The Number `E' by Tanvi Jain
Offered By: International Centre for Theoretical Sciences via YouTube
Course Description
Overview
Syllabus
The number ' e'
What is e? Is this just a number
The first hint of
How will you solve this? We will need to solve for the equation:
A question on compound interest
If the amount is compounded twice, each time at the interest rate of 50%.
Observations:
Let's see...
Logarithm and John Napier
So the problem of multiplication and division can be reduced to that of addition and subtraction.
Squaring a hyperbola
Coming to the early seventeenth century
Area of the region bounded by y = x", x = and x = a.
Similarly, the area of the region bounded by the curves y = x-",
A look at the hyperbola
The appearance of logarithm
The series for and the work of Newton
which implies ao = 0. Comparing the coefficient of y.
Derivative of an exponential function
Derivative of bx
The "natural "exponent Derivative of any exponential function is a constant multiple of the function itself.
The notation for the natural exponent
Is an integer?
rational or irrational
Since is not an integer, q 2 2. Hence q + 1 2 3.
Euler's proof of the irrationality of
The exponential function on complex numbers
Occurrences of
e'" Paradox
Taught by
International Centre for Theoretical Sciences
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