Finite differences | Non-Newtonian calculus | Linear operators in calculus | Mathematical tables | Mathematical analysis
In discrete calculus the indefinite sum operator (also known as the antidifference operator), denoted by or , is the linear operator, inverse of the forward difference operator . It relates to the forward difference operator as the indefinite integral relates to the derivative. Thus More explicitly, if , then If F(x) is a solution of this functional equation for a given f(x), then so is F(x)+C(x) for any periodic function C(x) with period 1. Therefore, each indefinite sum actually represents a family of functions. However, due to the Carlson's theorem, the solution equal to its Newton series expansion is unique up to an additive constant C. This unique solution can be represented by formal power series form of the antidifference operator: . (Wikipedia).
Worldwide Calculus: Sums and Differences
Lecture on 'Sums and Differences' from 'Worldwide Integral Calculus' and 'Worldwide AP Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Continuous Sums: the Definite Integral
Worldwide Calculus: The Definite Integral (part A)
Lecture on 'The Definite Integral (part A)' from 'Worldwide Integral Calculus' and 'Worldwide AP Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Continuous Sums: the Definite Integral
Find the paticular solution given a reciprocal function and condition
👉 Learn how to find the particular solution to the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as indefinite integral or as a definite integral. A definite integral is an
From playlist The Integral
Worldwide Calculus: Numerical Techniques for Approximating Integrals
Lecture on 'Numerical Techniques for Approximating Integrals' from 'Worldwide Integral Calculus' and 'Worldwide AP Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Continuous Sums: the Definite Integral
Indefinite Integral of a Vector-Valued Function Example 1
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Indefinite Integral of a Vector-Valued Function Example 1
From playlist Calculus
Find the integral with a given condition
👉 Learn how to find the particular solution to the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as indefinite integral or as a definite integral. A definite integral is an
From playlist The Integral
Definite Integral Using Limit Definition
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definite Integral Using Limit Definition. In this video we compute a definite integral using the limit definition.
From playlist Calculus
Indefinite integrals: sums & multiples | AP Calculus AB | Khan Academy
An indefinite integral of a sum is the same as the sum of the integrals of the component parts. Constants can be "taken out" of integrals. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-ab/ab-antiderivatives-ftc/ab-reverse-power-ru
From playlist Antiderivatives and the fundamental theorem of calculus | AP Calculus BC | Khan Academy
Antiderivative of a Polynomial
Calculus: We note rules for the antiderivative of a sum and scalar multiple. With these, we are able to find the indefinite integral of any polynomial. We also give an example with negative powers of x and a cruder method for checking our answer.
From playlist Calculus Pt 2: Basic Integration
Calculus 1 (Stewart) Ep 35, Final Review (Dec 10, 2021)
This is a recording of a live class for Math 1171, Calculus 1, an undergraduate course for math majors (and others) at Fairfield University, Fall 2021. The textbook is Stewart. PDF of the written notes, and a list of all episodes is at the class website. Class website: http://cstaecker.f
From playlist Math 1171 (Calculus 1) Fall 2021
Indefinite Integral of a Vector-Valued Function Example 2
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Indefinite Integral of a Vector-Valued Function Example 2
From playlist Calculus
Evaluating Indefinite Integrals
We now have a pretty good grasp of what integration is, and how to do it. But what about when we see an integral without any limits of integration listed? This is extremely common, and these are called indefinite integrals. These won't be any harder to evaluate, because we just take the an
From playlist Calculus
Carsten Schneider, Johannes Kepler University An Algorithmic Difference Ring Theory for Symbolic Summation Inspired by Karr's pioneering work (1981) we developed an algorithmic difference ring theory for symbolic summation that enables one to rephrase indefinite nested sums and products
From playlist Fall 2019 Kolchin Seminar in Differential Algebra
Introduction to Indefinite Integration: Theory and Definitions
Introduction to Indefinite Integration: Theory and Definitions
From playlist Calculus 1
Math 031 Spring 2018 012618 Fundamental Theorem of Calculus
Finishing the Calculus I review: recall indefinite integral. Brief sketch of definition of definite integrals. Statement of Fundamental Theorem of Calculus II. Examples. Statement of Fundamental Theorem of Calculus I. Proof.
From playlist Course 3: Calculus II (Spring 2018)
Definite Integration by Trigonometric Substitution Calculus 2 BC
I show two ways to work through a definite integral that involves Trigonometric Substitution. I would like to send out a HUGE Shout Out to my awesome viewer or viewers that Closed Captioned this lesson for me. Your help touches my heart and I am greatly appreciative of all your effort. I
From playlist Calculus 2
Koen van den Dungen: Indefinite spectral triples and foliations of spacetime
Motivated by Dirac operators on Lorentzian manifolds, we propose a new framework to deal with non-symmetric and non-elliptic operators in noncommutative geometry. We provide a definition for indefinite spectral triples, and show that these correspond bijectively with certain pairs of spect
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Learn how to determine the paticular solution with the given condition
👉 Learn how to find the particular solution to the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as indefinite integral or as a definite integral. A definite integral is an
From playlist The Integral