bsc-v
25 Jun 2025
4 min read
Hamiltonian Dynamics and Mechanical Examples
Canonical momenta, cyclic coordinates, conservation laws, Hamilton equations, and representative systems.
Blog Posts 👇
bsc-v
24 Jun 2025
3 min read
Lagrangian Dynamics and Applications
Hamilton's principle, Euler-Lagrange equations, oscillators, uniform gravity, and electromagnetic coupling.
bsc-v
23 Jun 2025
2 min read
Least-Squares Linear and Polynomial Regression
Measurements $(x_i,y_i)$ generally do not lie exactly on one curve. Regression chooses model parameters that minimize the total squared vertic...
bsc-v
22 Jun 2025
2 min read
Euler and Fourth-Order Runge-Kutta Methods
Consider the initial-value problem
bsc-i
22 Jun 2025
3 min read
LC Circuit and Damped Oscillations
Electrical SHM in an ideal LC circuit and the underdamped, critically damped, and overdamped solutions.
bsc-v
21 Jun 2025
2 min read
Trapezoidal, Simpson, and Gaussian Quadrature
Numerical quadrature replaces
bsc-v
20 Jun 2025
2 min read
Numerical Differentiation with Finite Differences
Numerical differentiation estimates derivatives from tabulated or computed function values. Let the data be sampled at equally spaced points
bsc-v
19 Jun 2025
3 min read
Optical Fibres: Numerical Aperture, Index Profiles, and Modes
Acceptance cone, numerical aperture, step and graded indices, and single- and multimode fibres.
bsc-v
18 Jun 2025
3 min read
Planar Dielectric Waveguides and Guided-Wave Power
Total-reflection phase, slab continuity conditions, eigenvalue equations, velocities, field energy, and power.
bsc-i
18 Jun 2025
2 min read
Simple, Compound, and Torsional Pendulums
Small-oscillation equations and periods of three mechanical systems executing SHM.
