Polar Coordinates Formula In this video, I present a cool version of polar coordinates that is not taught in class. It is not only more elegant, but it also makes calculations with polar coordinates much more elegant. It can even be generalized to what is called the coarea formula. Enjoy!
From playlist Real Analysis
In this sequel to the Laplace-video, I solve Poisson’s equation by showing that Phi convolved with f solves the PDE (where Phi is the fundamental solution of Laplace's equation). Along the way we discover the coarea/onion formula, as well as a n-dimensional version of integration by parts.
From playlist Partial Differential Equations
Using sum and difference formula to find the exact value with cosine
👉 Learn how to evaluate the cosine of an angle in radians using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all
From playlist Sum and Difference Formulas
Evaluate cosine of an angle using the difference of two angles formula
👉 Learn how to evaluate the cosine of an angle in radians using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all
From playlist Sum and Difference Formulas
Surface area of sphere in n dimensions
In this sequel to the video "Volume of a ball in n dimensions", I calculate the surface area of a sphere in R^n, using a clever trick with the Gaussian function exp(-1/2 |x|^2). Along the way, we discover the coarea formula, which is the analog of polar coordinates, but in n dimensions. Fi
From playlist Cool proofs
How to evaluate for the cosine of an angle using the sum formula
👉 Learn how to evaluate the cosine of an angle in radians using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all
From playlist Sum and Difference Formulas
Pre-Calculus - Using the difference of angles for cosine to evaluate for an angle cos(225-30)
👉 Learn how to evaluate the cosine of an angle in radians using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all
From playlist Sum and Difference Formulas
Definition of spherical coordinates | Lecture 33 | Vector Calculus for Engineers
We define the relationship between Cartesian coordinates and spherical coordinates; the position vector in spherical coordinates; the volume element in spherical coordinates; the unit vectors; and how to differentiate the spherical coordinate unit vectors. Join me on Coursera: https://www
From playlist Vector Calculus for Engineers
How to evaluate for cosine using the sum and difference identities
👉 Learn how to evaluate the cosine of an angle in radians using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all
From playlist Sum and Difference Formulas
Write a Cylindrical Equations in Rectangular Form
This video provides 4 examples on how to write a cylindrical equation in rectangular form. http://mathispower4u.com
From playlist Triple Integrals in Cylindrical and Spherical Coordinates / Change of Variables (Jacobian)
Evaluate using the sum formula of two angles of cosine
👉 Learn how to evaluate the cosine of an angle in radians using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all
From playlist Sum and Difference Formulas
Evaluate cosine using the sum and difference formula
👉 Learn how to evaluate the cosine of an angle in radians using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all
From playlist Sum and Difference Formulas
Erik van Erp: Lie groupoids in index theory 1
The lecture was held within the framework of the Hausdorff Trimester Program Non-commutative Geometry and its Applications. 9.9.2014
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Lipschitz rigidity for scalar curvature - Bernhard Hanke
Analysis & Mathematical Physics Topic: Lipschitz rigidity for scalar curvature Speaker: Bernhard Hanke Affiliation: University of Augsburg, Member, School of Mathematics Date: October 05, 2022 Lower scalar curvature bounds on spin Riemannian manifolds exhibit remarkable rigidity properti
From playlist Mathematics
Pierre Bieliavsky: Universal deformation twists from evolution equations
A universal twist (or "Drinfel'd Twist") based on a bi-algebra B consists in an element F of the second tensorial power of B that satisfies a certain cocycle condition. I will present a geometrical method to explicitly obtain such twists for a quite large class of examples where B underlie
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Julie Rowlett: A Polyakov formula for sectors
Abstract: Polyakov's formula expresses a difference of zeta-regularized determinants of Laplace operators, an anomaly of global quantities, in terms of simple local quantities. Such a formula is well known in the case of closed surfaces (Osgood, Philips, & Sarnak 1988) and surfaces with sm
From playlist Women at CIRM
Jean Michel BISMUT - Fokker-Planck Operators and the Center of the Enveloping Algebra
The heat equation method in index theory gives an explicit local formula for the index of a Dirac operator. Its Lagrangian counterpart involves supersymmetric path integrals. Similar methods can be developed to give a geometric formula for semi simple orbital integrals associated with the
From playlist Integrability, Anomalies and Quantum Field Theory
Lecture 17: Discrete Curvature II (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
CCSS What is the difference between Acute, Obtuse, Right and Straight Angles
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships