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

www.avidsynergy.com/pdf/derivative_of_x_power_n.pdf

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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

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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

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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...

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

www.avidsynergy.com/pdf/SinOfXdividedByXintegration_article.pdf

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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