numerical-solutions

These projects utilize Python's NumPy and SciPy libraries alone to demonstration solution techniques, and Matplotlib to demonstrate the solutions graphically.

Systems of Linear Equations

Four projects explore numerical methods in the solution of systems of linear equations.

- HW1:
Code with output can be viewed here.

- HW2:
Code with output can be viewed here.

- HW3:
Code with output can be viewed here.

- HW4:
Code with output can be viewed here.

Partial Differential Equations

Two projects explore numerical methods in the solution of differential equations.

- HW5: exploring solutions to second-order boundary value problems
Code with output can be viewed here.
-- First Central Difference Method
-- Finite Difference Method
-- Newton-Raphson Iterative Method

- HW6: exploring solutions to elliptical, parabolic, and hyperbolic partial differential equations
Code with output can be viewed here.
-- Finite Difference Method
-- Gauss-Seidel Iterative Method
-- Forward-Difference Method (Forward-Time Central Space Scheme)
-- Backward-Difference Method

Footnote

I thoroughly enjoyed these projects, and as a student transitioning from her senior year in Data Science to her graduate studies in Artificial Intelligence, I was anxious to record all of my findings- as you'll see via commentary at the end of the files. I saw so many patterns unfolding between all of my studies and felt these projects gave me a peek into the Pandora's box of how representing physical continuums into discretized approaches- being able to approximate solutions where we can't find an exact solution- could be translatable to so many interdisciplinary mysteries. These projects were invigorating! Unfortunately, I haven't had time to iron out my commentary either in Markdown or in the structure of the coding itself to make it as explicit (ha) as I'd like quite yet. But as a labor of love, I hope to return to this either here or in future projects :)