Learning Partial Differential Equations and Numerical methods

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kdmfe

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Dear Experts,

I am trying to work on the book ‘Numerical methods in Computational Finance’ by Daniel J. Duffy. I understand that there is steep learning curve in Partial Differential Equation (PDE) and Numerical methods before I can understand the content in this book.


SO, I searched randomly on Amazon for books to learn PDE, I came across this book ‘Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach (The Wiley Finance Series)’ by Daniel J. Duffy. I bought this book now. I understand from the content that this book directly supports the learning/understanding the content of the former book.

My question to the members in this forum is ,keeping in relevance to Quantitative Finance field, is there a book or two which does the heavy lifting of explaining the concepts/related concepts in PDE and Numerical methods?

I have understood the concepts: PDE and numerical methods, and done a few problems from books at graduation level. In a way, my understanding my basic.

Kindly suggest.
 
SO, I searched randomly on Amazon for books to learn PDE, I came across this book ‘Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach (The Wiley Finance Series)’ by Daniel J. Duffy. I bought this book now. I understand from the content that this book directly supports the learning/understanding the content of the former book.

This topic of PDE has already been discussed in detail on this forum.
Those books support each other to a certain extent. But they are not the same. The conclusion is not really the issue.

I think there is an issue with prerequisite background that I feel you don't yet have. As I mentioned already, take an easier level in the short term.
 
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Thank you Daniel,


For the last time, at my humble request, can you please let me know the easier level in the short term? What steps I need to take. I am happy to take your guidance.


I think, I have requested deletion of my earlier post.

If you already mentioned the easier route in the short term I have lost those details.


I will continue with what I can in the meantime till I join the evening (part time ) course for MFE in London


Thank you
 
Of course, I'm not the only person on the planet who writes books on PDE.
 
Daniel Duffy said:
Of course, I'm not the only person on the planet who writes books on PDE.
Click to expand...
Hello Daniel, You have been kind/encouraging to take my questions. Thank you. I am not going to spam.

The reason I am here is because I feel lost in how to achieve my goal. I cannot be a regular student.

I am happy to take actions as per any experienced person in this field. My journey in this field is not going to short term (in other words, just to seek a job).

So can anyone suggest me the easier steps for the below point I raised earlier in this post:
"My question to the members in this forum is ,keeping in relevance to Quantitative Finance field, is there a book or two which does the heavy lifting of explaining the concepts/related concepts in PDE and Numerical methods?"

Thank you

NB: I will request deletion of this question in a day or two if my post is not correct for this forum/I do not see much traction.
 
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This book is probably good enough for self-study, It's green/blue belt level.


And do the exercises; it's not enough to get a conceptual idea. To quote Paul Halmos

“Don’t just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? Where does the proof use the hypothesis?”

— Paul Halmos
 
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Daniel Duffy said:
This book is probably good enough for self-study, It's green/blue belt level.


And do the exercises; it's not enough to get a conceptual idea. To quote Paul Halmos

“Don’t just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? Where does the proof use the hypothesis?”

— Paul Halmos
Click to expand...
Thank you.

I found these two books are you able to give me a little more help in advising if I should buy both book or only one of these two. I do not mind buying both if there is a slight advantage in order to understand the concepts.



Thank you a lot for your valuable guidance and time.
 
Daniel Duffy said:
This book is probably good enough for self-study, It's green/blue belt level.


And do the exercises; it's not enough to get a conceptual idea. To quote Paul Halmos

“Don’t just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? Where does the proof use the hypothesis?”

— Paul Halmos
Click to expand...
I will follow your advice. Thank you

When I did Real Analysis. I wrote my notes for every theorem, answered all exercise questions and answered almost all of end of chapter questions.

Similarly, I used the same approach while trying to understand Steven Shreve's Book 2 Stochastic calculus-Continuous Time series. There are areas where I could not achieve much progress. So I parked those topics aside, for the time being, and try to complete my notes when I join evening (Part time) college for MFE/Quant Finance.
 
kdmfe said:
Thank you.

I found these two books are you able to give me a little more help in advising if I should buy both book or only one of these two. I do not mind buying both if there is a slight advantage in order to understand the concepts.



Thank you a lot for your valuable guidance and time.
Click to expand...
Second book is ODE I realise that and the first time one is Partial Differential Equation and it matches with the authors name you have suggested.
 
kdmfe said:
Thank you.

I found these two books are you able to give me a little more help in advising if I should buy both book or only one of these two. I do not mind buying both if there is a slight advantage in order to understand the concepts.



Thank you a lot for your valuable guidance and time.
Click to expand...
yep, get that great book by Bronson.

You are ready to go, fasten seat belts and lift off.
 
Daniel Duffy said:
This book is probably good enough for self-study, It's green/blue belt level.
Click to expand...
Hello Daniel,

I am lucky, one of the book shops had this book. I bought it today. Now I am happy to say, I have enough on my plate to keep me busy. Hope I will be write my notes on this book.
Thank you for your valuable guidance.
 
Daniel Duffy said:
Here's a representative set of exercises (1st batch of the course) on ODEs.
Click to expand...
Thank you Daniel, Went through the list. I only wish I knew about the depth of this subject much earlier when I started my ground work for Quant finance. A lot of time has passed through. I cannot help it now. Once I complete the books you have recommended, I will come to these questions.

Thank you for taking your time to help me.
 
All
I do not know if this will annoy maths pundits in this forum. But I will be bold to ask.

I have reached this stage of understanding mathematics with the help of a Phd Math student (I quit my job and I am doing maths).

I need some guidance here, as I am not a regular college student, is there any online tutoring channel which will train me on Schaum's PDE? I have the understanding of PDE in the undergraduate college, ie given a PDE how to find its solutions. I have not dealt with the depth in Schaum's book.

Thought my PhD sir is volunteering to teach me this book as well, but over a period of time things change, people become busy in their lives. So I need an alternative plan in place, to ensure continuity in my learning. As my idea is to gain knowledge from this book.

In the meantime, I am also looking at online portals (edu, course era) who can help me with my studies.

Kindly guide.

Thank you
 
Gilbert Strang of MIT - who incidentally is my academic grandfather - has many great lectures.
He developed the Strang splitting method that I discuss in my 2022 PDE book.

 
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