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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Menu (linked Index) The Derivative Last Update: August 6, 2025 Introduction The Derivative Derivative Rules Derivatives of Some Useful Functions Ordinary Derivative 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 of change of a function
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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Menu (linked Index) Integration Rules Last Update: July 1, 2025 Introduction Integral Definition Integral Notation Integration: Basic Formulas Beyond basic integration Introduction Finding the area under a curve in physics is very useful. For example, the work done on an object that is displaced a distance d is computed as W = force x distance.
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Menu (linked Index) Geometry and Trigonometry Rules Last Update: October 20, 2024 Introduction Similar Triangles Exterior and Interior Angles of Triangles Law of Cosines and Sines Right Triangle Trigonometric Functions Small Angle Approximations Radius of Curvature Normal (Perpendicular) Line to Circle Surface Introduction This post summarizes some useful geometric and trigonometric functions and rules. Return
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Exploring Euler’s Formula Exploring Euler’s Formula Last Update: December 18, 2024 Euler’s Identity It all started for me when I came across the formula below. It’s called Euler’s Identity. If you are a mathematician, you are getting pretty excited right now just seeing this equation. Kind of like a sportscaster’s reaction when you talk about
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Menu (linked Index) Unit Circle and Definitions of Radian and π Last Update: June 9, 2025 Introduction Properties of a Circle The Unit Circle and The Radian Conclusion Introduction In this post we’ll review some of the important mathematical formulas and properties derived from the circle. You probably know that the constant pi = π
Menu (linked Index) Number Classifications Last Update: November 25, 2024 Introduction Number Classification Organization Chart Number Classification Description Number Classification – Venn Chart – High Level Number Classification – Venn Chart – Real Numbers Number Classification – Venn Chart – Full Chart Introduction Understanding the various number types (classifications) is critical to gaining a deeper
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Menu (linked Index) Euler’s Formula Derivation Last Update: December 12, 2024 Introduction The Derivative Derivative Rules Derivatives of Useful Functions Taylor and Maclaurin Power Series Euler Formula Derivation Summary of the Derivation Conclusion Appendix 1 – Graphical meaning of (x-a) Appendix 2 – Full Derivation of Taylor and Maclaurin Power Series Appendix 3 – Unit
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Menu (linked Index) Euler’s Number Last Update: December 11, 2024 Introduction What is e e History Outline e Definition As A Limit Derivation of the Continuous Compounding Equation e Definition as an Infinite Series Summation Unique Properties of e Conclusion Introduction In this article we’ll describe and define Euler’s constant e, which is a non
