This is a 5-days mini-course I gave in Brazil last week, at the CBPF (Brazilian Center for Physics Research). The material will still receive polishment and improvements, towards evolving into a sort of manual, but it is also interesting to see it exactly as it was presented to people during the course. This material uses the update of Physics available at the Maplesoft Physics R&D webpage.

Mini-Course: Computer Algebra for Physicists

Edgardo S. Cheb-Terrab

Maplesoft

This course is organized as a guided experience, 2 hours per day during five days, on learning the basics of the Maple language, and on using it to formulate algebraic computations we do in physics with paper and pencil. It is oriented to people not familiar with computer algebra (sections 1-5), as well as to people who are familiar but want to learn more about how to use it in Physics.

Motivation

Among other things, with computer algebra:

You can concentrate more on the ideas (the model and its formulation) instead of on the algebraic manipulations

You can extend your results with ease

You can explore the mathematics surrounding your problem

You can share your results in a reproducible way - and with that exchange about a problem in more productive ways

After you learn the basics, the speed at which algebraic results are obtained with the computer compensates with dramatic advantage the extra time invested to formulate the problem in the computer.

All this doesn't mean that we need computer algebra, at all, but does mean computer algebra can enrich our working experience in significant ways.

What is computer algebra - how do you learn to use it?

What is this mini-course about?

What can you expect from this mini-course?

Explore. Having success doesn't matter, using your curiosity as a compass does - things can be done in so many different ways. Have full permission to fail. Share your insights. All questions are valid even if to the side. Computer algebra can transform the algebraic computation part of physics into interesting discoveries and fun.

1. Arithmetic operations and elementary functions

2. Algebraic Expressions, Equations and Functions

3. Limits, Derivatives, Sums, Products, Integrals, Differential Equations

4. Algebraic manipulation: simplify, factor, expand, combine, collect and convert

5. Matrices (Linear Algebra)

6. Vector Analysis

7. Tensors and Special Relativity

8. Quantum Mechanics

9. General Relativity

10. Field Theory

BrasilComputacaoAlgebrica.mw.zip

Edgardo S. Cheb-TerrabPhysics, Maplesoft

Well, it’s been more than 17 years since First Leaves: A Tutorial Introduction to Maple V was first published as a hardcover book, and since that time, Maple, the Maple documentation, and the world have undergone huge changes. We are now in a state where all our documentation is available electronically, including both in-product and online; where the vast majority of our customers receive our products electronically and never even see the printed...

I would like to be able to read Maple manuals and the AEM book that I have bought on the ipad. I can understand that I will not be able to run the commands. But it woud be nice to read through the different sections while reclining on my bed. Hope that you will make it possible.

The (new, Maple 15) Programming Guide is available for download from the Documentation Center.

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