Math

AC Circuits: I-V Relationships, Impedance, Admittance, and Power

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Menu (linked Index) AC Circuit Basics: i-v Relationships, Impedance, Admittance, and Power Last Update: January 14, 2026 Introduction Pure Resistor AC Circuit Pure Inductor AC Circuit Pure Capacitor AC Circuit Pure Inductor and Capacitor Impedance – Frequency Domain Analysis Summary: Pure Element AC Circuits Phasor Basics Series RLC AC Circuits (Voltage → Impedance → Power […]

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Sine and Cosine – Definitions and Properites

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Menu (linked Index) Sine and Cosine – Definitions and Properties Last Update: December 23, 2025  Introduction History Etymology Unit Circle Trigonometry Sine and Cosine Wave From the Unit Circle Sinusoid Waveform General Characteristics Circular Motion Parameters Phase Angle Expression Using Rotational Kinematics General Equations for Instantaneous AC Voltage and Current Voltage and Current Waveform Characteristics

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AC Voltage and Current Equations

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Menu (linked Index) AC Voltage and Current Equations Last Update: November 29, 2025 Introduction Faraday’s Law and Magnetic Flux Derivation Model: Rotating Coil in a Magnetic Field Voltage Equation Derivation Current Equation Derivation Summary Introduction A three-phase power generator creates electricity by rotating a powerful magnet (the rotor) inside a stationary frame containing three separate

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Fourier Series and Transforms

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Menu (linked Index) Fourier Series and Transforms Last Update: November 22, 2025  Introduction Fourier Series Trigonometric form Fourier Series First Term Fourier Series Coefficient for Cosine Terms Fourier Series Coefficient for Sine Terms Fourier Series – Complex Exponential Form Fourier Transform  Difference between Fourier Series and Transform Appendix 1 – Integrals of sin(mt)dt and cos(mt)dt

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Rotational Motion Variables

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Menu (linked Index) Rotational Motion Variables Last Update: October 28, 2025  Introduction Angle Displacement and Radian Definition Angular Velocity ω Angular Acceleration α Rotational Motion Vectors Kinematic Equations (Linear, Rotational) Polar vs Axial Vectors Introduction This post addresses rotational (circular) motion and the key variables describing it.   We are probably familiar with linear movement described

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Field Operators: Grad, Div, and Curl

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Menu (linked Index) Field Operators: Grad, Div, and Curl Last Update: August 18, 2025 Introduction Definitions Graphing a Vector Field Differentiation Basics The Gradient Operator Divergence Operator The Laplacian Direction of Axis of Rotation The Curl Operator Excellent Educational Video References Appendix 1: Uses of the Derivative Introduction This post is about three fundamental operators

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The Derivative

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Menu (linked Index) The Derivative Last Update: October 18, 2025  Introduction The Derivative Derivative Rules Derivatives of Some Useful Functions Ordinary Derivative Velocity and Acceleration As Derivatives Partial Derivative Introduction This article is a high level introduction to the mathematical tool called differentiation.  At its core, differentiation is the process of finding the instantaneous rate

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Unit of Measure Conversion Factors

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Menu (linked Index) Unit of Measure Conversion Factors Last Update: July 13, 2025  Introduction Exponentials, Scientific Notation, and SI Prefixes Volume Equivalents (Conversion Factors)  Mass Equivalents (Conversion Factors)  Length Equivalents (Conversion Factors)  Pressure Equivalents I.(Conversion Factors)  Pressure Equivalents II.  (Conversion Factors)  Energy Equivalents I. (Conversion Factors) Energy Equivalents II. (Conversion Factors) Power Equivalents I. (Conversion

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