35 Answered Questions for the topic Analysis

27d

Vector Differentiation

Prove that (grad)^2 f(r) = D^2/dr^2 + (2/r) Df/DrWhere D^2/dr^2 refers to the second partial derivative of f , w.r.t. r and Df/ Dr refers to partial derivative of f, w.r.t rvector r = xi + yj + zk... more

06/27/19

Mathematical methods for analysing melodic contour?

Are there any mathematical methods for identifying melodic shape, identifying motifs and general pattern recognition?

06/22/19

If A minor doesn't have any accidentals, is it still minor?

As part of a music course, we have to compose a 3 minute long piece based on a river's journey. Having finished the composition, we now have to write a set of sleeve notes - basically an analysis... more

06/03/19

How would one create music based on the principles of Cubism?

How would one create music based on the principles of Cubism?(e.g., 20th century painters: Pablo Picasso, Georges Braque, Juan Gris, Fernand Léger)The basic definition of Cubism calls for the use... more

05/17/19

If A minor doesn't have any accidentals, is it still minor?

As part of a music course, we have to compose a 3 minute long piece based on a river's journey. Having finished the composition, we now have to write a set of sleeve notes - basically an analysis... more

05/02/19

Why are dolls, teddy bears, etc. used as horror objects in horror films?

In many horror films, toys such as dolls, teddy bears, and puzzle boxes are used as objects which the spirits/ghosts use to scare people. Some examples would be Annabelle, the crooked man musical... more

04/27/19

How would one create music based on the principles of Cubism?

How would one create music based on the principles of Cubism? (e.g., 20th century painters: Pablo Picasso, Georges Braque, Juan Gris, Fernand Léger) The basic definition of Cubism calls for the... more

04/23/19

How to provide traditional upper management early analyses in an agile project?

I was discussing moving our process to become more agile with our (mostly traditional) Chief Information Officer (CIO).The CIO's stance was that >=80% of the requirements need to be defined (and... more

03/26/19

What kind of "mathematical object" are limits?

When learning mathematics I tend to try to reduce all the concepts I come across to some matter of interaction between sets and functions (or if necessary the more general Relation) on them.... more

03/23/19

What kind of "mathematical object" are limits?

When learning mathematics I tend to try to reduce all the concepts I come across to some matter of interaction between sets and functions (or if necessary the more general Relation) on them.... more

03/15/19

What is a simple example of a limit in the real world?

This morning, I read Wikipedia's informal definition of a limit: > Informally, a function f assigns an output $f(x)$ to every input $x$. The > function has a limit $L$ at an input $p$ if... more

03/14/19

What are the official modes from Ionian to Locrian?

I am having some confusion is respects to the formal definition of what the various modes are. I know that their defined in relation to their scale, however, I've come to realise this may not be... more

03/14/19

What kind of "mathematical object" are limits?

When learning mathematics I tend to try to reduce all the concepts I come across to some matter of interaction between sets and functions (or if necessary the more general Relation) on them.... more

03/14/19

Who came up with the $\\varepsilon$-$\\delta$ definitions and the axioms in Real Analysis?

I've seen a lot of definitions of notions like boundary points, accumulation points, continuity, etc, and axioms for the set of the real numbers. But I have a hard time accepting these as "true"... more

03/14/19

How would one create music based on the principles of Cubism?

How would one create music based on the principles of Cubism?(e.g., 20th century painters: Pablo Picasso, Georges Braque, Juan Gris, Fernand Léger)The basic definition of Cubism calls for the use... more

03/13/19

Why do movie coroners eat while they do an autopsy?

I have seen this in movies and in TV. They are either already eating, un wrapping their lunch or offering food to the cop that wants info on the body. I would have though food within range of a... more

06/14/18

Proving continuity of a differentiable function

Hi I have been given a function f:(a,b)→R, which is differentiable on (a,b). How do I use this information to prove that f is also continuous on (a,b)? Thanks.

06/11/18

What is the definition of a regulated function?

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06/10/18

Proving continuity of a differentiable function.

Hi   I have been given a function f:(a,b)→R, which is differentiable on (a,b). How do I use this information to prove that f is also continuous on (a,b)?   Thanks.

06/06/18

How do I prove that a set of closed sets is itself closed.

Hi, I have been asked the following but am struggling.   Let {Ωa : a ∈ I} be an arbitrary family of closed sets Ωa ⊆ Rd with an index set I. Prove that   ∩     Ωa a ∈ I   is a closed... more

02/21/18

Tough analysis related question - please help!

Let A= a b           c  d   be an arbitrary 2x2 matrix. Let xn ⊆ R2 and suppose that (xn)→x for some x∈R2. Prove that (Axn)→Ax

02/11/18

Show that the set GL(n, R) of invertible n × n real matrices is open in the space of n × n matrices (metric spaces, Real analysis)

Show that the set GL(n, R) of invertible n × n real matrices is open in the space of n × n matrices, with the metric being the Euclidean metric in Rn^2 when a matrix is identified with a long, n2... more

01/14/18

Limits of sequences and series

How do I go about proving limits for given sequences and series, for example how would i prove that the limit when x tends to infinity of n^(1/n)=1?

01/12/18

Can someone help me prove the below by induction please? Thanks :)

Prove by induction:nΣ(q^i) = (q^(n+1)-1)/(q-1)i=0

11/28/17

How would I define a bounded series?

Please note that I am talking about a series and NOT  a sequence
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