Maxima Tutorial 1 - Introduction

Hello folks,

There are not many resources on Maxima on internet, that's why I thought to write a series of tutorials.
I had conducted one workshop on Maxima in KTHM college and I intend to conduct more workshops on Maxima and other related softwares (Pari GP, Sage) at KTHM College. Interested candidates can contact me at manas.princeton@gmail.com.

For those who don't know what Maxima is all about, it's a Computer Algebra System (CAS). It can be used to solve a variety of problems in Mathematics including but not limited to algebra, limits, derivatives, integration, ODE, trigonometry, graph plotting, graph theory and what not!

In these tuts I'll show you how to use Maxima for most common mathematical problems.

Let's start.
Download the latest copy of Maxima from here. http://sourceforge.net/projects/maxima/files/
After installation, locate and start the application named wxMaxima.

PART 1 - Maxima as a Calculator

Write this:  1+1;
In Maxima, each statement must be terminated in order to carry on execution. There are two ways to do this. Either use ; or $ at the end of statement.
The difference between these two is
; executes and shows the output.
$ only executes WITHOUT showing the output.

What you see above is called as a cell. Now we have to evaluate the cell. Again, two ways.
Go to Cell menu at the top and click 'evaluate'.  OR Press SHIFT + ENTER.
Here is how it looks after evaluation.

Note the symbols %i1 and %o1.
i stands for input. o stands for output. 1 stands for cell number. This is nothing but pointers.
Let's do more calculations. 

These are pretty self explanatory.  5!=120.
% sign means last output here (that is 120).
The third statement %o1 - it's 2. It is the output of first cell. So you can see the output of this stmt (%o6) as 200.

Note the difference between 1/3 and 1.0/3.0
When you use decimal point, it essentially considers the number as a floating number and evaluates the fraction. Otherwise, it just simplifies the numbers and give you output in rational number format.
(Try doing 2/6)


Let's see how to define variables and assign value to them.

Suppose a & b be our variables.
To assign value to variable use : operator.
The variables are accessible throughout the worksheet and not just a particular cell.
To check the value assigned to variable, simply execute a;.


Exponents!

To expand the expression, use expand() function. It takes one argument, the expression. So we are passing the earlier (latest) output.



To find value of the expression, use numer command. It evaluates the numerical argument in floating point.

NOTE - To find more information about any particular function, just bring cursor on it and press F1 key. You'll get total documentation of that function.
I'd suggest you to do that for every information for detailed knowledge. My purpose here is to get you started, you are going to have to explore things yourself.

Moving on, let's do something our calculators fail to do.

100! Such a big number! It'll take us long to calculate such big numbers. But there's more. Here's the real beauty.
factor(arg)
It factorizes the arg i.e. the number passed. If you recall, Every natural number can be factored in one and only one way into a product of prime factors.
So here is the factorization of 100!
Try factorizing different numbers.

Here is a list of some of the common constants defined in Maxima.

• %e – Euler’s Number
• %pi –  
• %phi – the golden mean ()
• %i – the imaginary unit ()
• inf – real positive infinity ()
• minf – real minus infinity ()
• infinity – complex infinity

Now, in above screenshot, we are calculating sqrt of 2*PI. Maxima returns us the mathematical representation. To find the value, we are using another function here, float(arg). It calculates floating point value. It's essentially same as numer. If you were to use numer here, then it'd have been %,numer;

Try it, you'll get the same answer.

That's it for now. I have shared the worksheet consisting above examples here.

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For those with a substantial background in mathematics and passion for numbers, an unlimited number of career opportunities are available. Check out Top 7 careers options for Maths lovers-:
1) Chartered Accountant: With the rapid growth in economy, careers in finance and accounts have gained tremendous popularity and the most esteemed career option in this filed is that of Chartered Accountant. A Chartered accountant is somebody who specializes in accounting, auditing and taxation.
2) Software Engineers: A highly fulfilling career, software engineers design and develop software. They apply the theories and principles of computer science and mathematical analysis to create, test, analyse and evaluate the software applications and systems that make computers work. Software engineers are also experts in theory of computing systems, the structure of software, and the nature and limitations of hardware to ensure that the underlying systems will work properly. Professionals in this field have excellent prospects in the next five to 10 years.
3) Operations Research Analysts: Operations research has been defined as an interdisciplinary branch of applied mathematics and formal science that uses advanced analytical methods such as mathematical modeling, statistical analysis, and mathematical optimization to arrive at optimal or near-optimal solutions to complex decision-making problems. Operations research analysts formulate and apply mathematical modeling methods to develop and interpret information that assists management with policy formulation and other managerial functions. They help managers to make better decisions and solve problems. If you're planning to take this profession be sure you have a thorough knowledge of strong quantitative and computer skills; advanced knowledge in mathematics.
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Welcome Function (Fresher's Party)

On 3rd of August, we, the students of M.Sc. - II had organized a welcome function for the new (M.Sc. - I) students. Here are the details of the function.

Event started at 12pm sharp. Almost every student from both the classes were present on the day.
All the faculties were present. First, Prof. P.K.Nehe, Head of Department, welcomed the new students, and gave introductory lecture. It was followed by a geeky lecture of Prof. Niwas Patil (Ph.D.). He spoke about the new thought that's been holding amongst mathematicians about changing the PI constant. (More on this in another post).
The other invited faculties were Prof. Sonawane, Prof. Shirore, Prof. Kamale madam, Prof. Dhokrat.


By 1pm the lectures were done. The refreshments were served. 2 Sabudana vada + 1 Samosa + 1 Sonpapadi. Chutney was awesome!

After the refreshments, we started with few interesting games.
1. Collection of maximum earrings and watches in 1 minute.
2. Bursting of max balloons with leg within 30 sec.
3. The reflex game. (Contestants had to jump/sit down/stand up upon a single call. Anyone with a slight wrong move was disqualified)
4. Musical Chair

In each game, 10 students participated and 2 were shortlisted. Leaving us 8 finalists - 4 pairs of 2.
Now, it was the time for Scavenger Hunt. 10 items were hidden on the whole floor of department, and finalist had to find them within 5 minutes. The team coming up with max items would win.

Everyone enjoyed the games.
We entered the final phase of the welcome function. It wasn't gonna end without talent show. So whoever wanted to perform anything, did so. Some sang songs, some acted, some danced, others listened, saw, enjoyed!

And that was the end of the ceremony! Everyone was left mesmerized by the day. People were longing for more, but due to shortage of time, couldn't.
The event helped build a very good rapport between the juniors and seniors. Perhaps this was the best welcoming function anyone had given to their juniors in our department and college.

P.S. Students had decorated the class beautifully. Thanks to our Pardeshi mama who granted us permission for the decoration and had been so very helpful throughout the event.

Here are some of the pics.