Preparing for Intro PDEs: What Topics from Calc III Are Essential?

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In summary, the person is currently taking an intro course in ODEs and will be taking an intro course in PDEs next semester. They are asking for advice on what to review from calc III for the PDEs course. They mention that they took calc III over the summer at a community college and don't feel they learned much. They believe they have a good understanding of calc I and II and the intro DEs course. They then ask for specific topics from calc III that are used in PDEs courses. The person also mentions their plans for taking more applied math in the future. Finally, someone responds with suggestions to review the inverse function theorem and level curves and surfaces, as they are often used in coordinate changes.
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Hey everyone,

I'm taking intro ODEs right now, and am taking intro PDEs next semester. I would like to know what i should review from calc III for this course.

I took calc III over the summer at a community college and didn't learn very much, if I'm being honest with myself. I think I am good as far as anything from calc I or II goes, and from this intro course in DEs as well. The title of this post could more suitably be "What from calc III is used in an intro PDEs course?" (and PDEs in the more general sense -- I plan on taking much more applied math in the coming three years).

So, what is used in partial differential equations form the typical calculus III course?


Thanks in advance

anonymous
 
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It would be nice to take a look at the inverse function theorem, and at least understand what it says and how to use it; it is used often in coordinate changes. Also level curves, surfaces.
 

1. What is the purpose of reviewing for introductory PDEs?

The purpose of reviewing for introductory PDEs is to refresh your understanding of the fundamental concepts and techniques used in solving partial differential equations. This will help you build a strong foundation for more advanced topics in PDEs and make it easier to tackle challenging problems.

2. What are some common methods used in solving PDEs?

Some common methods used in solving PDEs include separation of variables, the method of characteristics, Fourier series and transforms, and numerical methods such as finite difference and finite element methods.

3. How can I improve my problem-solving skills for PDEs?

To improve your problem-solving skills for PDEs, it is important to practice solving a variety of problems and to understand the underlying concepts and techniques. It can also be helpful to work with a study group or seek guidance from a tutor or instructor.

4. What are some real-world applications of PDEs?

PDEs have many real-world applications in fields such as physics, engineering, and finance. They are used to model phenomena such as heat transfer, fluid dynamics, electromagnetism, and option pricing in financial markets.

5. How can I prepare for a PDEs exam?

To prepare for a PDEs exam, it is important to review all the relevant material, practice solving problems, and make sure you understand the key concepts. It can also be helpful to create a study schedule and seek help from your instructor or classmates if needed.

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