Articles

Protocols 🇺🇸

September 21, 2026
Category: Frontend Notes

In today’s connected world, front-end developers do far more than style web pages and craft user interfaces. They also need to understand the underlying network protocols that shape how data travels between their applications and the servers that power them. By mastering the inner workings of protoc...

Ux 🇺🇸

September 21, 2026
Category: Frontend Notes

UX, or User Experience, focuses on designing products and services that meet user needs, preferences, and behaviors. The goal is to make important tasks useful, understandable, accessible, and effective; evaluate these outcomes with users rather than assuming any interface is universally intuitive...

Quizes 🇺🇸

September 21, 2026
Category: Frontend Notes

Use these expandable questions to test explanations, not just terminology. Before opening an answer, predict the result and try a small browser example. The categories cover HTML, CSS, JavaScript, protocols and hosting. Examples are illustrative; versions, browser support and hosting prices should b...

Hosting Websites 🇺🇸

September 21, 2026
Category: Frontend Notes

A website on your computer is not automatically reachable by other people. Hosting makes its files or application available over a network; DNS helps browsers find the hostname's destination; HTTPS protects communication between client and server. These are different concerns, and publishing a page ...

Testing 🇺🇸

September 21, 2026
Category: Frontend Notes

A frontend is not finished when its first demonstration works. It must still work after a CSS change, a pricing-rule update, a dependency upgrade, or a failed network request. Testing turns the promises a feature makes to its users into checks that can fail when those promises are broken. It reduces...

Css Frameworks 🇺🇸

September 21, 2026
Category: Frontend Notes

CSS preprocessors and frameworks are two important tools in a web developer's toolbox that can help streamline the process of building websites. CSS preprocessors allow developers to use new functionality that is typically borrowed from another programming language, while frameworks provide pre-writ...

Ui 🇺🇸

September 21, 2026
Category: Frontend Notes

UI is an important aspect of frontend development, as it deals with the elements that users directly interact with. When designing the UI, it’s important to think about how color choices, overall layout, responsiveness, and interactive elements come together to make the product look appealing and ea...

Javascript Frameworks 🇺🇸

September 21, 2026
Category: Frontend Notes

A static portfolio, a content website with minimal interactivity, and a client-heavy dashboard have different requirements. Begin with an explicit feature inventory: navigation/routing, persistence, data fetching, authentication boundaries, search requirements, accessibility, localization, bundle co...

Javascript 🇺🇸

September 21, 2026
Category: Frontend Notes

JavaScript is a programming language that is primarily used for client-side scripting (making web pages interactive). Since NodeJS we can also use JavaScript in server-side scripting (e.g. for APIs). ...

Css 🇺🇸

September 21, 2026
Category: Frontend Notes

A small card is a useful controlled experiment: keep the same HTML before and after, then toggle only the CSS class. This isolates the effect of styling from changes in text, structure or JavaScript. The actual Chromium screenshot shows both rendered states side by side...

Html 🇺🇸

September 21, 2026
Category: Frontend Notes

The browser parses HTML into a document tree. CSS styles that tree; JavaScript can update it. A semantic page can be styled to look identical to a page made entirely of generic

Additional Resources 🇺🇸

September 21, 2026
Category: Frontend Notes

This chapter is a directory, not a certification program. The sites below may offer free and paid assets, incompatible versions, or changing terms. When a resource looks useful, open its source and license, run the demo where possible, then test how it behaves in your own layout. Do not treat a beau...

Partial Differential Equations 🇺🇸

September 21, 2026
Category: Numerical Methods

A partial differential equation (PDE) relates an unknown function of several independent variables to its partial derivatives. PDEs describe fields rather than single trajectories: temperature in space and time, pressure in a fluid, displacement in an elastic body, or the amplitude of a wave...

Ordinary Differential Equations 🇺🇸

September 21, 2026
Category: Numerical Methods

An ordinary differential equation (ODE) relates an unknown function of one independent variable to one or more of its derivatives. ODEs are the natural language of dynamical systems: they describe how a state changes when its instantaneous rate of change is known...

Heuns Method 🇺🇸

September 21, 2026
Category: Numerical Methods

Heun's method improves Euler's method by using information from both ends of each step. It is a second-order explicit Runge--Kutta method and is also known as the explicit trapezoidal method or improved Euler method...

Picards Method 🇺🇸

September 21, 2026
Category: Numerical Methods

Picard iteration turns an initial value problem into a sequence of integral approximations. It is important less as a production ODE solver than as the constructive idea behind a fundamental existence-and-uniqueness theorem...

Runge Kutta 🇺🇸

September 21, 2026
Category: Numerical Methods

Runge--Kutta methods advance an ODE solution using several carefully chosen slope evaluations inside each step. They achieve higher-order accuracy without requiring explicit derivatives of $f$ beyond the first derivative already present in the ODE...

Eulers Method 🇺🇸

September 21, 2026
Category: Numerical Methods

Euler's method is the simplest explicit time-stepping method for an initial value problem (IVP). It is useful both as a practical first approximation and as a way to understand how numerical ODE solvers work...

Monte Carlo 🇺🇸

September 21, 2026
Category: Numerical Methods

Monte Carlo integration is a numerical technique for approximating integrals using randomness. Rather than systematically sampling a function at predetermined points, as done in methods like the trapezoidal rule or Simpson’s rule, Monte Carlo methods rely on random samples drawn from a prescribed do...

Simpsons Rule 🇺🇸

September 21, 2026
Category: Numerical Methods

Simpson's Rule is a powerful technique in numerical integration, utilized for approximating definite integrals when an exact antiderivative of the function is difficult or impossible to determine analytically. This method enhances the accuracy of integral approximations by modeling the region under ...

Midpoint Rule 🇺🇸

September 21, 2026
Category: Numerical Methods

The Midpoint Rule is a robust numerical method for approximating definite integrals. It seeks to estimate the area under a curve by partitioning it into a collection of rectangles and then summing the areas of these rectangles. This method is particularly useful when an antiderivative of the functio...

Integration Introduction 🇺🇸

September 21, 2026
Category: Numerical Methods

$$\int_{1}^{2} x^2 dx \approx \sum_{i=1}^{10} h \cdot f(1 + 0.1i)$...

Trapezoidal Rule 🇺🇸

September 21, 2026
Category: Numerical Methods

The Trapezoidal Rule is a fundamental numerical integration technique employed to approximate definite integrals, especially when an exact antiderivative of the function is difficult or impossible to determine analytically. This method is widely used in various fields such as engineering, physics, a...

Eigenvalues and Eigenvectors 🇺🇸

September 21, 2026
Category: Numerical Methods

Eigenvalues and eigenvectors are foundational concepts in linear algebra, with extensive applications across various domains such as physics, computer graphics, and machine learning. These concepts are instrumental in decomposing complex matrix transformations, thereby simplifying numerical computat...

Matrix Methods 🇺🇸

September 21, 2026
Category: Numerical Methods

Matrices are often described as rectangular arrays of numbers organized into rows and columns, and they form the bedrock of numerous processes in numerical methods. People use them for solving systems of linear equations, transforming geometric data, and carrying out many algorithmic tasks that lie ...

Singular Value Decomposition 🇺🇸

September 21, 2026
Category: Numerical Methods

Singular Value Decomposition (SVD) is a fundamental matrix decomposition technique widely used in numerous areas of science, engineering, and data analysis. Unlike the Eigenvalue Decomposition (EVD), which is restricted to square and diagonalizable matrices, SVD applies to any rectangular matrix. It...

Qr Method 🇺🇸

September 21, 2026
Category: Numerical Methods

The QR method is a widely used algorithm in numerical linear algebra for determining the eigenvalues of a given square matrix. Unlike direct methods such as solving the characteristic polynomial, which can be complicated and unstable numerically for large matrices, the QR method leverages iterative ...

Power Method 🇺🇸

September 21, 2026
Category: Numerical Methods

The power method is a fundamental iterative algorithm for estimating the eigenvalue of largest magnitude and its associated eigenvector for a given matrix. This technique is particularly appealing when dealing with large and sparse matrices, where direct eigenvalue computations (e.g., via the charac...

Eigen Value Decomposition 🇺🇸

September 21, 2026
Category: Numerical Methods

Eigenvalue Decomposition (EVD), also known as Eigendecomposition, is a fundamental operation in linear algebra that breaks down a square matrix into a simpler form defined by its eigenvalues and eigenvectors. This decomposition provides deep insights into the properties and structure of a matrix, en...

Inverse Matrix 🇺🇸

September 21, 2026
Category: Numerical Methods

The inverse of a matrix A is denoted as A^-1. It is a unique matrix such that when it is multiplied by the original matrix A, the result is the identity matrix I. Mathematically, this is expressed as...

Systems of Equations 🇺🇸

September 21, 2026
Category: Numerical Methods

A linear system of equations is a collection of one or more linear equations involving the same set of variables. Such systems arise in diverse areas such as engineering, economics, physics, and computer science. The overarching goal is to find values of the variables that simultaneously satisfy all...

Lu Decomposition 🇺🇸

September 21, 2026
Category: Numerical Methods

LU Decomposition (or LU Factorization) is a powerful and widely used technique in numerical linear algebra for solving systems of linear equations, computing inverses, and determining determinants. The core idea is to factorize a given square matrix $A$ into the product of a lower-triangular matrix ...

Jacobi Method 🇺🇸

September 21, 2026
Category: Numerical Methods

The Jacobi method is a classical iterative algorithm used to approximate the solution of a system of linear equations $A\mathbf{x} = \mathbf{b}$. Instead of attempting to solve the system directly using methods such as Gaussian elimination, the Jacobi method iteratively refines an initial guess for ...

Gauss Seidel 🇺🇸

September 21, 2026
Category: Numerical Methods

The Gauss-Seidel method is a classical iterative method for solving systems of linear equations of the form $A\mathbf{x} = \mathbf{b}$, where $A$ is an $n \times n$ matrix, $\mathbf{x}$ is the vector of unknowns $(x_1, x_2, \ldots, x_n)$, and $\mathbf{b}$ is a known vector. Unlike direct methods suc...

Gaussian Elimination 🇺🇸

September 21, 2026
Category: Numerical Methods

Gaussian elimination is a fundamental algorithmic procedure in linear algebra used to solve systems of linear equations, find matrix inverses, and determine the rank of matrices. The procedure systematically applies elementary row operations to transform a given matrix into an upper-triangular form ...