A unified derivation of the θ-method for time discretization, specializing to Forward Euler, Backward Euler, and Crank–Nicolson, with truncation error, A-/L-stability, and the heat-equation amplification factors.
A detailed exploration of the finite element method for the one-dimensional Poisson equation, including weak formulation, shape functions, and isoparametric mapping.
Analyzing the physics of a fly-board by calculating the thrust required to lift the rider and the power needed for steady flow.
A detailed analysis of the James Webb Space Telescope's orbit using gravitational physics and approximations.
An in-depth analysis of a ballistic pendulum problem, demonstrating conservation of angular momentum and energy.
Analyzing the physics behind a bicycle's jump over a container using kinematics and projectile motion.
Determining the launch angle of a ball given the work done on it and its kinetic energy at the highest point of the trajectory.
Analyzing and comparing the final angular velocities of a rotating rod in three distinct cases using conservation of angular momentum.
A body slides up and down an inclined plane. How fast is it moving when it returns to its starting point?
Analyzing the moments of inertia for various fractions of solid disks with different masses and radii.