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Course# MATH-123(b): Geometry

Summary

Ce cours donne une introduction à la géométrie des courbes et des surfaces.

Official source

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Instructor

Lectures in this course (35)

Related MOOCs (40)

Related courses (133)

Related concepts (406)

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Second Fundamental Tensor

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Explores geodesics as locally shortest paths and defines surface area using parametric squares.

Bezier Curves: Control Points and Regularity

Explores Bezier curves, emphasizing control points and curve regularity.

Principal Curvatures: Gaussian Curvature

Explores principal curvatures and Gaussian curvature in the context of minimal surfaces, demonstrating their real-world applications.

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PHYS-100: Advanced physics I (mechanics)

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Function of a real variable

In mathematical analysis, and applications in geometry, applied mathematics, engineering, and natural sciences, a function of a real variable is a function whose domain is the real numbers , or a subset of that contains an interval of positive length. Most real functions that are considered and studied are differentiable in some interval. The most widely considered such functions are the real functions, which are the real-valued functions of a real variable, that is, the functions of a real variable whose codomain is the set of real numbers.

Real coordinate space

In mathematics, the real coordinate space of dimension n, denoted Rn or , is the set of the n-tuples of real numbers, that is the set of all sequences of n real numbers. Special cases are called the real line R1 and the real coordinate plane R2. With component-wise addition and scalar multiplication, it is a real vector space, and its elements are called coordinate vectors. The coordinates over any basis of the elements of a real vector space form a real coordinate space of the same dimension as that of the vector space.

Semi-orthogonal matrix

In linear algebra, a semi-orthogonal matrix is a non-square matrix with real entries where: if the number of columns exceeds the number of rows, then the rows are orthonormal vectors; but if the number of rows exceeds the number of columns, then the columns are orthonormal vectors. Equivalently, a non-square matrix A is semi-orthogonal if either In the following, consider the case where A is an m × n matrix for m > n. Then The fact that implies the isometry property for all x in Rn. For example, is a semi-orthogonal matrix.

Scalar (mathematics)

A scalar is an element of a field which is used to define a vector space. In linear algebra, real numbers or generally elements of a field are called scalars and relate to vectors in an associated vector space through the operation of scalar multiplication (defined in the vector space), in which a vector can be multiplied by a scalar in the defined way to produce another vector. Generally speaking, a vector space may be defined by using any field instead of real numbers (such as complex numbers).

Cartesian coordinate system

In geometry, a Cartesian coordinate system (UKkɑːrˈtiːzjən, USkɑːrˈtiʒən) in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines, coordinate axes or just axes (plural of axis) of the system. The point where they meet is called the origin and has (0, 0) as coordinates.