3.1.2 Greatest hits from previous weeks

3.1.2.1 Calculate the 2D Fourier transform of an Image

https://mathematica.stackexchange.com/landing/r/newsletter?cta=question&id=29203

I am new to Mathematica, and using version 8.0.

I would like to calculate the 2D Fourier Transform of an Image with Mathematica and plot the magnitude and phase spectrum, as well as reconstruct the ...

asked by user8727 6 votes

answered by Nasser 28 votes

3.1.2.2 Finding Limits in several variables

https://mathematica.stackexchange.com/landing/r/newsletter?cta=question&id=21544

Is there a way to find a limit of a multivariable function, like

\[\lim _{(x,y)\to (0,0)} f(x,y)\]

with Mathematica?

When \(f\) is continuous, we can use

\[\lim _{(x,y)\to (0,0)} ... \]

asked by Dominic Michaelis 27 votes

answered by whuber 38 votes

3.1.2.3 Plotting the frequency spectrum of a data series using Fourier

https://mathematica.stackexchange.com/landing/r/newsletter?cta=question&id=18082

testData = Table[N@Sin[500 x], {x, 0, 100}]; 
ListLinePlot[Abs[Fourier[testData]], PlotRange -> Full]
 

Gives me

Which I do not expect because the Fourier Transform is FourierTransform..

asked by C. E. 12 votes

answered by KennyColnago 15 votes

3.1.2.4 Figuring when the minute and hour hand coincide on a clock

https://mathematica.stackexchange.com/landing/r/newsletter?cta=question&id=573

I would like to list all possible times in a 12-hour period, where the hour hand overlaps the minute hand completely. This is really a question about three distinct things - to be done in Mathematica ...

asked by Steve D 15 votes

answered by Verbeia 21 votes

3.1.2.5 Multivariable Taylor expansion does not work as expected

https://mathematica.stackexchange.com/landing/r/newsletter?cta=question&id=15023

The basic multivariable Taylor expansion formula around a point is as follows:

\[ f(\mathbf r + \mathbf a) = f(\mathbf r) + (\mathbf a \cdot \nabla )f(\mathbf r) + \frac {1}{2!}(\mathbf a \cdot ... \]

asked by matheorem 38 votes

answered by Jens 44 votes

3.1.2.6 Conversion of Sine to Cosine

https://mathematica.stackexchange.com/landing/r/newsletter?cta=question&id=67521

I’m solving equations with many Cosines and Sines. And I want to convert all the Sines to Cosines using trigonometric formulas such as cos(x)=sin(x+pi/2).

How can I do this?

asked by YongCheol Kwon 2 votes

answered by Sjoerd C. de Vries 1 vote

3.1.2.7 Labeling individual curves in Mathematica

https://mathematica.stackexchange.com/landing/r/newsletter?cta=question&id=4444

I need to create a plot for export and inclusion in a report. Is there a better way to label curves than PlotLegends? From what I’ve read and my personal experience, PlotLegends is pretty bad.

asked by Tianxiang Xiong 53 votes

answered by Artes 41 votes