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## Mini-Course: Computer Algebra for Physicists

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 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

Edgardo S. Cheb-Terrab
Physics, Maplesoft

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