euler
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Leonhard Euler was a Swiss mathematician and physicist born in 1707 in Basel, Switzerland who made seminal contributions to many areas of mathematics. Some of his key accomplishments included establishing the fundamental relationship between trigonometric and complex exponential functions known as Euler's identity, developing graph theory and topology, and making influential discoveries in mechanics and astronomy. He spent most of his career working in Berlin and Saint Petersburg, where he was a member of several academic institutions. Euler authored over 800 papers and books on diverse topics in pure and applied mathematics, physics, astronomy and engineering.
![Born 15 April 1707
Basel, Switzerland
Died 18 September 1783(aged 76)
[OS: 7 September 1783]
Saint Petersburg, Russian
Empire
Residence Kingdom of Prussia, Russian
Empire
Switzerland
Fields Mathematics and physics
Institutions Imperial Russian Academy of
Sciences
Berlin Academy
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euler
- 3. Born 15 April 1707 Basel, Switzerland Died 18 September 1783(aged 76) [OS: 7 September 1783] Saint Petersburg, Russian Empire Residence Kingdom of Prussia, Russian Empire Switzerland Fields Mathematics and physics Institutions Imperial Russian Academy of Sciences Berlin Academy http://alltypeim.blogspot.in/
- 4. Euler's formula, named after Leonhard Euler, is a mathematical formula incomplex analysis that establishes the fundamental relationship between thetrigonometric functions and the complex exponential function. Euler's formula states that, for any real number x: http://alltypeim.blogspot.in/
- 6. Homothetic function .allfor0iforallfor0is thatmonotonic,strictlyisfunctiontheiffunction homotheticaisthenfunction,shomogeneou aisifThisfunctin.shomogeneoua ofationtransformmontonicaisfunctionhomotheticA 21 yg'(y)yg'(y) g(y) g(y)z ),x,,xf(xy n 種 http://alltypeim.blogspot.in/
- 7. Any function f(x) that possesses the characteristic mapping: is said to be homogeneous, with respect to x, to degree 1. By the same token, if f(x) obeys the mapping: then f(x) is homogeneous to degree k. In general, a multivariable function f(x1,x2,x3,) is said to be homogeneous of degree k in variables xi(i=1,2,3,) if for any value of 了, For example, let us consider the function: http://alltypeim.blogspot.in/
- 8. How do we find out if this particular function is homogeneous, and if it is, to what degree? We evaluate this function at x=了x and y= 了y to obtain: http://alltypeim.blogspot.in/
- 9. partial derivatives , , and . Hence, to complete the discussion on homogeneous functions, it is useful to study the mathematical theorem that establishes a relationship between a homogeneous function and its partial derivatives. This isEulers theorem. http://alltypeim.blogspot.in/