

Unsure of a proof shorcut in a simple chasing the angle problem

Numerical solution's evolution's dependance on timestep and the absolute time passed.

Inverse operator in the space of infinite bounded sequences $l_2$

Understanding the proof of the Compactness principle

Cumulative distribution function of sample average of size 4

Double integral over a paremeterised and a general surface

Qualitative understanding of Fisher Information

If space projects onto a sphere inside our eye, why do we see flat photographs as normal-looking?

Confusion about how a dual space element is also a mapping.

Proof of Chebyshev's inequality question

Reducing to the canonical form of a linear pde with constant coefficients in 4 dimensions

Convert $-2xy+2zx-x^2$ into a sum of three squares of expressions of $x,y$ and $z$