Integral calculus | Multivariable calculus

Multiple integral

In mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z). Integrals of a function of two variables over a region in (the real-number plane) are called double integrals, and integrals of a function of three variables over a region in (real-number 3D space) are called triple integrals. For multiple integrals of a single-variable function, see the Cauchy formula for repeated integration. (Wikipedia).

Multiple integral
Video thumbnail

Multivariable Calculus | Double integrals over rectangular regions.

We give some example of evaluating double integrals over recetangular regions. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Multivariable Calculus | Multiple Integrals

Video thumbnail

Multivariable Calculus | A special double integral.

We describe a special case of a double integral over a rectangular region. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Multivariable Calculus | Multiple Integrals

Video thumbnail

What does a double integral represent?

► My Multiple Integrals course: https://www.kristakingmath.com/multiple-integrals-course It can be difficult to visualize what a double integral represents, which is why in this video we’ll be answering the question, “What am I finding when I evaluate a double integral?” In order to answ

From playlist Calculus III

Video thumbnail

What is a Double Integral?

Have you ever wondered what a double integral is and what it has to do with cake? If so, watch this video and find out. Here I show step-by-step how to calculate a double integral, which is the multivariable calculus analog of an integral, enjoy! Double and Triple Integrals: https://www.y

From playlist Double and Triple Integrals

Video thumbnail

Multivariable Calculus | Triple integrals with polar coordinates.

We give an example of a triple integral that is calculated using cylindrical coordinates -- that is and iterated single and double integral where the double integral uses polar coordinates. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Multivariable Calculus | Multiple Integrals

Video thumbnail

What does a triple integral represent?

► My Multiple Integrals course: https://www.kristakingmath.com/multiple-integrals-course Skip to section: 0:15 // Recap of what the double integral represents 1:22 // The triple integral has two uses (volume and mass) 1:45 // How to use the triple integral to find volume 8:59 // Why the

From playlist Calculus III

Video thumbnail

Simple double integral

Download the free PDF http://tinyurl.com/EngMathYT This video shows how to integrate over rectangles. The ideas use double integrals and are seen in university mathematics.

From playlist Several Variable Calculus / Vector Calculus

Video thumbnail

Math 032 Multivariable Calculus 14 102214: Integration of Functions of Several Variables, ct'd.

Integration of area integrals over "simple" (non-rectangular) regions; describing regions as x-simple (y-simple); changing the order of integration; simplifying a double iterated integral by changing the order of integration; statement of the Mean Value Theorem for double integrals.

From playlist Course 4: Multivariable Calculus (Fall 2014)

Video thumbnail

Teun van Nuland: The spectral action expanded in Yang-Mills and Chern-Simons forms

Talk by Teun van Nuland in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on December 15, 2020

From playlist Global Noncommutative Geometry Seminar (Europe)

Video thumbnail

How to Integrate Easier

hi, in this video I'm showing you a method I haven't seen that often regarding the manipulation of the differential of any integral. The concept described in it should help develop a better understanding of the relationship of integration and differentiation. I hope it has been helpful! C

From playlist Summer of Math Exposition Youtube Videos

Video thumbnail

Part V: Multiple Integration, Lec 5 | MIT Calculus Revisited: Multivariable Calculus

Part V: Multiple Integration, Lecture 5: Green's Theorem Instructor: Herbert Gross View the complete course: http://ocw.mit.edu/RES18-007F11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT Calculus Revisited: Multivariable Calculus

Video thumbnail

Georg Regensburger, University of Kassel

March 22, Georg Regensburger, University of Kassel Integro-differential operators with matrix coefficients

From playlist Spring 2022 Online Kolchin seminar in Differential Algebra

Video thumbnail

Iterated Shimura integrals - Yuri Manin

Geometry and Arithmetic: 61st Birthday of Pierre Deligne Yuri Manin Northwestern University October 19, 2005 Pierre Deligne, Professor Emeritus, School of Mathematics. On the occasion of the sixty-first birthday of Pierre Deligne, the School of Mathematics will be hosting a four-day con

From playlist Pierre Deligne 61st Birthday

Video thumbnail

Erik Panzer - Feynman integrals and hyperlogarithms

Many Feynman integrals evaluate to multiple polylogarithms and their special values like multiple zeta values. One particularly successful approach to understand this phenomenon is due to Francis Brown and uses iterated integrals called hyperlogarithms as a basis for the arising transcende

From playlist 5e Séminaire Itzykson : "Feynman Integrals"

Video thumbnail

Visual Group Theory, Lecture 7.1: Basic ring theory

Visual Group Theory, Lecture 7.1: Basic ring theory A ring is an abelian group (R,+) with a second binary operation, multiplication and the distributive law. Multiplication need not commute, nor need there be multiplicative inverses, so a ring is like a field but without these properties.

From playlist Visual Group Theory

Video thumbnail

Lecture 23 | The Fourier Transforms and its Applications

Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood lectures on linear systems, focusing on linear time and variance systems. The Fourier transform is a tool for solving physical problems. In thi

From playlist Lecture Collection | The Fourier Transforms and Its Applications

Video thumbnail

Federico Zerbini - Amplitudes de cordes et équations de type Knizhnik–Zamolodchikov

Les amplitudes de diffusion nous donnent la probabilité d'interaction des particules élémentaires. L'approche perturbative nous amène à considérer une série dont les coefficients sont calculés par les intégrales de Feynman. En théorie des cordes, un tel développement perturbatif est indexé

From playlist 10e séminaire ITZYKSON – Valeurs zêta multiples et fonctions modulaires de graphes en théorie des cordes

Video thumbnail

Multivariable Calculus | Transformations of the plane.

Working towards a formula for change of variables in multiple integrals, we introduce the notion of a one to one transformation of the plane. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Multivariable Calculus | Multiple Integrals

Related pages

Jacobian matrix and determinant | Fubini's theorem | Change of variables | Antiderivative | Iterated integral | Continuous function | Orthographic projection | Volume | Riemann sum | Stokes' theorem | Multivariable calculus | Grigorii Fichtenholz | Maxwell's equations | Electric charge | Domain of a function | Function of several real variables | Conditional convergence | Divergence theorem | Density | Lebesgue integration | Tetrahedron | Simplex | Pythagorean trigonometric identity | Rectangle | Bounded function | Volume element | Signed measure | Real analysis | Polar coordinate system | Ball (mathematics) | Bounded set | Cartesian coordinate system | Improper integral | Even and odd functions | Limit (mathematics) | Mathematics | Maxima (software) | Prism (geometry) | Sphere | Spherical coordinate system | Charge density | Euclidean space | Cartesian product | Wacław Sierpiński | Constant function | Radius | Cauchy formula for repeated integration | Area | Inequality (mathematics) | Measure (mathematics) | Volume integral | Hyperrectangle | Borel measure | Moment of inertia | Green's theorem | Cylindrical coordinate system