calculus

The definition of a continuous function at a point ##x_0## is: $$\forall \epsilon >0 \exists \delta >0 \forall x(|x-x_0|<\delta \rightarrow |f(x)-f(x_0)|<\epsilon)$$ What would happen if we change it to another defintion as: ##\exists \epsilon >0 \forall \delta>0 \forall x(|x-x_0|<\delta... Read more

Mathematics > History and Overview Title:Simplifying and Refactoring Introductory Calculus View PDF HTML (experimental) Abstract:First year calculus is often taught in a way that is very burdensome to the student. Students have to memorize a diversity of processes for essentially performing the same task. However, many calculus processes can be simplified and streamlined so that fewer…

I was going through a worksheet and got presented with the following problem: Given $$ \int_0^\infty e^{-tx}\sin(x)\,\mathrm dx = \frac{1}{1+t^2}, $$ find the resulting equation after taking the ...

Hello! I have a problem in understanding why ##x=e^y## is inverse function of ##y=\int_1^x \frac{1}{t} dt##. This question seems strange but I'll try to describe my problem. As is known, the function ##y= \int_1^x \frac{1}{t} dt## is defined as ##y=ln(x)## but I can't understand why. In... Read more

Nearly everyone who as seen partial fraction decomposition was introduced to it as a way to compute integrals. If P(x) and Q(x) are polynomials, then you can break their ratio P(x)/Q(x) into a sum of terms that can each be integrated in closed form. As with most topics in a calculus class, partial fractions go by in […] The post Partial fraction decomposition first appeared on John D. Cook .

I am asked to give a mini lecture about improper integrals for students of Computer Science in their second semester. So they know the classical Riemann integral on compact intervals for bounded ...

symmetric monoidal (∞,1)-category of spectra analysis (differential/integral calculus, functional analysis, topology) metric space, normed vector space open ball, open subset, neighbourhood convergence, limit of a sequence compactness, sequential compactness … … The different types of square root partial functions on the real numbers that satisfy the functional equation on some subset of the real…

So I'm new to engineering and have studied some of the calculus but until now, I still have a hard time to understand what is exactly Differential Equations, what is it for and how can I use it in the future classes as an Engineering Physics student

analysis (differential/integral calculus, functional analysis, topology) metric space, normed vector space open ball, open subset, neighbourhood convergence, limit of a sequence compactness, sequential compactness … … constructive mathematics, realizability, computability propositions as types, proofs as programs, computational trinitarianism basic constructions: strong axioms further In real ana…