Lectures and study notes in math, physics, etc.
These are the study and lecture notes. Some of them have been used in actual classes. If you want to find a specific
topic, press ctrl + F on the keyboard and then type the keyword that you want to seek.
How to derive the relativistic Hamiltonian of
a particle in the electromagnetic fields
A solution of Goldstein (the 2nd Ed.), problem 8.2
A solution of Goldstein (the 2nd Ed.), problem 8.4
A pertubation theory for the simple harmonic oscillator with a quadratic potential
The electric field and the potential from a charged disk
The method of images: one positive charge in front of a flat conducting surface
Electric fields derived from Gauss's law: sphere and thin-walled sphere
Strategy to obtain electric potentials and fields for each system
Strategy to obtain magnetic fields (Ampère's and Bio-Severt laws)
Differential forms of Maxwell's equations and Ohm's law
Gauge invariance of Maxwell's equations
The solution for Laplace's equation (2 dimension, square boundary)
The solution for Laplace's equation (2 dimension, polar coordinate)
The solutions for 1-D square-well potentials (1 infinite and 3 finite potentials)
The lecture of general angular momentum (quantum theory)
The time-independent perturbation theory
for the simple harmonic oscillation (1-D two particles)
The time-independent perturbation theory
for the simple harmonic oscillation with perturbation potential, Ax+bx3.
The time-independent perturbation theory
for the simple harmonic oscillation with perturbation potential, bx. (This is a case in which the solution
can also be given exactly.)
The time-dependent perturbation theory
with perturbation potential, exFsinωt.
The variational method
for the simple harmonic oscillation with the trial function, Cexp(-αx2).
The rotation operator for
quntum mechanics
Infinite integration with complex variables
Three objects attached with two springs: How to obtain the normal mode
The solution for a double pendulum: The second pendulum is
a long bar.
The summary of oscillatory classical systems
Derivations of each moment of inertia
Related fomulas of micro-canonical and canonical ensembles
The algorithm of the bisection method and an exmple of the transcendental equation
Verlet method to solve Newton's equation of motion
Aharonov-Bohm effect
Baysien statistics I: The basic concept and its formulation
Baysien statistics II: Probability of coin toss
Baysien statistics III: The Bayesian statistics with Gaussian distribution
Baysien statistics IV: The derivation of the mean
and variance for the posterior probability with Gaussian distribution
Some interesting problems related to geometry
Newton's equation of motion with a sliding object on frictional surface
Vertical spring motion - its energy and force
The velocity of a simple pendulum at the bottom
Fibonacci sequence
Japanese letters (how to pronounce)
How to add two vectors with the graphical method more accurately I,
II, III
Application of conservation of thermal energy
Time to stick together two bodies due to gravitational force
Comparison of final velocities for three different projectile motions
The first, second, third, cosmic velocities, and blackholes
Physics for a sliding-down bobsleigh
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