26
Apr
What Is Differential Geometry. Many areas of research are in the intersection of different subjects and if person A tells you that person B is doing algebraic geometry. Let me expand Thomas good answer by saying that local differential geometry is the study of properties of a geometric structure that at each point depend only on the neighborhood of a given point or more precisely the germ of the structure at that point. The course itself is mathematically rigorous but still emphasizes concrete aspects of geometry centered on the notion of curvature. I will only mention one book here for the breadth of topics discussed.
Differential geometry exactly tells us how to do this and it allows us to extend calculus to just about any nice space we want. You will notice that everything that you have learned and will learn about physical systems fits in the language of differential geometry. Differential geometry branch of mathematics that studies the geometry of curves surfaces and manifolds the higher-dimensional analogs of surfaces. For example is arithmetic geometry part of algebraic geometry or of number theory. This course is an introduction to differential geometry. I doubt however that you will have a direct application in engineering.
Differential geometry is fun to do and can be very useful when it comes into play.
Many areas of research are in the intersection of different subjects and if person A tells you that person B is doing algebraic geometry. The course itself is mathematically rigorous but still emphasizes concrete aspects of geometry centered on the notion of curvature. Differential geometry branch of mathematics that studies the geometry of curves surfaces and manifolds the higher-dimensional analogs of surfaces. Differential geometry is fun to do and can be very useful when it comes into play. The calculation of the curvature of a curve is made through its first differential knowing that the differential is the tangent line to a curve at a point and therefore what varies this differential as soon as the point in the line changes gives us its Degree of curvature. It satis es Lpq d Upq where d Upq inffLj t 2U.