Examples of applied mathematics
The post presents some techniques available in Python ecosystem in order to approximate periodic functions using the Fourier series.
The post presents some librareis and some techniques available in Python ecosystem in order to solve numerically delay differential equations.
The post presents some librareis and some techniques available in Python ecosystem in order to compute integrals. Precisely, the post shows how to compute single, double, triple and more integrals both numerically and symbolically.
The post shows a Python program that analyzes the behavior of a dynamical system on the linear, homogeneous plane given the coefficients of the matrix A representing the system of two differential equations dx/dt=Ax. Precisely, the program calculates the critical points, studies the behavior at the critical points, calculates the general integral of the solutions and optionally calculates a particular solution. Finally it draws the portrait of the phases and optionally the graph of the particular solution.
The post presents a Python program that analyzes the behavior of a nonlinear and autonomous dynamic system on the plane given two differential equations put into a system. Precisely, the program calculates the critical points, calculates the Jacobian at the critical points, verifies that they are hyperbolic and in this case it studies the behavior at the critical points linearizing around these points by applying Hartman-Grobman theorem.
Examples of use of the SymPy library to solve in symbolic way first-order differential equations of different types
Time Delayed Systems can be modeled with Delay Differential Equations which in turn can be solved numerically, in some specific cases, using Lambert W function. This post shows and explains the implementation of a program to compute the solutions supplied by a paper cited in the bibliography.