This repository contains assignments and materials from the course "Numerical Analysis" for the Computer Engineering program.
The course aims to provide students with the knowledge and tools to solve engineering problems using numerical methods. The assignments in this repository cover a variety of topics, including Jupyter Notebook, Numpy, vectorization, truncation errors, linear system solving, root-finding algorithms, hybrid root-finding algorithms, topic modeling, PageRank algorithm, and linear regression.
The following topics are covered in this repository:
This section covers the basics of Jupyter Notebook, including how to create and run a notebook, how to use markdown, and how to use code cells.
This section covers the basics of Numpy, including how to create arrays, how to manipulate arrays, and how to use Numpy functions.
This section covers the concept of vectorization, which is the process of rewriting a non-vectorized code into a vectorized code. You will learn how to use Numpy to perform vectorized operations.
This section covers the concept of truncation errors, which are errors that occur when a mathematical function is approximated by a finite sum or product. You will learn how to calculate truncation errors and how to minimize them.
This section covers the basics of solving linear systems, including how to represent a linear system, how to solve it using Gaussian elimination, and how to solve it using LU decomposition.
This section covers the basics of root-finding algorithms, which are numerical methods for finding the roots of a function. You will learn about the Bisection method, the Secant method, and the Newton-Raphson method.
This section covers the hybrid root-finding algorithm, which is a combination of the Bisection method and the Newton-Raphson method. You will learn how to implement the hybrid root-finding algorithm and how to choose appropriate initial values.
This section covers topic modeling, which is the process of automatically identifying the topics that occur in a collection of documents. You will learn how to use Latent Dirichlet Allocation (LDA) to perform topic modeling.
This section covers the PageRank algorithm, which is an algorithm used by Google Search to rank websites in their search engine results. You will learn how to implement the PageRank algorithm and how to interpret the results.
This section covers the basics of linear regression, including how to represent a linear regression model, how to estimate the parameters of the model using the Least Squares method, and how to evaluate the model.
This repository serves as a reference for the topics covered in the course "Numerical Analysis". You can use the assignments provided to deepen your understanding of the topics and implement them in your own projects.
- Rafael Guimarães - Computer Engineering at IFPB