Mathematics for Physics
Definition of the Natural Logarithm
Derivation of a logarithm with an unknown base “a”. A special property emerges when “a” equals the limit of a sequence, that is 2.71828…, known as Euler’s constant “e”: Log.pdf
Tangent Spaces and Osculating Spaces
Examples of tangent and osculating spaces: Tangent_and_Osculating_Spaces.pdf
Computation of π
Proof of John Machin’s formula (1706) for computing the decimal digits of π: Number_Pi.pdf
Square Roots and nth Roots
Proof of Heron’s formula for computing roots of numbers: Nth_roots.pdf
Normal Distribution
The expression of the normal distribution is derived from the binomial distribution: Normal_distribution.pdf
Central Limit Theorem
Under certain conditions, the distribution of the sum of a large number of random variables tends toward the normal distribution: Central_Limit_Theorem.pdf
Least Squares Method
The least-squares interpolation method is justified by the central limit theorem: Least_squares.pdf
Stirling’s Approximation
A possible proof of the factorial approximation for large numbers: Stirling_approx.pdf
Conic Sections
Some notions about conics, particularly useful for Kepler’s problem: Conics.pdf
Fourier Transform
Origin of the Fourier transform: Fourier_Transform.pdf
Trigonometry
Proofs of the main trigonometric formulas: Trigonometry.pdf