The property of matter by which it retains its state of rest or its velocity along a straight line so long as it is not acted upon by an external force.
Work
The transfer of energy measured as the scalar product of the force applied to a body and the displacement of that body in the direction of the force ($W = \vec{F} \cdot \vec{d}$).
Entropy
A thermodynamic quantity representing the unavailability of a system's thermal energy for conversion into mechanical work, often interpreted as the measure of disorder in the system.
Half-Life
The time required for a quantity to reduce to half of its initial value; commonly used in nuclear physics to describe the rate of radioactive decay.
Doppler Effect
The change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source.
Heisenberg Uncertainty
A fundamental limit in quantum mechanics stating that the position and momentum of a particle cannot be simultaneously measured with arbitrary precision ($\sigma_x \sigma_p \geq \frac{\hbar}{2}$).
Superposition
The principle that a physical system—such as an electron—exists in all its theoretically possible states (or configurations) simultaneously; but when measured it gives a result corresponding to only one of the possible configurations.
Escape Velocity
The minimum speed needed for a free, non-propelled object to escape from the gravitational influence of a massive body.
∑ Mathematics
Derivative
The instantaneous rate of change of a function with respect to one of its variables. Geometrically, the slope of the tangent line to the function's graph.
Integral (Definite)
the accumulation of quantities, which can be interpreted as the area under the curve of a function. The fundamental theorem of calculus links integrals and derivatives.
Function
A relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
Vector Space
A collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
Eigenvalue
An eigenvector of a linear transformation is a non-zero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding scalar is the eigenvalue.
Complex Number
A number that can be expressed in the form $a + bi$, where $a$ and $b$ are real numbers, and $i$ is the imaginary unit ($i^2 = -1$).
Limit
The value that a function (or sequence) approaches as the input (or index) approaches some value.
Standard Deviation
A measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean.
💻 Computer Science
Algorithm
A step-by-step procedure or set of rules to be followed in calculations or other problem-solving operations, especially by a computer.
Big O Notation
A mathematical notation used to classify algorithms according to how their run time or space requirements grow as the input size grows (e.g., $O(n)$, $O(n^2)$).
Recursion
The process of defining a problem (or the solution to a problem) in terms of (a simpler version of) itself. E.g., a function calling itself.
Data Structure
A specialized format for organizing, processing, retrieving and storing data (e.g., Arrays, Linked Lists, Trees, Hash Maps).
API
Application Programming Interface. A set of definitions and protocols for building and integrating application software, allowing two pieces of software to communicate.
Polymorphism
The provision of a single interface to entities of different types, or the use of a single symbol to represent multiple different types.
⚙️ Engineering
Stress vs. Strain
Stress is the force applied per unit area ($\sigma = F/A$). Strain is the deformation or displacement of material that results from an applied stress.
Young\'s Modulus
A mechanical property that measures the stiffness of a solid material. It is the ratio of tensile stress to tensile strain.
Torque
The rotational equivalent of linear force. It represents the capability of a force to produce change in the rotational motion of the body.
Bernoulli\'s Principle
States that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy.
🧬 Biology & Chemistry
Homeostasis
Any process that living things use to actively maintain fairly stable conditions necessary for survival.
Isotopes
Variants of a particular chemical element which differ in neutron number, and consequently in nucleon number.
Covalent Bond
A chemical bond that involves the sharing of electron pairs between atoms.
Activation Energy
The minimum quantity of energy which the reacting species must possess in order to undergo a specified reaction.
Mitosis
A part of the cell cycle when replicated chromosomes are separated into two new nuclei.
pH
A scale used to specify the acidity or basicity of an aqueous solution. Lower values are acidic, 7 is neutral, and higher values are alkaline.