# Gd of curve and surfaces or functional analysis before?

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• Jianphys17

#### Jianphys17

Hello everyone, i just finished a course of analysis(2)\vector calculus.Now iI'm interested in doing Gd of curves and surfaces(Do Carmo), and functional analysis(Rudin'sbook), but do not know what may have precedence between the two, on which i should start before you think?

Both are valid options. The one doesn't depend on the other.

Ah well, since at first i planned to study both, but i know that this would not be possible in theory,then of whom i could start earlier,alongside an introductory course in complex analysis?

Jianphys17 said:
Ah well, since at first i planned to study both, but i know that this would not be possible in theory,then of whom i could start earlier,alongside an introductory course in complex analysis?

That's entirely up to you.

Ah, ok thanks for everything , now i see with what should i start more!

## 1. What is the purpose of studying "Geometry of curves and surfaces" in functional analysis?

The study of "Geometry of curves and surfaces" in functional analysis helps us understand the properties and behavior of curves and surfaces in a mathematical sense. It also allows us to analyze and manipulate these mathematical objects to solve real-world problems in various fields such as physics, engineering, and computer graphics.

## 2. What are the main techniques used in functional analysis for studying the geometry of curves and surfaces?

The main techniques used in functional analysis for studying the geometry of curves and surfaces include differential and integral calculus, linear algebra, and topology. These tools help us define, analyze, and manipulate curves and surfaces in a rigorous and systematic manner.

## 3. How do curves and surfaces differ in terms of their geometric properties?

Curves and surfaces have different geometric properties due to their different dimensionalities. For instance, a curve is a one-dimensional object, while a surface is a two-dimensional object. This difference leads to variations in their curvature, tangents, and normals, which are essential properties in the study of geometry.

## 4. Can functional analysis be applied to real-world problems involving curves and surfaces?

Yes, functional analysis can be applied to real-world problems involving curves and surfaces. For example, in physics, functional analysis is used to study the motion of particles along curved paths, and in engineering, it is used to design and analyze curved surfaces for objects such as aircraft wings and car bodies.

## 5. What are the applications of functional analysis in the study of curves and surfaces?

Functional analysis has various applications in the study of curves and surfaces, such as in optimization problems, shape analysis, and computer-aided geometric design. It also has applications in other fields, including data analysis, signal processing, and image reconstruction.