Formulas and methods for solving applied problems

• Calculation of the average value of the current when charging a capacitor
• Energy of the phase shift of the current in the inductor
• The electrical capacity of the connection. The method of calculation
• The potential of a charged sphere. The method of calculation
• Values of certain functions
• Approximation formulas for potential difference
• Calculation secluded capacitance unevenly charged sphere
• Sum of squares and sum square in electrodynamics
• Some of the amounts of rows with squares of integrals
• Integral with sine in degrees and the cosine module
• Integral of an exponential with an imaginary exponent and a cosine modulus

Numerical solution of differential equations

• Simple methods of numerical solution of some differential equations
• Method of numerical solution of differential equations of the second order
• Table of algorithms for the numerical solutions of some differential equations

Transients in RLC circuits

• Analytical equation for current and energy in a coil according to the Stoletov curve
• Inductance as an energy storager
• Connecting a series resonant circuit to a DC voltage source
• Changing the voltage of the power supply in the circuit, the initial values of the current in the inductor and the voltage in the capacitance

Mathematics of Unit Space

• Hyperbolic Numbers and Vector Algebra in Unit Space Theory
• Vector Sine and Cosine
• Multiplication with Different Angles
• Vector Hyperbolic sine and cosine
• Phase shift of vector sine and cosine
• Property of the derivative of a unit vector
• A series with random signs and its sum

Split geometry

• From Euler's formula to split geometry
• Split sine and split cosine of two-phase geometry
• Multilevel idempotent splitting of phase planes. How to split an electron
• Two-periodic mode of multilevel idempotent splitting
• On the relationship between complex and hyperbolic units
• Origins of the i-basis: from hyperbolic unity to idempotent geometry
• The Two-Phase Operator J: From Euler’s Formula to an Extended Normalized State
• Random Choice in Idempotent Splitting: Probability Distributions and the Square-Root Law
• Splitting and combining amplitudes: the quadratic structure of observables
• Split geometry and positive geometry: correspondence and computational simplicity
• Radius vector in split-geometry. Spherical and cylindrical forms

Equations of degrees 2-5 and split geometry

• Idempotent hierarchy of algebraic equations. From second to fourth degree and back
• The degree of a polynomial as the number of active sheets of a split geometry

Hyperbolic mathematics

• The square root of the hyperbolic unit and 4D space. What cannot be
• Structure and Properties of the Hypercomplex Exponential in 4D Space
• Absorption and transfer of the hyperbolic unit by some formulas
• Hyperbolic Numbers

Other notes

• God as Engineer: A View Through Mathematics
• Two Rockets Paradox
• Yin-Yang in 3D