Ordinary Differential Equations by V Arnold

In summary, "Ordinary Differential Equations" by V Arnold assumes basic topology knowledge and does not require any algebraic topology for understanding. The recommended sources for basic topology are Munkres and Mendelson.
  • #1
prash_neo
9
0
"Ordinary Differential Equations" by V Arnold

Hello,

I recently bought "Ordinary Differential Equations" by V I Arnold to study differential equation. In that book he assumes we know basic topology. I want to know which subfield of topology should I know, in order to study this book.

Regards
Prashanth
 
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  • #2


As you said, basic topology. The early chapters of Munkres or Mendelson will be more than enough.
 
  • #3


In Munkres there are two parts, general & algebraic. So then as per your reply, there is no need to study algebraic topology. Am I correct?
 
  • #4


Correct, no algebraic topology is necessary for reading Arnold.
 
  • #5


ok, Thanks a lot !
 

1. What is an ordinary differential equation (ODE)?

An ODE is a mathematical equation that describes how a dependent variable changes with respect to an independent variable. It involves derivatives of the dependent variable with respect to the independent variable.

2. Who is V.I. Arnold and why is his work on ODEs important?

Vladimir Igorevich Arnold (1937-2010) was a Russian mathematician who made significant contributions to the study of ordinary differential equations. His work provided new insights and techniques for solving ODEs, making them more accessible to a wider audience.

3. What is the difference between an ordinary and a partial differential equation?

An ordinary differential equation involves only one independent variable, while a partial differential equation involves multiple independent variables. ODEs are also typically used to model systems with one-dimensional behavior, while PDEs are used for systems with multi-dimensional behavior.

4. How are ODEs used in science and engineering?

ODEs are used to model a wide range of physical phenomena, such as the motion of objects, chemical reactions, and electrical circuits. They are also used in engineering to design and analyze systems, such as control systems and mechanical systems.

5. How can I learn more about ODEs and V Arnold's work?

There are many resources available to learn about ODEs and V Arnold's contributions, including textbooks, online courses, and academic papers. You can also attend conferences and workshops on the topic or consult with experts in the field. Reading "Ordinary Differential Equations" by V Arnold is a great place to start.

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