Harmonic oscillator equation solved without guessing the solution

From the Newton's second law of motion harmonic oscillator equation is obtained which is solved without guessing the solution
www.avidsynergy.com/pdf/harmonic_oscillator.pdf

Note on derivative of x power n

Angular Momentum in Quantum Mechanics

Why the square pyramidal number formula is interesting? (It is just the formula for the sum of squares of the natural numbers which happens also to give the number of cannon balls or oranges of equal size in a pyramid with a square base.) It can be used in the derivation of the expected value of angular momentum in Quantum Mechanics.
www.avidsynergy.com/pdf/angular_momentum_in_QM.pdf

Limits of Fresnel integrals calculated in an easy way

Here below square root of the negative imaginary unit i is applied to compute the limits of Fresnel integrals in a note "Limits of Fresnel integrals calculated in an easy way"
www.avidsynergy.com/pdf/Fresnel_integrals.pdf

Square pyramidal numbers and the multiplication table

Please, take another look at the multiplication table
The Mathematical Gazette / Volume 100 / Issue 547 / March 2016, pp 108 - 111
Note entitled: "100.02 Square pyramidal numbers and the multiplication table"

http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid...

Sum of Cosines and the Improper Integral of Sin(x)/x

Error Function, Dirichlet Kernel and the Improper Integral of Sin(x)/x

Here you will find mathematics article for high school and college students: "Error Function, Dirichlet Kernel and the Improper Integral of Sin(x)/x"
www.avidsynergy.com/pdf/sin_x_div_by_x_integral.pdf

Note on calculating Ax(t) = x′(t) and Ax(t) = λx(t) with eigenfunctions x(t) and eigenvalues λ

Note on calculating Ax(t) = x′(t) and Ax(t) = λx(t) with eigenfunctions x(t) and eigenvalues λ

http://www.avidsynergy.com/pdf/eigenvalues_diff_eqs.pdf

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