Mathematicians' Original Work: Riemann & Taylor Theorems

In summary, the Riemann and Taylor theorems are two important theorems in mathematics that deal with functions and their derivatives. The Riemann theorem states that a continuous function on a closed interval is also integrable on that interval, while the Taylor theorem states that any function can be approximated by a polynomial of a certain degree around a given point. Both theorems were discovered by mathematicians in the 18th and 19th centuries and have numerous applications in various fields such as physics, engineering, and economics. They are still relevant today and are considered fundamental theorems in calculus and analysis. However, there are limitations and exceptions to these theorems, such as the requirement for continuity and differentiability,
  • #1
Winzer
598
0
Can anyone provide me with a website that has copies of the original works of Riemann, Taylor, famous mathematicians. I am looking for papers on proved theorems.
 
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  • #2
I don't know about a website but God Created the Integers by Steven Hawking has most of the famous original works in it.
 
  • #3
For Riemann, his papers (in German) can be found at The Electronic Library of Mathematics, http://www.emis.de/classics/Riemann/
 

Related to Mathematicians' Original Work: Riemann & Taylor Theorems

1. What are the Riemann and Taylor theorems?

The Riemann and Taylor theorems are two important theorems in mathematics that deal with functions and their derivatives. The Riemann theorem states that if a function is continuous on a closed interval, then it is also integrable on that interval. The Taylor theorem, on the other hand, states that any function can be approximated by a polynomial of a certain degree around a given point.

2. Who discovered the Riemann and Taylor theorems?

The Riemann theorem was discovered by German mathematician Bernhard Riemann in the 19th century. The Taylor theorem was discovered by English mathematician Brook Taylor in the 18th century.

3. What are the applications of the Riemann and Taylor theorems?

The Riemann theorem has many applications in physics and engineering, particularly in the fields of mechanics and electromagnetism. The Taylor theorem is commonly used in numerical analysis and approximation methods, and is also applied in fields such as physics, engineering, and economics.

4. Are the Riemann and Taylor theorems still relevant today?

Yes, both theorems are still very relevant today and are widely used in various fields of mathematics and its applications. They are considered fundamental theorems that have greatly influenced the development of calculus and analysis.

5. Are there any limitations or exceptions to the Riemann and Taylor theorems?

Like any theorem, there are limitations and exceptions to the Riemann and Taylor theorems. For example, the Riemann theorem does not apply to functions that are discontinuous on the given interval. The Taylor theorem may also not hold for functions that are infinitely differentiable. Additionally, both theorems have certain requirements and conditions that must be met in order for them to be applied.

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