Here's an idea for anyone in search for a project: Some papers define a lot of ad-hoc variable symbols. It would be easier to follow them if one could hover over a symbol used in an equation and see its definition, just like in an IDE.
which generates LaTex from headings, paragraphs and other document controls. And it also generates formulas from descriptions. I copied some text from my article and got a fully functional LaTex with formulas:
Fundamental Theorem of Calculus
The Fundamental Theorem of Calculus links differentiation and integration. It consists of two parts:
If f of x is continuous on the interval [a, b] and F of x is its antiderivative, then:
integral from a to b of f of x with respect to x equals F of b minus F of a.
If F of x is defined as an integral function:
F of x equals integral from a to x of f of t with respect to t,
then F of x is differentiable, and its derivative is the original function:
d by dx of F of x equals f of x.
Taylor Series Expansion
A function f of x can be expressed as an infinite Taylor series around x equals a:
summation from n equals zero to infinity of (nth derivative of f at a) divided by (n factorial) times (x minus a) to the power of n.
For example, the Taylor series expansion of e to the power of x at x equals zero is:
summation from n equals zero to infinity of (x to the power of n) divided by (n factorial), which expands as 1 plus x plus (x squared divided by 2 factorial) plus (x cubed divided by 3 factorial) and so on.
Complex Line Integrals
In complex analysis, contour integrals play a crucial role. The contour integral of a function f of z along a curve C is given by:
closed contour integral along C of f of z with respect to z.
A key result is Cauchy's Integral Formula:
f of a equals (1 divided by 2 pi i) times the closed contour integral along C of (f of z divided by (z minus a)) with respect to z,
which holds if f of z is analytic inside and on C, and a is within C.
https://products.aspose.ai/pdf/form-generator
which generates LaTex from headings, paragraphs and other document controls. And it also generates formulas from descriptions. I copied some text from my article and got a fully functional LaTex with formulas:
Fundamental Theorem of Calculus
The Fundamental Theorem of Calculus links differentiation and integration. It consists of two parts:
If f of x is continuous on the interval [a, b] and F of x is its antiderivative, then:
integral from a to b of f of x with respect to x equals F of b minus F of a.
If F of x is defined as an integral function:
F of x equals integral from a to x of f of t with respect to t,
then F of x is differentiable, and its derivative is the original function:
d by dx of F of x equals f of x.
Taylor Series Expansion
A function f of x can be expressed as an infinite Taylor series around x equals a:
summation from n equals zero to infinity of (nth derivative of f at a) divided by (n factorial) times (x minus a) to the power of n.
For example, the Taylor series expansion of e to the power of x at x equals zero is:
summation from n equals zero to infinity of (x to the power of n) divided by (n factorial), which expands as 1 plus x plus (x squared divided by 2 factorial) plus (x cubed divided by 3 factorial) and so on.
Complex Line Integrals
In complex analysis, contour integrals play a crucial role. The contour integral of a function f of z along a curve C is given by:
closed contour integral along C of f of z with respect to z.
A key result is Cauchy's Integral Formula:
f of a equals (1 divided by 2 pi i) times the closed contour integral along C of (f of z divided by (z minus a)) with respect to z,
which holds if f of z is analytic inside and on C, and a is within C.