Integral calculus | Theorems in analysis | Theorems in calculus

Integration using Euler's formula

In integral calculus, Euler's formula for complex numbers may be used to evaluate integrals involving trigonometric functions. Using Euler's formula, any trigonometric function may be written in terms of complex exponential functions, namely and and then integrated. This technique is often simpler and faster than using trigonometric identities or integration by parts, and is sufficiently powerful to integrate any rational expression involving trigonometric functions. (Wikipedia).

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Euler's formulas, Rodrigues' formula

In this video I proof various generalizations of Euler's formula, including Rodrigues' formula and explain their 3 dimensional readings. Here's the text used in this video: https://gist.github.com/Nikolaj-K/eaaa80861d902a0bbdd7827036c48af5

From playlist Algebra

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Euler’s method - How to use it?

► My Differential Equations course: https://www.kristakingmath.com/differential-equations-course Euler’s method is a numerical method that you can use to approximate the solution to an initial value problem with a differential equation that can’t be solved using a more traditional method,

From playlist Differential Equations

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Euler's Identity (Equation)

This video given Euler's identity, reviews how to derive Euler's formula using known power series, and then verifies Euler's identity with Euler's formula http://mathispower4u.com

From playlist Mathematics General Interest

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''Euler's Formula'' for the Exponential and (Co)Sine Integrals!

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From playlist Number Theory

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Euler's formula: A cool proof

How to derive Euler's formula using differential equations! Free ebook http://bookboon.com/en/introduction-to-complex-numbers-ebook A somewhat new proof for the famous formula of Euler. Here is the famous formula named after the mathematician Euler. It relates the exponential with cosin

From playlist Intro to Complex Numbers

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Euler's Formula for the Quaternions

In this video, we will derive Euler's formula using a quaternion power, instead of a complex power, which will allow us to calculate quaternion exponentials such as e^(i+j+k). If you like quaternions, this is a pretty neat formula and a simple generalization of Euler's formula for complex

From playlist Math

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Proving Euler's Formula (4 of 4: Evaluating constants)

More resources available at www.misterwootube.com

From playlist Introduction to Complex Numbers

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Proving Euler's Formula (2 of 4: Differentiating both sides)

More resources available at www.misterwootube.com

From playlist Introduction to Complex Numbers

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B11 The improved Euler Formula

The improved Euler Formula using Python.

From playlist A Second Course in Differential Equations

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The Basel Problem Part 1: Euler-Maclaurin Approximation

This is the first video in a two part series explaining how Euler discovered that the sum of the reciprocals of the square numbers is π^2/6, leading him to define the zeta function, and how Riemann discovered the surprising connection between the zeroes of the zeta function and the distrib

From playlist Analytic Number Theory

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Mod-01 Lec-33 Predictor-Corrector Formulae

Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in

From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics

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James Arthur - Zeta functions and orbital integrals

We shall review the work of Z. Yun on zeta functions of orders, and of A. Altug on elliptic terms in the trace formula for GL(2). We shall then study the problem of Poisson summation for general linear groups. A suitable solution would be an important step in Langlands' proposed reformula

From playlist Reductive groups and automorphic forms. Dedicated to the French school of automorphic forms and in memory of Roger Godement.

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Ext-analogues of Branching laws – Dipendra Prasad – ICM2018

Lie Theory and Generalizations Invited Lecture 7.5 Ext-analogues of Branching laws Dipendra Prasad Abstract: We consider the Ext-analogues of branching laws for representations of a group to its subgroups in the context of p-adic groups. ICM 2018 – International Congress of Mathematic

From playlist Lie Theory and Generalizations

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Dipendra Prasad - Branching laws: homological aspects

By this time in the summer school, the audience will have seen the question about decomposing a representation of a group when restricted to a subgroup which is referred to as the branching law. In this lecture, we focus attention on homological aspects of the branching law. The lecture

From playlist 2022 Summer School on the Langlands program

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Convex Integration and Synthetic Turbulence - László Székelyhidi

Clay Research Conference Topic: Convex Integration and Synthetic Turbulence Speaker: László Székelyhidi Affiliation: Distinguished Visiting Professor, School of Mathematics Date: September 30, 2021  In the past decade convex integration has been established as a powerful and versatile

From playlist Mathematics

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Mandelbrot fractal zoom // featuring Euler bio

Mandelbrot fractal zoom // featuring Euler bio Come hang out and watch a fractal zoom through the Mandelbrot set. To celebrate Euler's contributions to mathematics, this video features a brief bio. of Leonhard Euler! ---------------------------------------------------------------------

From playlist Misc.

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Talk by Rahul Dalal (University of California, Berkeley, USA)

Statistics of Automorphic Representations Through the Stable Trace Formula

From playlist Seminars: Representation Theory and Number Theory

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An Euler System for the Symmetric Square of a Modular Form - Chris Skinner

An Euler System for the Symmetric Square of a Modular Form - Chris Skinner Joint IAS/PU Number Theory Seminar Topic: An Euler System for the Symmetric Square of a Modular Form Speaker: Chris Skinner Affiliation: Princeton University Date: February 16, 2023 I will explain a new construct

From playlist Mathematics

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Informal Proof of Euler's Formula (2 of 2: Trigonometric calculus)

If you enjoyed this, you can also check out my expanded series of videos that introduces Euler's Formula from "first principles" and concludes with Euler's Identity: https://www.youtube.com/playlist?list=PLHZZ0otaqNsWV01h2ZssT17Tj8fbtLiuM More resources available at www.misterwootube.com

From playlist Introduction to Complex Numbers

Related pages

Integral | Trigonometric functions | Rational function | Complex number | Integration by substitution | Integration by parts | Euler substitution | Partial fraction decomposition | Trigonometric substitution | Euler's formula