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Mathematical Representations: Mathematical Equations
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Mathematical Equations
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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}
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