PHP Science Class Library

Table of Contents

• Introduction
• Installation
• Usage
• Modules
  • Architecture Calculations
  • Astrophysics Calculations
  • Biology Calculations
  • Building Drawing Calculations
  • Chemistry Calculations
  • Computer Science Calculations
  • Electronics Calculations
  • Geoscience Calculations
  • Mathematics Calculations
  • Mechanics Calculations
  • Physics Calculations
  • Telecommunications Calculations
  • Thermodynamics Calculations
• Contributing
• License

Introduction

The PHP Science Class Library is a comprehensive collection of PHP classes designed to perform a wide array of scientific calculations. This library aims to assist developers, researchers, and students in implementing scientific computations across various disciplines, including physics, chemistry, biology, engineering, and more.

Installation

To incorporate this library into your project, use Composer:

composer require your-vendor/php-science-class

Replace your-vendor with the appropriate vendor name.

Usage

After installation, you can utilize the classes as follows:

require 'vendor/autoload.php';

use YourVendor\Science\PhysicsCalculations;

$physics = new PhysicsCalculations();
$force = $physics->calculateForce(10, 9.81);
echo "Force: " . $force . " N";

Ensure to replace YourVendor with the correct namespace.

Classes

Below are detailed descriptions of each class in the PHP Science Class library, including their purpose, features, and advanced sub-topics with corrected mathematical expressions for GitHub rendering.

MathCalculations

The MathCalculations class provides an extensive suite of mathematical operations, ranging from basic arithmetic (addition, subtraction, multiplication, division) to advanced topics in algebra, calculus, trigonometry, statistics, matrix operations, graph theory, and machine learning. Implemented in PHP, it includes methods for solving polynomial equations up to cubic order, numerically computing derivatives and integrals, and performing complex matrix operations such as determinant calculation and inversion. It also supports statistical analyses (e.g., mean, variance, skewness, kurtosis), machine learning algorithms (e.g., k-Nearest Neighbors, Support Vector Machines, Naive Bayes), and graph algorithms (e.g., Dijkstra’s shortest path, Hamiltonian paths, Eulerian circuits). The class is equipped with comprehensive error handling for invalid inputs (e.g., division by zero, negative factorials) and unit-aware calculations, making it a versatile tool for educational purposes, scientific research, and computational mathematics. Its extensive test suite, organized by mathematical domains, ensures robustness and reliability across diverse applications, enhancing its suitability for academic and professional use.

• Comprehensive Scope: Covers arithmetic, algebra, calculus, trigonometry, statistics, matrix operations, graph theory, and machine learning algorithms.
• Error Handling: Robustly implemented with checks for invalid inputs (e.g., division by zero, negative factorials), returning descriptive error messages.
• Numerical Methods: Employs numerical approximations for calculus operations (e.g., derivatives, integrals) with adjustable precision via step size or intervals.
• Flexibility: Supports various mathematical constructs like polynomials, sequences, and statistical distributions without unit conversions, focusing on pure numerical computation.
• Testing: Includes an extensive runTests() method with grouped test cases (e.g., Basic Operations, Algebra, Calculus) to validate functionality across all major features.
• Modularity: Functions are standalone and logically grouped, facilitating easy extension or integration into larger systems.

Advanced Algebra

• Cubic Formula
  Solves cubic equations (e.g., $x^3 - 6x^2 + 11x - 6 = 0$) using Cardano’s method, handling real roots with intricate discriminant analysis (cubicFormula). This method involves calculating the discriminant $\Delta = \left(\frac{g^2}{4} + \frac{f^3}{27}\right)$ and determining roots via cube roots and trigonometric functions, demonstrating deep algebraic manipulation beyond simple quadratics.
• Polynomial Roots
  Determines roots for polynomials up to degree 3, integrating quadratic ($ax^2 + bx + c = 0$) and cubic solvers into a unified framework (polynomialRoots). For quadratics, it uses $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, showcasing adaptability to polynomial complexity.

Calculus Mastery

• Second Derivative
  Numerically computes the second derivative using finite differences ($f''(x) \approx \frac{f'(x+h) - f'(x-h)}{2h}$), enabling analysis of curvature and inflection points (secondDerivative). This builds on the first derivative approximation $f'(x) \approx \frac{f(x+h) - f(x-h)}{2h}$, critical for optimization and curve analysis.
• Integration by Parts
  Implements the advanced calculus technique $\int u , dv = uv - \int v , du$ numerically, handling complex integrands with nested function evaluations (integralByParts). This method approximates the integral by discretizing the domain, a hallmark of sophisticated numerical integration.

Matrix Operations

• Matrix Inverse
  Calculates the inverse of a square matrix using the adjoint and determinant ($A^{-1} = \frac{\text{adj}(A)}{\det(A)}$), involving recursive minor computations (inverse). For a 2x2 matrix $\begin{bmatrix} a & b \ c & d \end{bmatrix}$, the inverse is $\frac{1}{ad - bc} \begin{bmatrix} d & -b \ -c & a \end{bmatrix}$, demonstrating computational intensity central to linear algebra solutions.
• Determinant
  Recursively computes the determinant via cofactor expansion for any $n \times n$ matrix, showcasing recursive algorithmic depth (determinant). For a 3x3 matrix $\begin{bmatrix} a & b & c \ d & e & f \ g & h & i \end{bmatrix}$, it’s $a(ei - fh) - b(di - fg) + c(dh - eg)$.

Statistical Distributions

• Chi-Square Cumulative Distribution Function (CDF)
  Approximates the CDF for the chi-square distribution using the incomplete gamma function $\Gamma(s, x) = \int_0^x t^{s-1} e^{-t} , dt$, critical for statistical hypothesis testing (chiSquareCDF). The CDF is $F(x; k) = \frac{\gamma(k/2, x/2)}{\Gamma(k/2)}$, involving complex gamma approximations.
• Cumulative Normal Distribution
  Uses a high-precision polynomial approximation (e.g., Abramowitz-Stegun formula) to compute the cumulative probability of a standard normal distribution $\Phi(z) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^z e^{-t^2/2} , dt$, vital for advanced statistical analysis (cumulativeNormalDistribution).

Machine Learning and Clustering

• Support Vector Machine (SVM) Classification
  Implements a linear SVM with gradient descent optimization for binary classification, balancing margin maximization and error minimization (svmClassify). It optimizes $w$ and $b$ in $y_i(w \cdot x_i + b) \geq 1$, reflecting cutting-edge machine learning complexity.
• DBSCAN Clustering
  Performs density-based spatial clustering with noise handling, using epsilon-neighborhoods and minimum points criteria (dbscan). It identifies core points where $|N_\epsilon(x)| \geq \text{MinPts}$, a sophisticated unsupervised learning approach.

Graph Theory

• Hamiltonian Path
  Finds a Hamiltonian path in a graph using backtracking, solving an NP-complete problem with recursive exploration (hamiltonianPath). This ensures each vertex is visited exactly once, highlighting combinatorial optimization prowess.
• Dijkstra’s Algorithm
  Computes shortest paths in a weighted graph with a min-priority queue approach, optimized for sparse graphs with complexity $O((V + E) \log V)$ (dijkstra). It minimizes $d[u] + c(u,v)$ for each vertex $v$.

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PhysicsCalculations

The PhysicsCalculations class is a robust PHP implementation of fundamental and advanced physics computations, covering mechanics (kinematics and dynamics), thermodynamics, electromagnetism, optics, relativity, quantum mechanics, and nuclear physics. It leverages physical constants (e.g., gravitational constant $G = 6.67430 \times 10^{-11} , \text{m}^3 \text{kg}^{-1} \text{s}^{-2}$, speed of light $c = 299792458 , \text{m/s}$) to calculate quantities such as motion parameters, forces, electric fields, thermodynamic properties, and relativistic effects. The class supports flexible unit conversions (e.g., meters to kilometers, joules to calories) and includes rigorous error checking for physical validity (e.g., non-negative masses, non-zero distances). Designed for educational and research applications, its comprehensive test suite, organized by physics subfields, validates accuracy across diverse scenarios, making it an invaluable resource for students, educators, and physicists exploring theoretical and applied physics.

• Broad Physics Coverage: Encompasses mechanics, thermodynamics, electromagnetism, optics, relativity, quantum mechanics, and nuclear physics, leveraging constants like $G$, $c$, and $h$.
• Unit Flexibility: Supports multiple unit systems (e.g., m/s to km/h, J to cal) with automatic conversions for inputs and outputs.
• Error Checking: Ensures physical validity with checks for negative masses, zero distances, or velocities exceeding $c$.
• Comprehensive Constants: Defines constants like $G_\text{CONST}$, $\epsilon_0 = 8.8541878128 \times 10^{-12} , \text{F/m}$, $\sigma = 5.670374419 \times 10^{-8} , \text{W/m}^2\text{K}^4$ for consistent calculations.
• Testing Suite: Features a detailed runTests() method organized by subfields (e.g., Mechanics, Thermodynamics), verifying accuracy across scenarios.
• Interdisciplinary Utility: Serves as a foundational class for other physics-related classes (e.g., ElectronicsCalculations, ThermodynamicsCalculations) via inheritance.

Mechanics - Dynamics

• Gravitational Force
  Applies Newton’s universal gravitation ($F = G \frac{m_1 m_2}{r^2}$) with unit conversions, handling astronomical-scale calculations (gravitationalForce). For Earth ($m_1 = 5.972 \times 10^{24} , \text{kg}$, $r = 6371 , \text{km}$), it computes surface gravity.
• Torque
  Computes torque ($\tau = F r \sin\theta$) with angular considerations and unit flexibility (e.g., N·m to lbf·ft), critical for rotational dynamics (torque). This models lever arms and rotational forces.

Thermodynamics

• Work in Isothermal Process
  Calculates work ($W = nRT \ln\left(\frac{V_2}{V_1}\right)$) for an ideal gas under isothermal conditions, integrating logarithmic complexity with unit conversions (e.g., J to cal) (workIsothermal). This is essential for thermodynamic cycles like the Carnot cycle.
• Carnot Efficiency
  Determines maximum efficiency ($\eta = 1 - \frac{T_\text{cold}}{T_\text{hot}}$) with temperature validation in Kelvin, a pinnacle of thermodynamic analysis (carnotEfficiency). For $T_\text{hot} = 400 , \text{K}$, $T_\text{cold} = 300 , \text{K}$, $\eta = 0.25$.

Electricity and Magnetism

• Faraday’s Law
  Computes induced EMF ($\varepsilon = -\frac{d\Phi_B}{dt}$) for electromagnetic induction, handling dynamic flux changes (faradayLaw). For a coil with $\Phi_B = B A \cos(\omega t)$, it derives $\varepsilon = B A \omega \sin(\omega t)$.
• Electric Field Energy
  Calculates energy density in an electric field ($U = \frac{1}{2} \epsilon_0 E^2 V$), integrating field strength and volume with units (e.g., J to µJ) (electricFieldEnergy), vital for capacitor design.

Relativity

• Relativistic Velocity Addition
  Applies the relativistic formula ($u' = \frac{u + v}{1 + \frac{uv}{c^2}}$) to combine velocities near light speed, ensuring $u' < c$ (relativisticVelocityAddition). For $u = v = 0.5c$, $u' \approx 0.8c$.
• Relativistic Momentum
  Computes momentum ($p = \gamma m v$) with Lorentz factor ($\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$), reflecting high-energy physics precision (relativisticMomentum). At $v = 0.9c$, $\gamma \approx 2.294$.

Quantum Mechanics

• Quantum Probability
  Approximates probability via numerical integration of a wave function’s squared magnitude ($P = \int |\psi|^2 , dx$), a complex quantum mechanics application (quantumProbability). For $\psi(x) = \sin(x)$, it computes probability over $[0, \pi]$.
• Quantum Energy Level
  Calculates energy in a particle-in-a-box model ($E = \frac{n^2 h^2}{8 m L^2}$), integrating quantum principles with constants like $h = 6.62607015 \times 10^{-34} , \text{J·s}$ (quantumEnergyLevel).

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ChemistryCalculations

The ChemistryCalculations class offers a sophisticated PHP framework for chemical computations, integrating a complete periodic table with 118 elements and properties (e.g., atomic mass, electronegativity, electron configuration). It supports calculations in stoichiometry (e.g., molar conversions), thermodynamics (e.g., enthalpy, Gibbs free energy), bonding analysis, and analytical chemistry (e.g., pH). Key features include ideal gas law applications, dynamic molecular bond analysis, and THREE.js-based 3D visualization of molecular shapes (e.g., tetrahedral for CH₄, trigonal planar for BF₃), enhancing structural chemistry studies. With built-in unit flexibility (e.g., g to kg, Pa to atm) and extensive error handling (e.g., negative values, invalid formulas), it’s a powerful tool for chemistry education, research, and laboratory simulations. Its thorough test suite, grouped by subfields, ensures precision and reliability across diverse chemical computations.

• Periodic Table Integration: Includes data for all 118 elements with properties like atomic mass (e.g., H: 1.00794 u), electronegativity, and electron configuration.
• Chemical Computations: Supports stoichiometry, thermodynamics (e.g., $\Delta H$, $\Delta G$), bonding, and analytical chemistry (e.g., pH).
• Visualization: Generates THREE.js code for 3D molecular shapes (e.g., CH₄ as tetrahedral), leveraging VSEPR theory.
• Unit Support: Handles conversions (e.g., g to kg, Pa to atm, J/mol to kJ/mol) for mass, pressure, and energy.
• Error Management: Validates inputs (e.g., non-negative moles, valid formulas), returning detailed error messages.
• Testing: Provides a runTests() method grouped by subfields (e.g., Thermodynamics, Bonding), ensuring reliability.

Thermodynamics

• Gibbs Free Energy
  Computes $\Delta G = \Delta H - T \Delta S$ with multi-unit support (e.g., J/mol, kJ/mol, K, °C), essential for predicting reaction spontaneity (gibbsFreeEnergy). For $\Delta H = 40 , \text{kJ/mol}$, $T = 298 , \text{K}$, $\Delta S = 20 , \text{J/mol·K}$, $\Delta G \approx 34 , \text{kJ/mol}$.
• Clausius-Clapeyron
  Calculates vapor pressure changes ($\ln\left(\frac{P_2}{P_1}\right) = -\frac{\Delta H_\text{vap}}{R} \left(\frac{1}{T_2} - \frac{1}{T_1}\right)$), a sophisticated tool for phase transitions (clausiusClapeyron). For water at $T_1 = 373 , \text{K}$, $P_1 = 100 , \text{kPa}$, $\Delta H_\text{vap} = 40.67 , \text{kJ/mol}$, it predicts $P_2$.

Bonding and Molecular Shape

• Molecular Bond
  Dynamically determines bond types and counts (e.g., CH₄: 4 C-H bonds) using electronegativity differences ($\Delta EN$) and valence, showcasing chemical structure analysis (molecularBond). For NaCl, $\Delta EN > 1.7$ indicates ionic bonding.
• Molecule Shape Drawing
  Generates THREE.js code for 3D visualization of molecular geometries (e.g., tetrahedral for CH₄, trigonal bipyramidal for PF₅) based on VSEPR theory, a cutting-edge feature (drawMoleculeShape).

Physical Chemistry

• Ideal Gas Volume
  Solves for volume using the ideal gas law ($V = \frac{nRT}{P}$) with inherited precision from PhysicsCalculations, handling unit conversions (e.g., m³ to L) (idealGasVolume). For $n = 1 , \text{mol}$, $T = 298 , \text{K}$, $P = 101325 , \text{Pa}$, $V \approx 0.0244 , \text{m}^3$.
• pH Calculation
  Computes pH ($-\log_{10}[H^+]$) with concentration unit flexibility (e.g., mol/L to mmol/L), critical for acid-base chemistry (pH). For $[H^+] = 0.001 , \text{mol/L}$, pH = 3.

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ComputerScienceCalculations

The ComputerScienceCalculations class is a comprehensive PHP library tailored for computer science applications, featuring a wide array of algorithms for sorting (e.g., Quick Sort, Radix Sort), searching (e.g., Binary Search), graph traversal (e.g., DFS, BFS), and optimization (e.g., Knapsack Problem, Dijkstra’s Algorithm). It includes tools for time complexity estimation (e.g., $O(n \log n)$), memory usage analysis (e.g., bytes to MB), and cryptographic operations (e.g., Caesar Cipher). Designed for educational and professional use, its detailed test suite validates correctness and efficiency across functionalities, making it suitable for teaching foundational concepts, developing prototypes, and analyzing performance in academic and industry settings.

• Algorithmic Focus: Implements sorting, searching, graph traversal, and dynamic programming algorithms.
• Performance Analysis: Estimates time complexity (e.g., $O(n \log n)$) and memory usage with unit conversions.
• Error Handling: Checks for invalid inputs (e.g., empty arrays, negative values) with clear error messages.
• Data Structure Support: Uses arrays for versatility, supporting comparison-based and non-comparison-based algorithms.
• Testing: Features a detailed runTests() method with sample data (e.g., sorting arrays, graph traversals), validating correctness and efficiency.
• Educational Design: Structured to demonstrate algorithmic concepts, ideal for teaching and prototyping.

Sorting Algorithms - Advanced

• Merge Sort
  Implements an $O(n \log n)$ divide-and-conquer sort with recursive merging, optimizing for large datasets (mergeSort). It splits an array into halves, sorts, and merges them efficiently.
• Radix Sort
  Performs non-comparison sorting by digit with complexity $O(nk)$, showcasing advanced integer sorting techniques (radixSort). For base-10 numbers, it processes each digit iteratively.

Graph Algorithms

• Dijkstra’s Algorithm
  Finds shortest paths in a weighted graph using a greedy approach ($O((V + E) \log V)$), optimized for pathfinding (dijkstra). For a graph with weights, it minimizes $d[u] + c(u,v)$.
• Knapsack Problem
  Solves the 0/1 knapsack problem using dynamic programming ($O(nW)$), a classic optimization challenge (knapsack). For items with weights and values, it maximizes value within a capacity $W$.

Dynamic Programming and String

• Longest Common Subsequence (LCS)
  Computes the LCS length between two strings using a 2D dynamic programming table ($O(mn)$), vital for sequence alignment (longestCommonSubsequence). For "ABCD" and "ACDF", LCS length is 3 ("ACD").
• Simple Hash Function
  Generates a hash value using a polynomial rolling hash ($O(n)$), foundational for data structures like hash tables (simpleHash). For a string $s$, it computes $h(s) = \sum s[i] \cdot p^i \mod m$.

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AstrophysicsCalculations

The AstrophysicsCalculations class is a specialized PHP toolkit for astrophysical computations, focusing on celestial mechanics and stellar properties. It employs constants like the gravitational constant ($G = 6.67430 \times 10^{-11} , \text{m}^3 \text{kg}^{-1} \text{s}^{-2}$) and Stefan-Boltzmann constant ($\sigma = 5.670374419 \times 10^{-8} , \text{W/m}^2\text{K}^4$) to calculate escape velocities, orbital periods via Kepler’s Third Law, and stellar luminosities. With robust error handling for invalid inputs (e.g., negative masses), it’s ideal for modeling planetary and stellar phenomena in educational contexts or preliminary research. Its concise test suite validates calculations against known examples (e.g., Earth’s escape velocity, Sun’s luminosity), offering reliability for astrophysics studies.

• Specialized Scope: Focuses on escape velocity, Kepler’s Third Law, and stellar luminosity using constants like $G$ and $\sigma$.
• Simplicity: Offers a concise set of methods tailored to celestial mechanics and stellar properties.
• Error Handling: Ensures positive inputs for mass and radius, returning error messages for invalid values.
• Unit Consistency: Operates in SI units (e.g., meters, kilograms) without explicit conversion options.
• Testing: Includes a minimal runTests() method with examples like Earth’s escape velocity (11.2 km/s) and Sun’s luminosity.
• Research-Oriented: Designed for quick astrophysical calculations, suitable for education and preliminary research.

Celestial Mechanics

• Kepler’s Third Law
  Calculates orbital period ($T = \sqrt{\frac{4\pi^2 r^3}{G m}}$), a complex relationship for planetary motion (keplerThirdLaw). For Earth ($r = 1.496 \times 10^{11} , \text{m}$, $m = 1.989 \times 10^{30} , \text{kg}$), $T \approx 365.25 , \text{days}$.
• Escape Velocity
  Computes escape velocity ($v = \sqrt{\frac{2GM}{r}}$), critical for space travel analysis (escapeVelocity). For Earth ($M = 5.972 \times 10^{24} , \text{kg}$, $r = 6371 , \text{km}$), $v \approx 11.2 , \text{km/s}$.

Stellar Physics

• Luminosity
  Calculates stellar luminosity ($L = 4\pi r^2 \sigma T^4$) using the Stefan-Boltzmann law, integrating radius and temperature effects (luminosity). For the Sun ($r = 6.96 \times 10^8 , \text{m}$, $T = 5778 , \text{K}$), $L \approx 3.828 \times 10^{26} , \text{W}$.

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GeoscienceCalculations

The GeoscienceCalculations class provides a PHP-based solution for geoscientific modeling, computing atmospheric pressure variations with altitude and earthquake energy based on Richter scale magnitude. It uses constants like gravitational acceleration ($g = 9.81 , \text{m/s}^2$) and the universal gas constant ($R = 8.314462618 , \text{J/mol·K}$) for accurate geophysical processes. Tailored for educational exploration and basic research, its simple test suite verifies core functionalities with realistic inputs. With straightforward design and error checking, it’s a practical tool for teaching geoscience concepts and simulating environmental phenomena.

• Geophysical Focus: Calculates atmospheric pressure and earthquake energy using constants like $g$ and $R$.
• Minimalistic Design: Features a focused set of methods for simplicity and ease of use.
• Error Checking: Validates inputs (e.g., non-negative magnitudes, valid pressures) with basic error messages.
• Unit Consistency: Uses SI units (e.g., Pa, J) without conversion support, aligning with geophysical standards.
• Testing: Provides a succinct runTests() method with realistic geophysical inputs (e.g., pressure at 1 km altitude).
• Educational Utility: Ideal for teaching geoscience concepts and simple environmental simulations.

Atmospheric Physics

• Atmospheric Pressure
  Computes pressure variation with altitude ($P = P_0 e^{-\frac{g M h}{RT}}$), a non-linear exponential model (atmosphericPressure). For $P_0 = 101325 , \text{Pa}$, $h = 1000 , \text{m}$, $T = 288 , \text{K}$, $P \approx 89.9 , \text{kPa}$.

Seismology

• Earthquake Energy
  Estimates seismic energy ($E = 10^{1.5M + 4.8}$) based on Richter magnitude, an advanced logarithmic calculation (earthquakeEnergy). For $M = 5$, $E \approx 2 \times 10^{12} , \text{J}$.

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ElectronicsCalculations

The ElectronicsCalculations class is a PHP implementation of essential electrical engineering calculations, addressing circuit analysis (resistance, capacitance, inductance, impedance) in DC and AC contexts. Integrated with PhysicsCalculations for consistency (e.g., Ohm’s Law $V = IR$), it supports unit conversions (e.g., $\Omega$ to k$\Omega$, F to µF). With comprehensive error handling and a detailed test suite covering Kirchhoff’s laws, RC time constants, and reactance, it’s well-suited for educational purposes, circuit design simulations, and prototyping, providing a reliable foundation for academic and practical applications.

• Circuit Analysis: Computes resistance, capacitance, inductance, impedance, and power, integrating with PhysicsCalculations.
• Unit Flexibility: Supports conversions (e.g., $\Omega$ to k$\Omega$, F to µF, V to mV) for practical use.
• Error Handling: Checks for negative values, zero divisors, and invalid configurations (e.g., zero time change).
• Physical Constants: Uses $\epsilon_0$ and $\mu_0$ for electromagnetic calculations, ensuring accuracy.
• Testing: Features a comprehensive runTests() method grouped by circuit types (e.g., resistive, capacitive), validating diverse scenarios.
• Practical Design: Tailored for electronics education and circuit design, balancing theory and application.

AC Circuit Analysis

• Impedance
  Calculates AC impedance ($Z = \sqrt{R^2 + (X_L - X_C)^2}$), integrating resistance and reactance (impedance). For $R = 10 , \Omega$, $X_L = 5 , \Omega$, $X_C = 2 , \Omega$, $Z \approx 10.44 , \Omega$.
• Inductive Reactance
  Computes $X_L = 2\pi f L$ for inductors, vital for AC frequency analysis (inductiveReactance). For $f = 50 , \text{Hz}$, $L = 0.1 , \text{H}$, $X_L \approx 31.4 , \Omega$.

Dynamic Elements

• Inductor Voltage
  Calculates $V_L = L \frac{di}{dt}$ with unit conversions (e.g., V to mV), key for transient analysis (inductorVoltage). For $L = 0.1 , \text{H}$, $\frac{di}{dt} = 2 , \text{A/s}$, $V_L = 0.2 , \text{V}$.
• Capacitor Current
  Computes $I_C = C \frac{dv}{dt}$, essential for dynamic circuit behavior (capacitorCurrent). For $C = 10 , \mu\text{F}$, $\frac{dv}{dt} = 100 , \text{V/s}$, $I_C = 1 , \text{mA}$.

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ThermodynamicsCalculations

The ThermodynamicsCalculations class is a PHP library for thermodynamic analyses, calculating ideal gas behavior, work in isothermal and isobaric processes, heat transfer, and efficiency metrics like the Carnot cycle. Built upon PhysicsCalculations, it uses constants (e.g., $R = 8.314462618 , \text{J/mol·K}$, $k_B = 1.380649 \times 10^{-23} , \text{J/K}$) and supports unit conversions (e.g., J to kJ, K to °C). Its extensive test suite validates accuracy, making it effective for teaching thermodynamics, energy system simulations, and research in physical chemistry and engineering.

• Thermodynamic Focus: Calculates pressure, work, heat, efficiency, and entropy, relying on PhysicsCalculations.
• Unit Support: Handles conversions (e.g., J to kJ, K to °C) for energy, temperature, and volume.
• Error Management: Ensures positive inputs and valid temperature differences, with detailed error messages.
• Constants Utilization: Uses $R$, $N_A$, $k_B$ for consistent results.
• Testing: Includes a structured runTests() method with grouped tests (e.g., ideal gas, efficiency), confirming reliability.
• Educational and Research Use: Supports teaching thermodynamics and modeling energy systems.

Thermodynamic Processes

• Work in Isothermal Process
  Calculates $W = nRT \ln\left(\frac{V_2}{V_1}\right)$ with logarithmic complexity and unit support, critical for heat engines (workIsothermal). For $n = 1 , \text{mol}$, $T = 300 , \text{K}$, $V_2/V_1 = 2$, $W \approx 1728 , \text{J}$.
• Coefficient of Performance (COP) for Refrigerator
  Computes $\text{COP} = \frac{T_\text{cold}}{T_\text{hot} - T_\text{cold}}$, a key refrigeration metric (copRefrigerator). For $T_\text{cold} = 263 , \text{K}$, $T_\text{hot} = 298 , \text{K}$, $\text{COP} \approx 7.51$.

Statistical Thermodynamics

• Entropy Change
  Calculates $\Delta S = \frac{Q_\text{rev}}{T}$ with unit flexibility (e.g., J/K to cal/K), fundamental for thermodynamic equilibrium (entropyChange). For $Q_\text{rev} = 1000 , \text{J}$, $T = 300 , \text{K}$, $\Delta S \approx 3.33 , \text{J/K}$.
• Specific Heat Capacity at Constant Volume
  Computes $C_v$ for monatomic ($\frac{3}{2}R$) and diatomic ($\frac{5}{2}R$) gases, integrating molecular theory (specificHeatCapacityVolume). For monatomic gas, $C_v \approx 12.47 , \text{J/mol·K}$.

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TelecommunicationsCalculations

The TelecommunicationsCalculations class is a focused PHP utility for telecommunication engineering, computing wavelength from frequency and received power via the Friis Transmission Equation. Using the speed of light ($c = 299792458 , \text{m/s}$), it ensures precise modeling of electromagnetic wave propagation. With error handling and a basic test suite (e.g., 1 GHz wavelength), it’s a valuable resource for educational demonstrations, signal design, and telecommunications research, emphasizing simplicity and precision.

• Signal Processing: Computes wavelength and received power using the Friis Transmission Equation.
• Minimalistic Approach: Features a small set of methods with $c$ as a core constant.
• Error Handling: Validates positive frequencies and distances, returning error messages.
• Unit Consistency: Uses SI units (e.g., Hz, m, W) without conversion options, aligning with signal analysis norms.
• Testing: Provides a simple runTests() method with examples like 1 GHz wavelength.
• Application-Oriented: Designed for educational demonstrations and basic telecommunication simulations.

Signal Propagation

• Friis Transmission Equation
  Calculates received power ($P_r = P_t G_t G_r \left(\frac{\lambda}{4\pi d}\right)^2$), integrating antenna gains, wavelength, and distance for wireless communication analysis (friisTransmission). For $P_t = 1 , \text{W}$, $G_t = G_r = 1$, $\lambda = 0.3 , \text{m}$, $d = 10 , \text{m}$, $P_r \approx 7.16 \times 10^{-5} , \text{W}$.

List of Functions

ArchitectureCalculations

ArchitectureCalculations provides methods for architectural design and structural analysis, aiding architects and engineers in computing key properties.

Function Name	Function Description	Function Scientific Description
calculateArea	Calculate the area of a rectangle	A = length * width
calculateVolume	Calculate the volume of a prism	V = length * width * height
calculateBeamDeflection	Calculate beam deflection under load	δ = (F * L³) / (3 * E * I)
calculateColumnLoad	Calculate load on a column	P = F / A
calculateFootingSize	Calculate footing area	A = P / σ

AstrophysicsCalculations

AstrophysicsCalculations offers tools for astrophysical computations, useful for astronomers studying celestial mechanics and properties.

Function Name	Function Description	Function Scientific Description
calculateGravitationalForce	Calculate gravitational force	F = G * (m₁ * m₂) / r²
calculateOrbitalVelocity	Calculate orbital velocity	v = √(G * M / r)
calculateEscapeVelocity	Calculate escape velocity	v = √(2 * G * M / r)
calculateLuminosity	Calculate luminosity of a star	L = 4πr²σT⁴
calculateRedshift	Calculate redshift	z = (λ_observed - λ_rest) / λ_rest

BiologyCalculations

BiologyCalculations supports biological computations, assisting researchers in genetics, ecology, and biochemistry.

Function Name	Function Description	Function Scientific Description
calculatePopulationGrowth	Calculate population growth	N(t) = N₀ * e^(r * t)
calculateHardyWeinberg	Calculate allele frequencies	p² + 2pq + q² = 1
calculateDNAMeltingTemp	Calculate DNA melting temperature	Tm = 64.9 + 41 * (GC - 16.4) / N
calculateEnzymeKinetics	Calculate enzyme reaction rate	v = V_max * [S] / (K_m + [S])
calculateCellDivisionTime	Calculate cell division time	t = ln(2) / μ

BuildingDrawingCalculations

BuildingDrawingCalculations facilitates calculations for building design and drafting, ideal for civil engineers and architects.

Function Name	Function Description	Function Scientific Description
calculateScaleFactor	Calculate scale factor	SF = real_size / drawing_size
calculateWallLoad	Calculate load on a wall	P = weight * height
calculateRoofPitch	Calculate roof pitch angle	θ = atan(rise / run)
calculateFoundationDepth	Calculate foundation depth	d = P / (σ * width)
calculateBeamSpan	Calculate beam span	L = F / (w * σ)

ChemistryCalculations

ChemistryCalculations provides methods for chemical computations, supporting chemists in analyzing reactions and solutions.

Function Name	Function Description	Function Scientific Description
calculateMolarMass	Calculate molar mass	M = Σ(atomic_mass)
calculateConcentration	Calculate concentration	C = moles / volume
calculatePH	Calculate pH	pH = -log₁₀[H⁺]
calculateReactionRate	Calculate reaction rate	r = k * [A]^m * [B]^n
calculateEquilibriumConst	Calculate equilibrium constant	K = [products] / [reactants]

ComputerScienceCalculations

ComputerScienceCalculations offers tools for computer science computations, useful for developers and analysts.

Function Name	Function Description	Function Scientific Description
calculateBigO	Calculate Big-O complexity	O(n)
calculateHashValue	Calculate hash value	h(k) = k % m
calculateBinaryConversion	Convert decimal to binary	bin(decimal)
calculateNetworkBandwidth	Calculate network bandwidth	B = data / time
calculateEncryptionTime	Calculate encryption time	t = size / speed

ElectronicsCalculations

ElectronicsCalculations assists in electronics-related calculations, beneficial for electrical engineers and technicians.

Function Name	Function Description	Function Scientific Description
calculateOhmsLaw	Calculate voltage	V = I * R
calculatePower	Calculate power	P = V * I
calculateCapacitance	Calculate capacitance	C = Q / V
calculateResonanceFreq	Calculate resonance frequency	f = 1 / (2π * √(L * C))
calculateVoltageDrop	Calculate voltage drop	V_drop = I * R

GeoscienceCalculations

GeoscienceCalculations provides methods for geoscientific analysis, supporting geologists and earth scientists.

Function Name	Function Description	Function Scientific Description
calculateEarthquakeMag	Calculate earthquake magnitude	M = log₁₀(A) + 3log₁₀(d) - 2.92
calculatePlateVelocity	Calculate plate velocity	v = distance / time
calculateRockDensity	Calculate rock density	ρ = mass / volume
calculateSedimentRate	Calculate sedimentation rate	r = thickness / time
calculateGeothermalGrad	Calculate geothermal gradient	G = ΔT / Δz

MathCalculations

MathCalculations is a comprehensive class for mathematical computations, covering algebra, calculus, and more, ideal for students and researchers.

Function Name	Function Description	Function Scientific Description
add	Add two numbers	a + b
subtract	Subtract two numbers	a - b
multiply	Multiply two numbers	a * b
divide	Divide two numbers	a / b
quadraticFormula	Solve quadratic equation	ax² + bx + c = 0
absoluteValue	Calculate absolute value	|x|
power	Raise to a power	x^y
squareRoot	Calculate square root	√x

MechanicsCalculations

MechanicsCalculations supports mechanics computations, useful for engineers and physicists studying motion and forces.

Function Name	Function Description	Function Scientific Description
calculateForce	Calculate force	F = m * a
calculateWork	Calculate work	W = F * d * cos(θ)
calculateKineticEnergy	Calculate kinetic energy	KE = ½ * m * v²
calculateMomentum	Calculate momentum	p = m * v
calculateTorque	Calculate torque	τ = F * r * sin(θ)

PhysicsCalculations

PhysicsCalculations provides tools for physical computations, aiding physicists in various domains.

Function Name	Function Description	Function Scientific Description
calculateAcceleration	Calculate acceleration	a = Δv / Δt
calculateEnergy	Calculate potential energy	PE = m * g * h
calculateWaveSpeed	Calculate wave speed	v = f * λ
calculatePressure	Calculate pressure	P = F / A
calculateDensity	Calculate density	ρ = m / V

TelecommunicationsCalculations

TelecommunicationsCalculations facilitates calculations for telecommunications systems, useful for engineers in signal processing.

Function Name	Function Description	Function Scientific Description
calculateSignalPower	Calculate signal power	P = V² / R
calculateBandwidth	Calculate bandwidth	B = f_max - f_min
calculateSNR	Calculate signal-to-noise ratio	SNR = P_signal / P_noise
calculateDataRate	Calculate data rate	R = B * log₂(1 + SNR)
calculateAttenuation	Calculate attenuation	A = 10 * log₁₀(P_in / P_out)

ThermodynamicsCalculations

ThermodynamicsCalculations offers methods for thermodynamic analysis, supporting engineers and scientists in energy studies.

Function Name	Function Description	Function Scientific Description
calculateHeatTransfer	Calculate heat transfer	Q = m * c * ΔT
calculateEntropyChange	Calculate entropy change	ΔS = Q / T
calculateWorkDone	Calculate work done	W = P * ΔV
calculateEfficiency	Calculate efficiency	η = W / Q_in
calculatePressureVolume	Calculate pressure-volume relation	P * V = n * R * T

Architecture Calculations

Provides methods for architectural computations, such as structural analysis and material estimations.

Astrophysics Calculations

Offers functions to compute celestial mechanics, stellar properties, and cosmological parameters.

Biology Calculations

Includes tools for modeling biological processes, population dynamics, and genetic probabilities.

Building Drawing Calculations

Assists in generating and interpreting building plans, including area calculations and material requirements.

Chemistry Calculations

Features functions for chemical reaction kinetics, equilibrium constants, and molecular properties.

Computer Science Calculations

Contains algorithms for computational theory, data structures, and complexity analysis.

Electronics Calculations

Provides methods to analyze electrical circuits, signal processing, and semiconductor properties.

Geoscience Calculations

Offers tools for geological surveys, seismic analysis, and resource estimations.

Mathematics Calculations

Includes a wide range of mathematical functions, from basic arithmetic to advanced calculus and linear algebra.

Mechanics Calculations

Assists in solving problems related to classical mechanics, including kinematics and dynamics.

Physics Calculations

Features comprehensive tools for various physics computations, such as optics, thermodynamics, and electromagnetism.

Telecommunications Calculations

Provides methods for analyzing communication systems, signal propagation, and network performance.

Thermodynamics Calculations

Offers functions to compute thermodynamic properties, phase transitions, and energy transformations.

Contributing

We welcome contributions from the community. Please read our Contributing Guidelines to get started.

License

This project is licensed under the MIT License. See the LICENSE file for details.