User Twenty-six colours

10 votes

3 answers

20k views

Derivative and partial derivative of complex functions

complex-analysis

asked Jul 18, 2017 at 15:22

8 votes

2 answers

4k views

How does proof by contradiction work?

proof-writing

asked May 3, 2017 at 7:37

7 votes

2 answers

5k views

Inverse Function Theorem and global inverses

inverse-function-theorem

asked Apr 28, 2017 at 10:46

5 votes

1 answer

7k views

What does it mean if divergence of a vector field is zero?

divergence-operator

asked May 27, 2017 at 12:38

5 votes

3 answers

704 views

Simplifying the sum $\sum\limits_{t=1}^{n} t(t+1)v^t$

algebra-precalculus summation

asked May 29, 2017 at 12:08

5 votes

1 answer

6k views

the 2-D divergence theorem and Green's Theorem

integration greens-theorem

asked May 29, 2017 at 12:41

5 votes

2 answers

77 views

Condition on a matrix so that its determinant is $2$

matrices diophantine-equations

asked Jun 21, 2017 at 9:14

4 votes

4 answers

1k views

Fractional Linear Transformations and their matrix form

complex-analysis

asked Jul 18, 2017 at 12:12

4 votes

1 answer

420 views

Simple connectedness of an ellipse

general-topology

asked Jul 25, 2017 at 13:55

4 votes

2 answers

7k views

Definition of a "region"

complex-analysis terminology

asked Jul 25, 2017 at 14:00

4 votes

2 answers

344 views

"Note that connectedness is not defined for closed sets" explanation

general-topology complex-analysis

asked Aug 22, 2017 at 1:05

4 votes

0 answers

46 views

Is this an OK proof to show that eigenvectors of a symmetric matrix are orthogonal?

linear-transformations spectral-theory

asked May 14, 2017 at 10:40

4 votes

2 answers

222 views

Proving $\int_{0}^\pi \frac{2\cos 2\theta + \cos 3\theta}{5+4\cos\theta} = \frac{\pi}{8}$

complex-analysis

asked Sep 24, 2017 at 14:17

3 votes

3 answers

1k views

Why is the dot product of two vectors $\mathbf{x},\mathbf{y}$ the same as $x^T y$?

matrices inner-products

asked Sep 9, 2017 at 10:32

3 votes

3 answers

232 views

solving $\cos z + \sin z = i$

complex-analysis

asked Aug 20, 2017 at 8:41

3 votes

1 answer

685 views

Show that $E(Z^p) = p \int_0^\infty (1-F_Z(x))x^{p-1} \, dx$ for every $p>0$ and nonnegative random variable $Z$ [duplicate]

probability-theory probability-distributions expectation

asked May 21, 2017 at 2:54

3 votes

3 answers

70 views

Is this a valid proof to prove that if $a_n$ converges, then $a_{n+1}-a_{n}$ converges to $0$? by definition

sequences-and-series proof-explanation epsilon-delta

asked May 27, 2017 at 10:17

3 votes

2 answers

18k views

Multivariate Chain Rule and second order partials

partial-derivative chain-rule

asked Jun 7, 2017 at 1:54

3 votes

1 answer

935 views

Intuition on why a field is not conservative

vector-fields

asked May 7, 2017 at 3:51

3 votes

3 answers

689 views

$\sqrt{z+1}\sqrt{z-1} = -\sqrt{z^2 - 1}$ when $\Re(z) < -1$

complex-analysis

asked Aug 22, 2017 at 12:59

3 votes

3 answers

212 views

Showing that $f$ is linear function if $\forall z \in \mathbb{C}$, $|f(z)| \leq 1 + |z|$.

complex-analysis

asked Sep 6, 2017 at 9:42

3 votes

3 answers

297 views

Proving $|\cos z\ |^2 + |\sin z\ |^2 \geq 1$

analysis trigonometry

asked Aug 2, 2017 at 11:23

3 votes

1 answer

11k views

Solving $\cos z = 2$

complex-analysis

asked Aug 2, 2017 at 11:45

3 votes

1 answer

68 views

Is it possible to define an inner product in this vector space to make it an inner product space?

linear-algebra vector-spaces inner-products

asked Jul 19, 2017 at 7:24

3 votes

2 answers

693 views

Limits in complex analysis

complex-analysis

asked Jul 19, 2017 at 13:58

3 votes

3 answers

747 views

Image of a circle under a complex valued function

complex-analysis circles

asked Jul 13, 2017 at 10:28

3 votes

2 answers

126 views

The exponential of a straight line is a straight line if and only if the line is horizontal

complex-analysis functions proof-verification

asked Jul 14, 2017 at 13:28

2 votes

2 answers

466 views

Complex roots of polynomials, proving this particular property

complex-numbers

asked Jul 5, 2017 at 14:02

2 votes

2 answers

215 views

Inequality for a complex root of a polynomial

complex-analysis complex-numbers

asked Jul 13, 2017 at 6:32

2 votes

5 answers

484 views

Intuition why the function $f(z) = \frac{1}{z}$ maps lines to circles

complex-analysis complex-numbers

asked Jul 13, 2017 at 7:20

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182 Questions

Derivative and partial derivative of complex functions

How does proof by contradiction work?

Inverse Function Theorem and global inverses

What does it mean if divergence of a vector field is zero?

Simplifying the sum $\sum\limits_{t=1}^{n} t(t+1)v^t$

the 2-D divergence theorem and Green's Theorem

Condition on a matrix so that its determinant is $2$

Fractional Linear Transformations and their matrix form

Simple connectedness of an ellipse

Definition of a "region"

"Note that connectedness is not defined for closed sets" explanation

Is this an OK proof to show that eigenvectors of a symmetric matrix are orthogonal?

Proving $\int_{0}^\pi \frac{2\cos 2\theta + \cos 3\theta}{5+4\cos\theta} = \frac{\pi}{8}$

Why is the dot product of two vectors $\mathbf{x},\mathbf{y}$ the same as $x^T y$?

solving $\cos z + \sin z = i$

Show that $E(Z^p) = p \int_0^\infty (1-F_Z(x))x^{p-1} \, dx$ for every $p>0$ and nonnegative random variable $Z$ [duplicate]

Is this a valid proof to prove that if $a_n$ converges, then $a_{n+1}-a_{n}$ converges to $0$? by definition

Multivariate Chain Rule and second order partials

Intuition on why a field is not conservative

$\sqrt{z+1}\sqrt{z-1} = -\sqrt{z^2 - 1}$ when $\Re(z) < -1$

Showing that $f$ is linear function if $\forall z \in \mathbb{C}$, $|f(z)| \leq 1 + |z|$.

Proving $|\cos z\ |^2 + |\sin z\ |^2 \geq 1$

Solving $\cos z = 2$

Is it possible to define an inner product in this vector space to make it an inner product space?

Limits in complex analysis

Image of a circle under a complex valued function

The exponential of a straight line is a straight line if and only if the line is horizontal

Complex roots of polynomials, proving this particular property

Inequality for a complex root of a polynomial

Intuition why the function $f(z) = \frac{1}{z}$ maps lines to circles