A good textbook in Differential Equations for pure mathematicians

In summary, the person is a physics major and looking for a good textbook on Differential Equations for pure mathematicians. They specifically want a book that will help build intuition for proofs and has a lot of solutions. They are currently watching MIT Herb Gross videos and have received a recommendation for the book "Ordinary Differential Equations" by Arnold. Other suggestions include DE by Ross and Lectures on DE, but for a first course, they highly recommend "Braun."
  • #1
Eng_physicist
30
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Hi I am a physics major and I am trying to double major in math,I will be taking a differential equations course for pure math students this semester. I need advice on a good textbook in Differential Equations for pure mathematicians that will build up a great intuition for proofs and will have a lot of solutions(if possible).
Also any websites would be helpful.
I am watching the MIT Herb Gross videos and find them quite helpful.
Thanks in advance
 
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  • #2
'Ordinary Differential Equation" by Arnold.is the best.
others, DE by Ross, Lectures on DE etc.
 
  • #3
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Related to A good textbook in Differential Equations for pure mathematicians

1. What is the difference between a good and a bad textbook in differential equations for pure mathematicians?

A good textbook in differential equations for pure mathematicians should have a clear and concise presentation of concepts, provide plenty of examples and exercises for practice, and include proofs and rigorous mathematical reasoning. A bad textbook may have confusing explanations, lack of examples, or may not cover all necessary topics.

2. How do I know if a textbook is suitable for pure mathematics?

A textbook suitable for pure mathematics should have a strong emphasis on theory and mathematical rigor, rather than just practical applications. It should also cover a wide range of topics and provide challenging exercises for further understanding.

3. Are there any specific prerequisites for studying differential equations in pure mathematics?

To understand differential equations in pure mathematics, one should have a solid understanding of calculus, linear algebra, and basic mathematical proofs. Some knowledge of real and complex analysis may also be helpful.

4. Can you recommend a good textbook in differential equations for pure mathematicians?

Some popular and highly recommended textbooks in differential equations for pure mathematicians include "Ordinary Differential Equations" by Morris Tenenbaum and Harry Pollard, "Differential Equations, Dynamical Systems, and an Introduction to Chaos" by Morris W. Hirsch and Stephen Smale, and "Partial Differential Equations" by Lawrence C. Evans.

5. How can I make the most out of studying from a textbook in differential equations for pure mathematicians?

To make the most out of studying from a textbook in differential equations for pure mathematicians, it is important to actively engage with the material. This can include taking thorough notes, working through all examples and exercises, and seeking help from a professor or tutor if needed. It can also be helpful to form a study group with other students to discuss and review the material together.

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