Preface

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This is a tutorial made solely for the purpose of education and it was designed for students taking Applied Math 0330. It is primarily for students who have very little experience or have never used Mathematica before and would like to learn more of the basics for this computer algebra system. As a friendly reminder, don't forget to clear variables in use and/or the kernel.

Finally, the commands in this tutorial are all written in bold black font, while Mathematica output is in regular fonts. This means that you can copy and paste all comamnds into Mathematica, change the parameters and run them. You, as the user, are free to use the scripts to your needs for learning how to use the Mathematica program, and have the right to distribute this tutorial and refer to this tutorial as long as this tutorial is accredited appropriately.

Recurrences

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We can define the Fibonacci recurrence (which is a second order difference equation \( F_{n+2} = F_{n+1} + F_n , \quad F_0 =1, \ F_1 =1 \) ) as

Next example from the Mathematica docs shows one way down values are more expressive (dynamic programming): Another efficient way to define the Fibonacci recurrence is to use the explicit formula (which is not available for most other nonlinear recurrences): ` Mathematica also has a special command to evalaute n-th Fibonacci number: Fibonacci[n] .

Tail recursive Fibonacci sequence generator

Pattern matching Fibonacci sequence generator Matrix method: Another useful way uses LinearRecurrence: