Objective: Getting acquainted with IDE and functional programming language, solving simple iterative tasks in functional style.
Make sure you have configured your F# environment and are able to execute code. All options to set up F# on your operating system are described at F# Official Web Site [USE menu option]. We recommend the following options (in the recommended order):
- Install Visual Studio Code with Ionide Extension
- Install Full Visual Studio with F# support (then use F# Interactive window to execute files line-by-line interactively)
- Set up local Jupyter Notebook environment with .NET Support
- Run F# Online in the browser (for example, using Repl.it)
Once you are able to execute F# scripts, make the assignments below.
Write a program in a functional language that will print the table of values of some elementary function f(x) on the interval [a,b], calculated in the following ways:
- Using built-in functions
- Using dumb Taylor series, where each term is calculated according to the formula
- Using smart Taylor series, where each term is calculated from the previous one (this would yield better efficiency)
In both cases, you should continue adding terms to the series until next term becomes sufficiently small (eg. smaller than a given value eps). You should print the number of terms in the table as well.
Here is how the output table should look like:
| x | Builtin | Smart Taylor | # terms | Dumb Taylor | # terms |
|---|---|---|---|---|---|
| a | ... | ... | ... | ... | |
| ... | |||||
| b | ... | ... | ... | ... |
Actual functions and corresponding Taylor series are given in the PDF Handout. Your personal task is defined by your number in the class list (please refer to the teacher for specific instructions where to find this list).
Develop a function to solve transcendental algebraic equations numerically, using the following root-finding methods:
- Bisection method (also called dichotomy method)
- Iterations method
- Newthon's method
All equations should be specified as functional parameters, to make functions sufficiently generic. Also, take advantage of the fact that Newthon's method is a special case for more generic method of iterations, and make sure to re-use the code.
Please apply three procedures for three methods to three consecutive equations in the table 2 of the handout, starting from the row specified by your personal number from the class list. You should produce a table with a total of 9 solutions.