Euler Identity

Group Members✘ Hamza Farooq 14-

EE(E&T)-051✘ M Ahmad Kamal 14-

EE(E&T)-045✘ Arslan Riaz 14-

EE(E&T)-047

Euler’s identity

Table OF Contents✘ Introduction of Euler’s identity.✘ What is Euler’s identity?✘ Why Euler’s identity required?✘ Practical applications.✘ Uses in Electrical Engineering.✘ Conclusion✘ References

Introduction✘ Leonhard Euler(1710-1783).✘ Wrote a total of 886 works.✘ The epitome of his

mathematical analysis is summed up in his formula.

✘  According to 1800s mathematician Benjamin Peirce:

“It is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth”.

What is Euler’s identity✘ e is  the base of natural logarithms.✘  iota is the imaginary unit, which

satisfies i2 = −1, ✘  pi the ratio of the circumference of a circle

to its diameter .✘ The  number0, the additive identity.✘ The  number1, the multiplicative identity

✘ Euler's Identity is also sometimes called Euler's Equation.

Continue.✘ The identity is a special case of 

Euler's formula from complex analysis, which states that

for any real number x. In particular

Since

which gives the identity.

Why We need Euler identity?

✘ . iota is the imaginary unit, which satisfies i2 = −1

✘e is  the base of natural logarithms.

✘ e^i (imaginary power of exponent) .

Applications✘ Euler’s formula represents polar

form of a complex number.✘ Euler’s formula provides us a

convenient way to move in a circle. ✘ Well in differential equations, which

may be differential equations solving phenomena that we see in nature (such as the weather), you may find that you need Euler's identity to simplify systems that have complex solutions.

Continue

✘ It is used in so many contexts that it is like asking for the applications of matrix multiplication.

✘ If you “don't understand why it is useful”, try picturing electrical engineering without it. Or any other branch of science, which studies ((sinusoidal)) signals of any kind ((acoustic, visual, magnetic, etc)

Continue:

✘ The Sylvester-Gallai Theorem.✘ Pick’s Theorem.

.

Uses in Electrical engineering✘ Euler’s formula abounds in

electronics and engineering. Underlying electric functions and laws of capacitance and reactance is the famous identity.

✘ It is implemented in linear, time-invariant function input-output machines, otherwise known as LTI boxes.

✘ The particular use of Euler is in electrical engineering is in case of .

Continued:

✘ The trigonometric functions and e raised to powers involving imaginary numbers is a form of Euler’s Identity that electrical engineers use regularly.

✘ The context of this equation is bandwidths mainly in radio station wavelengths.

Continued:

✘ Ideally, engineers could put a radio signal through an LTI (Linear time-invariant) box and get a “zero phase distortion” meaning that a signal is perfectly unaltered as it passes through the filter. And for obvious reasons, the less a sound wave is distorted as it is broadcast, the better is the quality.

Refrences:

✘ http://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/

✘ http://www.livescience.com/51399-eulers-identity.html

✘ http://www.mathscareers.org.uk/article/beautiful-equation/

✘ http://tetrahedral.blogspot.com/2011/01/our-jewel-eulers-formula-and-eulers.html

✘ https://www.researchgate.net/post/What_is_Special_in_Eulers_identity_e_ipi_102

Credits

Special thanks to:✘ Presentation template by Ahmad

Kamal✘ Photographs by Ahmad Kamal

THANKS!Any questions?