Several complex variables | Topological vector spaces
In mathematics, the n-dimensional complex coordinate space (or complex n-space) is the set of all ordered n-tuples of complex numbers. It is denoted , and is the n-fold Cartesian product of the complex plane with itself. Symbolically, orThe variables are the (complex) coordinates on the complex n-space. Complex coordinate space is a vector space over the complex numbers, with componentwise addition and scalar multiplication. The real and imaginary parts of the coordinates set up a bijection of with the 2n-dimensional real coordinate space, . With the standard Euclidean topology, is a topological vector space over the complex numbers. A function on an open subset of complex n-space is holomorphic if it is holomorphic in each complex coordinate separately. Several complex variables is the study of such holomorphic functions in n variables. More generally, the complex n-space is the target space for holomorphic coordinate systems on complex manifolds. (Wikipedia).
Complex Numbers as Vectors (2 of 3: Subtraction)
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From playlist Complex Numbers
Introduction to Cylindrical Coordinates
This video introduces cylindrical coordinates and shows how to convert between cylindrical coordinates and rectangular coordinates. http://mathispower4u.yolasite.com/
From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates
Space Coordinates Plotting Points in 3 Dimensions
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From playlist Calculus 3
Special Relativity: 2 - Spacetime Diagrams
An introduction to spacetime diagrams which are a valuable tool used to understand special relativity. The second in a series on special and general relativity. Let us know what you think of these videos by filling out our short survey at http://tinyurl.com/astronomy-pulsar. Thank you!
From playlist Special Relativity
The Equations of the Coordinate Planes in R3
This video identifies the three coordinate planes in the 3D coordinate system. Site: http://mathispower4u.com
From playlist Equations of Planes and Lines in Space
Minkowski Space-Time: Spacetime in Special Relativity
Includes discussion of the space-time invariant interval and how the axes for time and space transform in Special Relativity.
From playlist Physics
Ex: Identifying the Coordinates of Points on the Coordinate Plane
This video explains how to determine the coordinates of points on the coordinate plane. Complete Video List at http://www.mathispower4u.com Search by Topic at http://www.mathispower4u.wordpress.com
From playlist The Coordinate Plane, Plotting Points, and Solutions to Linear Equations in Two Variables
Complex Numbers as Points (1 of 4: Geometric Meaning of Addition)
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From playlist Complex Numbers
Some elementary remarks about close complex manifolds - Dennis Sullivan
Event: Women and Mathmatics Speaker: Dennis Sullivan Affiliation: SUNY Topic: Some elementary remarks about close complex manifolds Date: Friday 13, 2016 For more videos, check out video.ias.edu
From playlist Mathematics
Hilbert Space Techniques in Complex Analysis and Geometry (Lecture 1) by Dror Varolin
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From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
Simon Donaldson - Introduction to Differential geometry on toric varieties [2013]
Name: Simon Donaldson Event: Workshop 2012-2013ay - Graduate Workshop on Kahler Geometry Event URL: view webpage Title: Introduction to Differential geometry on toric varieties- 1 hr Date: 2013-06-24 @9:00 AM Location: 102 http://scgp.stonybrook.edu/video_portal/video.php?id=742
From playlist Mathematics
B. Deroin - Monodromy of algebraic families of curves (Part 2)
The mini-course will focus on the properties of the monodromies of algebraic families of curves defined over the complex numbers. One of the goal will be to prove the irreducibility of those representations for locally varying families (Shiga). If time permit we will see how to apply this
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
Colloquium MathAlp 2019 - Claude Lebrun
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From playlist Colloquiums MathAlp
Tropical Geometry - Lecture 5 - Fundamental Theorem | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
MATH331: Riemann Surfaces - part 1
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From playlist The Riemann Sphere
Tom Sutherland: Stability conditions and flat connections
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From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
Field Equations 2 - The Klein-Gordon Equation
In this video we review two ways to arrive at the Klein-Gordon equation. The first is via classical Lagrangian mechanics and the second is the quantization of the relativistic energy-momentum-mass relation. Please consider supporting this channel on Patreon: https://www.patreon.com/XYLYX
From playlist QED- Prerequisite Topics
Jie Liang: Non-Diffusive Vortexes at Transition State of Activated Process by Persistent Homology
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From playlist AATRN/STMS