Dive into a comprehensive 1-hour 15-minute video lecture exploring the natural logarithm and its significance in mathematics. Uncover the reasons behind the "natural" aspect of ln(x) through a series of questions, answers, and in-depth explanations. Explore prime numbers in infinite geometric series, their relationship with the natural logarithm, and the Basel problem. Examine families of curves, imaginary exponentials, and derivatives of exponential terms. Learn about the Taylor Series for e^x, derivatives of polynomial terms, and the derivative of the natural logarithm using graphical representations. Investigate the Euler-Mascheroni constant and connect various mathematical expressions. Benefit from a detailed timeline, related video recommendations, and information on contributing translated subtitles to enhance accessibility.
Overview
Syllabus
- Question 1.
- Answer 1.
- Prime nos. in Infinite Geometric Series (Basel problem) and their relationship with Natural logarithm.
- More examples of prime numbers in infinite series and their relationship with ln.
- Question 2.
- Answer 2 and explanation using ln.
- Question 3 and families of curves.
- Answer 3 and explanation.
- Imaginary exponential.
- Derivatives of exponential terms.
- Why derivative of e^t is the same as that e^t itself?.
- Question 4.
- Answer 4 and explanation using Python.
- Taylor Series for e^x.
- Derivatives of polynomial terms/Derivatives of e^x.
- Derivative of natural logarithm using graph .
- Question 5.
- Answer 5 and explanation .
- Euler–Mascheroni constant.
- Question 6.
- Connecting dots to the familiarity of different expression in math.
Taught by
3Blue1Brown
