Differential forms | Differential geometry
In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many applications, especially in geometry, topology and physics. For instance, the expression f(x) dx is an example of a 1-form, and can be integrated over an interval [a, b] contained in the domain of f: Similarly, the expression f(x, y, z) dx ∧ dy + g(x, y, z) dz ∧ dx + h(x, y, z) dy ∧ dz is a 2-form that can be integrated over a surface S: The symbol ∧ denotes the exterior product, sometimes called the wedge product, of two differential forms. Likewise, a 3-form f(x, y, z) dx ∧ dy ∧ dz represents a volume element that can be integrated over a region of space. In general, a k-form is an object that may be integrated over a k-dimensional manifold, and is homogeneous of degree k in the coordinate differentials On an n-dimensional manifold, the top-dimensional form (n-form) is called a volume form. The differential forms form an alternating algebra. This implies that and This alternating property reflects the orientation of the domain of integration. The exterior derivative is an operation on differential forms that, given a k-form , produces a (k+1)-form This operation extends the differential of a function (a function can be considered as a 0-form, and its differential is ) This allows expressing the fundamental theorem of calculus, the divergence theorem, Green's theorem, and Stokes' theorem as special cases of a single general result, the generalized Stokes theorem. Differential 1-forms are naturally dual to vector fields on a differentiable manifold, and the pairing between vector fields and 1-forms is extended to arbitrary differential forms by the interior product. The algebra of differential forms along with the exterior derivative defined on it is preserved by the pullback under smooth functions between two manifolds. This feature allows geometrically invariant information to be moved from one space to another via the pullback, provided that the information is expressed in terms of differential forms. As an example, the change of variables formula for integration becomes a simple statement that an integral is preserved under pullback. (Wikipedia).
Find the particular solution given the conditions and second derivative
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Solve Differential Equation (Particular Solution) #Integration
Introduction to Differential Equations
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Introduction to Differential Equations - The types of differential equations, ordinary versus partial. - How to find the order of a differential equation.
From playlist Differential Equations
Differential Forms | What is a differential m-form?
We define the notion of a differential m-form and look at some examples. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal Website: http://www.michael-penn.net Randolph College Math: http://www.randolphcollege.edu/mathematics/ Research Gate profile: ht
From playlist Differential Forms
Solve the general solution for differentiable equation with trig
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Differential Equations
How to solve a separable differential equation
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Solve Differential Equation (Particular Solution) #Integration
How to determine the general solution to a differential equation
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Differential Equations
Find the particular solution with exponential and inverse trig
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Solve Differential Equation (Particular Solution) #Integration
How to solve differentiable equations with logarithms
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Differential Equations
How to solve a differentialble equation by separating the variables
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Solve Differential Equation (Particular Solution) #Integration
Lecture 5: Differential Forms (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
Lecture 8: Discrete Differential Forms (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
Standard and Differential Form of First-Order Differential Equations
This video provides several examples of how to write a first order DE in standard form and differential form. website: http://mathispower4u.com blog: http://mathispower4u.wordpress.com
From playlist First Order Differential Equations: Separation of Variables
Lecture 6: Exterior Derivative (Discrete Differential Geometry)
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From playlist Discrete Differential Geometry - CMU 15-458/858
Ordinary Differential Equations and Applications by A. K. Nandakumaran,P. S. Datti & Raju K. George,Department of Mathematics,IISc Bangalore.For more details on NPTEL visit http://nptel.ac.in.
From playlist IISc Bangalore: Ordinary Differential Equations and Applications | CosmoLearning.org Mathematics
Georg Regensburger, University of Kassel
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From playlist Spring 2022 Online Kolchin seminar in Differential Algebra
Pre-recorded lecture 19: One cohomology lemma and some applications to PDEs
MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Nijenhuis Geomet
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Differential Equations: Exact DEs Introduction 1
The third analytic method for solving first order differential equations only works on exact differential equations. In this video, part one of the introduction, I explain what it means for a differential equation to be exact and why it's useful for solving it.
From playlist Differential Equations
Henri Moscovici. Differentiable Characters and Hopf Cyclic Cohomology
Talk by Henri Moscovici in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/... on October 20, 2020.
From playlist Global Noncommutative Geometry Seminar (Europe)
Pre-recorded lecture 2: Nijenhuis torsion and its basic properties
MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Nijenhuis Geomet
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)
Particular solution of differential equations
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Solve Differential Equation (Particular Solution) #Integration