Parametric Integration is an Integration technique that was popularized by Richard Feynman but was known since Leibinz’s times. But this technique rarely gets discussed beyond a niche set of problems mostly in graduate school in the context of Contour Integration.
A while ago, having become obsessed with this technique I wrote this note on applying it to Laplace transform problems and it is now public for everyone to take a look.
The principle of Least/Stationary action remains central in modern physics and mathematics, being applied in thermodynamics, fluid mechanics, the theory of relativity, quantum mechanics, particle physics, and string theory.
If you ever find yourself trying to remember any one of those basic trigonometric formulas, the ideal starting point is the De Moivre’s formula:
Above we have given you some examples of identities that can be easily derived using this formula. In fact, most trigonometric relations can be obtained from this formula after performing some basic algebra.
Try to obtain your favorite identity using this method and let us know how that went. Have a good one!
But adding new gestures to the game reduces the odds of getting a tie but increases the complexity of the game. One popular five-weapon expansion is “rock-paper-scissors-Spock-lizard”, invented by Sam Kass and Karen Bryla.
What looks like a drip irrigation system on a farm land is actually a close up of your hands when sweating.
The reason why this visualization is fascinating is because modern techniques (like full field optical coherence tomography (FF-OCT) )in Forensics can extract sweat pores information from the fingerprint offering more information about the perpetrator crucial to the investigation.
hits only the palm and not the third(ring) finger, there will be a significant
reduction in the total ‘snap’ sound. Try it out!
When you get tired of snapping your fingers, try cracking your knucles. The sharp sound that you hear is caused by the collapse of a cavitation bubble (see image above) in the sinuovial fluid present at the joint.
Fingers, shadows and the transit of Venus
If you are wondering how on earth can all of these words be possibly related, then try answering this question:
When you bring two of your fingers closer in the back drop of a light source, long before your fingers actually touch, the edges magically seem to touch each other.
When one is solving problems on the two dimensional plane and you are using polar coordinates, it is always a challenge to remember what the velocity/acceleration in the radial and angular directions () are. Here’s one failsafe way using complex numbers that made things really easy :
From the above expression, we can obtain and
From this we can obtain and with absolute ease.
Something that I realized only after a mechanics course in college was done and dusted but nevertheless a really cool and interesting place where complex numbers come in handy!