In-depth guides on structural analysis, geotechnics, hydrology, construction, statistics and AI for engineers, written for students and working professionals.
The Laplacian filter finds edges, spots and fine detail by measuring the curvature of brightness. This guide starts from the derivative of a 1-D signal, derives the familiar 3 × 3 kernels from Taylor series, explains what the sign and the zero crossings mean, shows why the filter amplifies noise and how the Laplacian of Gaussian fixes it, and ends with blob detection, sharpening and the Laplacian in physics. Four live demos let you test each idea.
The Gaussian filter is the most widely used smoothing filter in image processing, remote sensing and computer vision. This guide builds it from nothing: what filtering is, how convolution works, where the bell curve comes from, how to compute a kernel by hand, why the filter is separable, what it does to frequencies and noise, and how to choose σ. Every idea comes with a worked example or a live demo
Four equations describe every classical electric and magnetic phenomenon, from a compass needle to Wi-Fi to sunlight. This guide states each law in integral and differential form, explains what it means physically with an example,
Every power station, transformer, electric guitar pickup and wireless charger works because a changing magnetic flux induces a voltage. This guide explains magnetic flux, Faraday's law, the direction rule of Lenz's law, motional EMF, the AC generator, transformers, inductance and eddy currents, with worked examples and an animated generator you can control.
Infiltration decides how much rain becomes runoff. This guide explains the three classic infiltration models, gives the Rawls Green-Ampt parameters for all 11 soil textures, shows how to compute ponding time, and works through the φ-index and W-index.
The FAO-56 Penman-Monteith equation is the international standard for reference evapotranspiration. This guide explains every term, walks through all twelve calculation steps, reproduces the official FAO worked example (ET₀ = 3.9 mm/day),
Rain gauges measure rainfall at points, but floods, water budgets and hydrological models need the average over an area. This guide explains the three classical methods, lets you drag gauges on a live catchment and watch the Thiessen polygons
The rational method is the most widely used way to size storm drains, culverts and gutters for small catchments. This guide covers the formula in SI and US units, where each term comes from, how to pick C, how to compute the time of concentration and
A hydrograph is a graphical representation of the variation of discharge (or stage) of a stream at a given gauging station plotted against time. In hydrology, it is the single most important tool for understanding and quantifying the rainfall-runoff response of a catchment. Every flood estimate, reservoir design, culvert sizing, and floodplain mapping exercise depends either directly on a measured hydrograph or on a model capable of reproducing one.
The 3-point bending test (also written as three-point bend test or flexure test) is a standardised mechanical test that measures the flexural properties of a material by loading a beam specimen at its midpoint while it rests on two supports
he complete reference for the Hollomon power law
: derivation, physical meaning of K and n, true-vs-engineering stress-strain conversion, worked examples for annealed copper and structural steel, comprehensive K and n table for 20+
A complete reference covering the normal distribution formula, the 68-95-99.7 empirical rule, Z-scores and probability tables, skewness, kurtosis, real-world examples across engineering, biology, finance, and education - plus an interactive calculator.
The displacement method (also called the stiffness method or equilibrium method) is the second fundamental approach to analysing statically indeterminate structures. Instead of treating unknown forces as primary unknowns, the displacement method takes joint displacements and rotations as unknowns and enforces equilibrium at every free joint.
The force method, also called the compatibility method, flexibility method, or method of consistent deformations, is a classical technique for analysing statically indeterminate structures. It was developed......
In the realm of artificial neural networks (ANNs), the loss function serves as a critical component that guides the training process. It quantifies the difference between the model's predictions and the actual target values, enabling optimization algorithms to adjust the network's parameters for better performance.
This paper, “Knowledge-informed deep learning for hydrological model calibration: an application to Coal Creek Watershed in Colorado,” mainly focuses on improving the efficiency and reducing the computational load in hydrological model calibration...
Discover the structural behaviour and how retaining walls transform landscapes, from choosing materials to planning installation, maintenance, and creative landscaping.
The Gaussian filter is the most widely used smoothing filter in image processing, remote sensing and computer vision. This guide builds it from nothing: what filtering is, how convolution works, where the bell curve comes from, how to compute a kernel by hand, why the filter is separable, what it does to frequencies and noise, and how to choose σ. Every idea comes with a worked example or a live demo
Apply the 4-neighbour, 8-neighbour or isotropic Laplacian kernel, the Laplacian of Gaussian or a Difference of Gaussians to a test image or your own photo. View the signed response, find edges as zero crossings, sharpen the image, and see why smoothing must come before the second derivative. Click any pixel to see the arithmetic.
Generate a normalized Gaussian kernel for any sigma, see exactly how its weights are computed, and apply it to a test image or your own photo. Add noise, measure the improvement in PSNR, find the best sigma, and compare the filter's frequency response with a box filter. Every calculation runs in your browser.
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