Complex Sequences & Series

If you have ever studied real or complex analysis and in particular, sequences, recurrence relations or series, then this application may be of interest. You can define constants and expressions using a rich set of mathematical functions and then step through a sequence to help you understand its long-term behaviour. For instance, you may already know that a series converges to a particular value, but this application will allow you to actually see the convergence happening, one step at a time. Real and complex plots provide visual feedback as you step through a sequence. The real plot can display either Re(z), Im(z), Mod(z), Arg(z), Re(sum), Im(sum), Mod(sum) or Arg(sum). The complex plot can display either sequence values or partial sums. You can change the plot modes at any point in a sequence, allowing you to clearly see how the values are changing over time. The plots make this application an invaluable tool for understanding the long-term behaviour of sequences and series. The powerful complex number expression evaluator means the application can also be used as a general purpose, albeit somewhat unconventional, calculator. Everything you enter on up to 10 worksheets is automatically saved as you go along, so everything looks exactly the same next time you launch the application. This means you can define up to 10 different sequences and then recall them for class demonstrations or discussions. Finally, you are not left alone to figure out how the application works. There is a brief user guide, help with expressions and a couple of detailed examples you can work through. We hope you enjoy using this application and learn at least a little bit more about this fascinating area of mathematics.