Most Laplace tables I have found online have either too little information or do not meet my standards for typesetting, so I made my own. Document Source Code 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 \documentclass[12pt]{article} \usepackage[margin=0....
Theory Step 1: Particle Characteristics Each particle is treated as a point mass, and each point mass has three intrinsic characteristics: a mass \(m_i\), a position vector \(\vec{r}_i=\left[\begin{array}{ccc}x_i & y_i & z_i\end{array}\right]\), and a velocity vector \(\vec{v}_i=\left[\begin{array}{ccc}u_i & v_i & w_i\end{array}\right]\). Step 2: Force Calculation According to Newton’s law of universal gravitation, given two distinct point masses in space, the gravitational force acting on the objects takes the form: $$F=G\frac{m_1m_2}{r^2}$$...
Theory Inline code \(y_t\). Numerical Implementation Normal: $$y_t = \beta_0 + \beta_1 x_t + \epsilon_t$$ see above.