Physics Fundamental Concepts and Laws

Fundamental Concepts:
- Matter: Anything that has mass and occupies space.
- Energy: The ability to do work; exists in various forms (kinetic, potential, thermal, etc.).
- Force: A push or pull acting upon an object; calculated via F = ma (Newton's Second Law).
Laws of Motion:
- Newton's First Law: An object at rest stays at rest, and an object in motion stays in motion unless acted upon by a net force.
- Newton's Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
- Newton's Third Law: For every action, there is an equal and opposite reaction.
Thermodynamics:
- Laws:
  - Zeroth Law (thermal equilibrium)
  - First Law (conservation of energy)
  - Second Law (entropy in isolated systems)
  - Third Law (absolute zero temperature).
Electromagnetism:
- Electric fields and forces (Coulomb's Law).
- Magnetic fields and forces (Lorentz Force Law).
- Maxwell's equations unify electricity and magnetism.

Atomic Structure:
- Atoms: Basic units of matter consisting of protons, neutrons, and electrons.
- Elements: Pure substances made of only one type of atom.
- Compounds: Substances formed by the chemical combination of two or more elements.
Chemical Bonds:
- Ionic Bonds: Formed through the transfer of electrons from one atom to another.
- Covalent Bonds: Formed by the sharing of electrons between atoms.
- Metallic Bonds: Bonds formed by the attraction between metal ions and delocalized electrons.
States of Matter:
- Solid: Defined shape and volume.
- Liquid: Defined volume but takes the shape of its container.
- Gas: No defined shape or volume, expands to fill the container.
Chemical Reactions:
- Reactants transform to products.
- Types: Synthesis, decomposition, single replacement, double replacement, combustion.
- Conservation of mass applies; mass of reactants equals mass of products.

Branches of Mathematics:
- Arithmetic: Basic operations (addition, subtraction, multiplication, division).
- Algebra: Study of symbols and rules for manipulating those symbols; includes solving equations.
- Geometry: Study of shapes, sizes, and properties of space.
- Calculus: Study of change and motion, focusing on derivatives and integrals.
Key Concepts:
- Numbers: Integers, rational numbers, real numbers, complex numbers.
- Functions: Relationships between sets of inputs and outputs; types include linear, quadratic, exponential.
- Probability and Statistics: Study of randomness, data collection, analysis, interpretation.
Theorems and Formulas:
- Pythagorean Theorem: a² + b² = c² for right triangles.
- Fundamental Theorem of Calculus: Connects differentiation and integration.
- Quadratic Formula: x = (-b ± √(b² - 4ac)) / (2a) for solving quadratic equations.

Matter is defined as anything that has mass and occupies space.
Energy enables work and exists in multiple forms, including kinetic, potential, and thermal.
Force is the push or pull on an object, calculable by the formula F = ma (Newton's Second Law).

Newton's First Law states an object remains at rest or in uniform motion unless influenced by a net force.
According to Newton's Second Law, object acceleration is proportional to the net force and inversely proportional to its mass.
Newton's Third Law asserts that every action has an equal and opposite reaction.

The Zeroth Law establishes thermal equilibrium between systems.
The First Law refers to energy conservation within isolated systems.
The Second Law indicates that entropy increases in isolated systems over time.
The Third Law states that as temperature approaches absolute zero, the entropy of a perfect crystal approaches zero.

Electric fields and forces are described by Coulomb's Law.
The Lorentz Force Law details the behavior of charged particles in magnetic fields.
Maxwell's equations provide a unified framework for understanding electricity and magnetism.

Atoms are the fundamental building blocks of matter, made up of protons, neutrons, and electrons.
Elements are pure substances composed of only one type of atom, while compounds are substances formed from the chemical combination of two or more elements.

Ionic bonds form when electrons are transferred from one atom to another, creating charged ions.
Covalent bonds arise from the sharing of electrons between atoms.
Metallic bonds involve attraction between metal ions and a sea of delocalized electrons.

Reactants undergo transformation to produce products, with types including synthesis, decomposition, single replacement, double replacement, and combustion.
The law of conservation of mass states that the mass of reactants equals the mass of products in a chemical reaction.

Arithmetic focuses on basic operations: addition, subtraction, multiplication, and division.
Algebra involves manipulating symbols and solving equations.
Geometry studies the attributes of shapes, sizes, and spatial relationships.
Calculus addresses change and motion, emphasizing derivatives and integrals.

Numbers include various types such as integers, rational, real, and complex numbers.
Functions describe relationships between inputs and outputs, classified as linear, quadratic, or exponential.
Probability and statistics encompass data collection, analysis, and interpretation regarding randomness.

The Pythagorean Theorem is represented as a² + b² = c² for right triangles.
The Fundamental Theorem of Calculus links differentiation with integration.
The Quadratic Formula is x = (-b ± √(b² - 4ac)) / (2a) for solving quadratic equations.