Simple to understand derivations similar to the Taylor Series

In summary, the conversation discusses the speaker's lack of knowledge in mathematics and their recent discovery of the derivation of the Taylor series. They ask if there are other mathematical derivations that are similarly easy to understand, and suggestions are made for topics that would be useful to learn such as the Fourier series, derivatives, integrals, and linear algebra.
  • #1
Annoying Twit
1
0
That I don't even know in which forum to post this questions shows my gaping lack of mathematics knowledge.

I've just learned the derivation of the Taylor series. I'm slapping myself on the head as it's so mind-bogglingly simple, but I never learned it. The Taylor series was just 'maths magic' to me.

Are there other mathematical derivations based on 'assume the result and work backwards' that are similarly easy to understand?

Maths is a wide field. If there are lots of options, then concepts useful in understanding digital signal processing such as the Fourier series would be good choices.
 
Physics news on Phys.org
  • #2
Other topics like derivatives, integrals, and linear algebra would also be helpful. You can find a lot of resources online to learn these topics. Good luck!
 

What is the Taylor Series?

The Taylor Series is a mathematical tool used to represent a function as an infinite sum of terms that are related to the derivatives of the function at a single point. It is named after the mathematician Brook Taylor.

How is the Taylor Series derived?

The Taylor Series is derived using the concept of a Maclaurin Series, which is a special case of the Taylor Series where the point of expansion is x = 0. The Maclaurin Series can be derived using the Taylor Series formula and the properties of derivatives.

Why is the Taylor Series important?

The Taylor Series is important because it allows us to approximate complicated functions with simpler polynomial expressions. It is also used in many areas of mathematics and science including physics, engineering, and economics.

What is the difference between the Taylor Series and the Maclaurin Series?

The main difference between the Taylor Series and the Maclaurin Series is the point of expansion. The Taylor Series can be expanded around any point, while the Maclaurin Series is specifically expanded around x = 0.

How accurate is the Taylor Series approximation?

The accuracy of the Taylor Series approximation depends on the number of terms used in the series and the behavior of the function. The more terms that are included, the closer the approximation will be to the actual function. However, the Taylor Series may not converge for all functions, so its accuracy may be limited in some cases.

Similar threads

Link between Z-transform and Taylor series expansion
    • Calculus and Beyond Homework Help
Replies
2
Views
1K
I What's the point of Taylor/Maclaurin series?
    • Calculus
Replies
17
Views
3K
B Why do I not understand what seems to be basic Calculus?
    • Calculus
Replies
11
Views
2K
How do I use a taylor series expansion to find effective spring constant
    • Introductory Physics Homework Help
Replies
17
Views
8K
Taylor Series about exp(-1/x^2)
    • Calculus and Beyond Homework Help
Replies
6
Views
10K
Taylor polynomial/series, series, function series
    • STEM Academic Advising
Replies
10
Views
1K
Understanding the Taylor Series in Euler's Method
    • Calculus and Beyond Homework Help
Replies
3
Views
3K
Derive Multivariable Taylor Series
    • Calculus
Replies
4
Views
7K
MHB How to use Taylor series to represent any well-behaved f(x)
    • Calculus
Replies
7
Views
2K
Calculus Will this calculus book 'clear' me for mechanics textbooks?
    • Science and Math Textbooks
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top