Mathematical Equations: Program 1

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsfonts}
\usepackage{bm}

\title{Physics Equations}
\author{}
\date{}

\begin{document}
	
	\maketitle
	
	\section*{Algebraic Equations}
	
	1. Newton's Second Law of Motion:
	\begin{equation}
		F = ma
	\end{equation}
	
	2. Gravitational Force:
	\begin{equation}
		F = G \frac{m_1 m_2}{r^2}
	\end{equation}
	
	3. Kinetic Energy:
	\begin{equation}
		KE = \frac{1}{2} mv^2
	\end{equation}
	
	4. Potential Energy (Gravitational):
	\begin{equation}
		PE = mgh
	\end{equation}
	
	5. Work Done by a Force:
	\begin{equation}
		W = Fd \cos \theta
	\end{equation}
	
	6. Power:
	\begin{equation}
		P = \frac{W}{t}
	\end{equation}
	
	7. Ohm's Law:
	\begin{equation}
		V = IR
	\end{equation}
	
	8. Coulomb's Law:
	\begin{equation}
		F = k_e \frac{q_1 q_2}{r^2}
	\end{equation}
	
	9. Hooke's Law:
	\begin{equation}
		F = -kx
	\end{equation}
	
	10. Momentum:
	\begin{equation}
		p = mv
	\end{equation}
	
	\section*{Vector Equations}
	
	11. Force as a Vector:
	\begin{equation}
		\bm{F} = m \bm{a}
	\end{equation}
	
	12. Velocity Vector:
	\begin{equation}
		\bm{v} = \frac{d\bm{r}}{dt}
	\end{equation}
	
	13. Acceleration Vector:
	\begin{equation}
		\bm{a} = \frac{d\bm{v}}{dt}
	\end{equation}
	
	14. Dot Product of Vectors:
	\begin{equation}
		\bm{A} \cdot \bm{B} = |\bm{A}| |\bm{B}| \cos \theta
	\end{equation}
	
	15. Cross Product of Vectors:
	\begin{equation}
		\bm{A} \times \bm{B} = |\bm{A}| |\bm{B}| \sin \theta \hat{n}
	\end{equation}
	
	16. Electric Field:
	\begin{equation}
		\bm{E} = \frac{1}{4 \pi \epsilon_0} \frac{q}{r^2} \hat{r}
	\end{equation}
	
	17. Lorentz Force:
	\begin{equation}
		\bm{F} = q \left( \bm{E} + \bm{v} \times \bm{B} \right)
	\end{equation}
	
	18. Magnetic Field of a Moving Charge:
	\begin{equation}
		\bm{B} = \frac{\mu_0}{4\pi} \frac{q \bm{v} \times \hat{r}}{r^2}
	\end{equation}
	
	19. Vector Form of Newton’s Second Law:
	\begin{equation}
		\sum \bm{F} = m \bm{a}
	\end{equation}
	
	20. Angular Momentum:
	\begin{equation}
		\bm{L} = \bm{r} \times \bm{p}
	\end{equation}
	
	\section*{Thermodynamics and Statistical Physics}
	
	21. First Law of Thermodynamics:
	\begin{equation}
		\Delta U = Q - W
	\end{equation}
	
	22. Ideal Gas Law:
	\begin{equation}
		PV = nRT
	\end{equation}
	
	23. Entropy Change:
	\begin{equation}
		\Delta S = \frac{\Delta Q}{T}
	\end{equation}
	
	24. Heat Transfer (Conduction):
	\begin{equation}
		Q = -k A \frac{dT}{dx}
	\end{equation}
	
	25. Stefan-Boltzmann Law:
	\begin{equation}
		P = \sigma A T^4
	\end{equation}
	
	26. Boltzmann Distribution:
	\begin{equation}
		f(E) = \frac{1}{Z} e^{-E/k_B T}
	\end{equation}
	
	27. Carnot Efficiency:
	\begin{equation}
		\eta = 1 - \frac{T_C}{T_H}
	\end{equation}
	
	28. Helmholtz Free Energy:
	\begin{equation}
		F = U - TS
	\end{equation}
	
	29. Gibbs Free Energy:
	\begin{equation}
		G = H - TS
	\end{equation}
	
	30. Heat Capacity:
	\begin{equation}
		C = \frac{dQ}{dT}
	\end{equation}
	
\end{document}

Mathematical Representations

Mathematical Equations: Program 1

Output 1