# 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+bx*^{3}.

### 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, *exF*sinω*t*.

### The variational method
for the simple harmonic oscillation with the trial function, *C*exp(-αx^{2}).

### 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)

### 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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