{"id":14977185,"url":"https://github.com/restrepo/computationalmethods","last_synced_at":"2026-04-02T15:01:53.909Z","repository":{"id":37561955,"uuid":"129130312","full_name":"restrepo/ComputationalMethods","owner":"restrepo","description":"Computational Methods Course at UdeA. 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These topics will be addressed from a formal context but also keeping\na practical and computational approach, illustrating many useful applications in\nproblems of physics and astronomy.\n\n\nThe practical component will be almost entirely developed in *Python* and\nslightly less in *C* (when computational performance is required).\nHowever students with knowledge in other programming languages (except\nprivative languages like MatLab, Mathematica) are also aimed to use them.\n\n\nIn this repository it can be found all the related material of the course,\nincluding the detailed program, notes and presentations, examples (ipython\nnotebooks) and homeworks. (This repository may be subject to changes continuously\nas the course advances).\n\n[Submodules help](https://git-scm.com/book/en/v2/Git-Tools-Submodules)\n\n[**SYLLABUS**](https://github.com/sbustamante/ComputationalMethods/raw/master/syllabus/Programa_M%C3%A9todos_Computacionales.pdf):\ndetailed description of the program of the course, including a brief motivation and presentation,\ntopics to be covered, evaluation and bibliography.\n\n\nContents\n--------\n\n### 1. **Python** *(1 week)*\n\n**Topics**\n- [Overview of python](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/overview-python.ipynb)\n- [Basic scripting](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/basic-scripting.ipynb)\n- [Implementation of scientific libraries](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/scientific-libraries.ipynb)\n- [Plotting with matplotlib](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/matplotlib.ipynb)\n- [Ipython notebooks](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/ipython-notebooks.ipynb)\n\n**Activities**\n- *Activity 01:* Solve the problems in the section [Exercises](https://github.com/sbustamante/ComputationalMethods/blob/master/material/Basic_exercises.ipynb).\n\n### 2. **Mathematical Preliminaries** *(1 week)*\n\n**Topics**\n- [Computer arithmetics and round-off methods](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/computer-arithmetics.ipynb)\n- [Algorithms and convergence](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/algorithms-convergence.ipynb)\n\n### 3. **One Variable Equations** *(2 weeks)*\n\n**Topics**\n- [Bisection method](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/one-variable-equations.ipynb#Bisection-Method)\n- [Fixed-point iteration](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/one-variable-equations.ipynb#Fixed-point-Iteration)\n- [Newton-Raphson method](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/one-variable-equations.ipynb#Newton-Raphson-Method)\n- [Secant method](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/one-variable-equations.ipynb#Secant-Method)\n\n### 4. **Interpolation Techniques** *(2 weeks)*\n\n**Topics**\n- [Linear interpolation](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/interpolation.ipynb#Linear-Interpolation)\n- [Lagrange polynomials](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/interpolation.ipynb#Lagrange-Polynomial)\n- [Divided differences](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/interpolation.ipynb#Divided-Differences)\n- [Hermite interpolation](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/interpolation.ipynb#Hermite-Interpolation)\n\n### 5. **Numerical Calculus** *(2 weeks)*\n\n**Topics**\n- [Numerical differentiation](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/numerical-calculus.ipynb#Numerical-Differentiation)\n- [Numerical integration](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/numerical-calculus.ipynb#Numerical-Integration)\n- [Composite numerical integration](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/numerical-calculus.ipynb#Composite-Numerical-Integration)\n- [Adaptive quadrature methods](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/numerical-calculus.ipynb#Adaptive-Quadrature-Methods)\n- [Improper integrals](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/numerical-calculus.ipynb#Improper-Integrals)\n\n**Activities**\n- *Activity:* [ Derivative exercise ](http://nbviewer.jupyter.org/github/sbustamante/ComputationalMethods/blob/master/activities/T-profile-bar.ipynb)\n\n### 6. **Linear Algebra** *(2 weeks)*\n\n**Topics**\n- [Linear systems of equations](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/linear-algebra.ipynb#Linear-Systems-of-Equations)\n- [Gaussian elimination](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/linear-algebra.ipynb#Gaussian-Elimination)\n- [Pivoting strategies](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/linear-algebra.ipynb#Pivoting-Strategies)\n- [Matrix inversion](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/linear-algebra.ipynb#Matrix-Inversion)\n- [Determinant of a Matrix](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/linear-algebra.ipynb#Determinant-of-a-Matrix)\n- [LU factorization](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/linear-algebra.ipynb#LU-Factorization)\n\n### 7. **Differential Equations** *(2 weeks)*\n\n**Topics**\n- [First order methods](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/differential-equations.ipynb#First-Order-Methods)\n- [High order methods](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/differential-equations.ipynb#High-Order-Methods)\n- [Two-Point boundary value problems](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/differential-equations.ipynb#Two-Point-Boundary-Value-Problems)\n\n### 8. **Statistics** *(1 week)*\n\n**Topics**\n- [Data adjust](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/statistics.ipynb)\n- [Random Numbers](http://nbviewer.ipython.org/github/sbustamante/ComputationalMethods/blob/master/material/statistics.ipynb#Random-Numbers)\n\n","funding_links":[],"categories":[],"sub_categories":[],"project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Frestrepo%2Fcomputationalmethods","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Frestrepo%2Fcomputationalmethods","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Frestrepo%2Fcomputationalmethods/lists"}