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Note: This may be an open ended question

I am willing to create/ teach with the help of Mathematica in the subject of Numerical methods. This includes, linear algebra, ODE, PDE, Optimizations, Roots, Boundary value problems, and so on.

The only 2 programming I know is MMA and Python. There are a lot of texts on this subject in Python, please advise any texts that may be helpful.

Rene Duchamp
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  • Indeed, if such books exist, it is good to know. You are aware, of course, of the tutorials on these subjects? – Alexei Boulbitch Sep 29 '17 at 12:38
  • @AlexeiBoulbitch Tutorials are helpful. But to teach from a textbook will offer the leverage of problems and their solutions, its a more structured way of learning. Correct me if I am wrong. – Rene Duchamp Sep 29 '17 at 12:47
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    Have you seen this and other books listed there ? http://www.wolfram.com/books/topics.html?topic=%22Calculus%20and%20Analysis%22 – Lotus Sep 29 '17 at 12:47
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    In the list offered by Lotus I have found the book "Numerical Analysis, ninth edition" Authors: Richard L. Burden, J. Douglas Faires. Maybe it can help. I am not sure that it is Mathematica based, though. Addressing your question, I prefer to select a material for the teaching based on my understanding, of what I want to teach, and then to find, but more often to create the Mma code fitting exactly these cases. This, is a personal taste, of course. – Alexei Boulbitch Sep 29 '17 at 14:34
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    Some years ago I taught a numerical analysis course where students used Mathematica. The text was the 1993 "Elementary Numerical Computing with Mathematica", by Robert D. Skeel and the late Jerry B. Keiper. Excellent text that treats the topics you list except for BVPs. I see on amazon.com that a 2001 reprint version is available (says "selected material" from the original). – murray Sep 29 '17 at 15:54
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    The Skeel & Keiper book integrates use of Mathematica with the mathematical development. – murray Sep 29 '17 at 16:02
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    If you're interested in that text, you may want to have a look at the homework exercises, many from the text, and my Mathematica notebooks used for demo purposes or homework solutions, that is used in a 1996 version of the course. Most of the notebooks have been updated as of 2015-2016, but may need further updating for current Mathematica versions. Contact me at the email address indicated at http://people.math.umass.edu/~murray/. – murray Sep 29 '17 at 16:02
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    There's a 2003 text "Numerical and Analytical Methods for Scientists and Engineers Using Mathematica", by Daniel Dubin, which as its title indicates mixes analytical methods with the numerical ones. And it's quite advanced and does not cover linear algebra. – murray Sep 29 '17 at 16:23
  • When searching for a suitable textbook, a question to ask yourself is what exactly you want students to learn in your course. Do you want them to "reinvent the wheel" by writing code to implement, say, Newton's Method, or RK5? or just to use the built-in capabilities of Mathematica to apply such methods without the students needing to implement the methods themselves? – murray Sep 29 '17 at 16:25
  • @murray Your comments on "reinventing the wheel" prompted me to think as that was often the case on the courses at universities. Nevertheless i found this excerpt from the preface of the book The Beginner's Guide to Mathematica by By Theodore W. Gray and Jerry Glynn very enlightening. – ercegovac Sep 29 '17 at 20:41
  • @ercegovac: I know that Gray & Glynn passage well! I repeat, though, the question as to whether and to what extent you want your students to implement numerical procedures themselves. I do think there is value in doing that to some extent. For example, after showing students how to implement Euler's Method for a 1st order IVP (with one function to do one step of the iteration, then a Nest or NestList to iterate it, I expect them to modify that to implement, say, the Improved Euler Method). – murray Sep 30 '17 at 19:28
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    @ercegovac: (continued) I do show students how to use an explicit Do or While, just to get the feel for what's "really" happening behind the scenes with Nest. – murray Sep 30 '17 at 19:32
  • As @Szabolcs reminded me (https://mathematica.stackexchange.com/questions/156803/package-to-simulate-a-computer/156807#156807), Mathematica comes with the ComputerArithmetic package that allows you to simulate numeric calculations on a hypothetical machine with specified base, number of digits, exponent range, and rounding rule. My experience teaching the subject is that students really appreciate the finite precision of an actual contemporary computer when they work in a hypothetical machine with more limited precision. – murray Sep 30 '17 at 19:40
  • @Lotus: No I haven't see that yet, never knew about that. Will take a look. – Rene Duchamp Oct 03 '17 at 18:47
  • @murray: I want them to re-write the code and learn it from the intermediate steps. Using MMA inbuilt functions comes later as a part of verifying their answers from their own codes. I have sent you an email , please do check. – Rene Duchamp Oct 03 '17 at 18:49
  • @AlexeiBoulbitch I think taht approach is a good idea. Especially since it serves me the opportunity to pick and select what exactly I want to teach. – Rene Duchamp Oct 03 '17 at 18:52

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