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Word Problems with Rates


Spherical Coordinates




Introduction - Calculus

The Limit

The Derivative

Taylor Series

The Chain Rule


Integration by Parts

Multiple Integrals: Area

Multiple Integrals: Volume

The Fundamental Theorem of Calculus



Minimization: Introduction

Shortest Distance between two Points


Calculus of Variations

Variation of a Derivative


Probability and Statistics



Statistical Parameters


Combined Probability: Event A and B

Example: Combined Probability: Event A or B

Physics and Probability

Physics and Probability: Loaded Dice

Discrete and Continuous Random Variables

Central Limit Theorem

Population Sampling





Representation of an Area by a Vector

Integral and Differential Form of Maxwell's Equations

The Field of a Magnetic Dipole

Faraday's Law of Induction

The Maxwell-Faraday Equation

The Electric Field Induced by Magnetism (General)

The Electric Field Induced by Magnetism (Example)



Classical Mechanics

Velocity and Acceleration in Polar Coordinates

Elastic Collision

Moment of Inertia of a Disk

Equations of Motion

Constraints: Simple Pendulum



Special Relativity


The Galilean Transformations

Invariance of a Transformation

The Problem with the Wave Equation

Invariance of the Interval

Proper Time

The Beta and the Gamma Parameter

Length and Time Units

The Light Triangle


The Lorentz Transformations for Space and Time

The Lorentz Transformations: Derivation

The Lorentz Transformations (Inverted)

The Lorentz Transformations: Summary

The Lorentz Transformation: Physical Units Conversion

Geometrical Interpretation: The Lorentz Grid

Time Dilation

Length Contraction


Velocity Transformations

Velocity Transformation

Addition of Velocities

The Classical Doppler Shift

The Relativistic Doppler Shift


Examples and Reflection

The Lorentz Transformations: The Pi-Meson

The Moving Rod and Doors

The Speed of Light: Einstein's Postulates

Relativity and the Lorentz Transformations

The Twin Paradox


Momentum and Energy


Four-Vectors: Position and Velocity

Four-Vectors: Momentum and Energy

Four-Vectors: Dot Product and Invariance

Four-Vectors: Summary

Energy and Momentum: Derivation

Conservation Laws and Collisions


General Relativity

Dual Basis

The Metric: Introduction

Metric Tensor Algebra

Lowering and Raising Indices

Norm of a Vector

Dot Product of Vectors

Path Element and Length of a Path

Invariants: Tangent Basis Vectors ("Velocity")

Christoffel Symbols

Schwarzschild Metric

Coordinate Transformations

Tensor Calculus

Derivatives Nomenclature



Asteroid Defense



Arduino Network Sensors







Asymptote Source Files

Web Design Notes

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