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Mathematics

 

Precalculus

Word Problems with Rates

Coordinates

Spherical Coordinates

 

 

Calculus

Introduction - Calculus

The Limit

The Derivative

Taylor Series

The Chain Rule

Integration

Integration by Parts

Multiple Integrals: Area

Multiple Integrals: Volume

The Fundamental Theorem of Calculus

 

Optimization

Minimization: Introduction

Shortest Distance between two Points

 

Calculus of Variations

Variation of a Derivative

 

Probability and Statistics

Introduction

Distributions

Statistical Parameters

Probability

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

 

Physics

 

Electromagnetism

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

Introduction

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

Momentum

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

 

Projects

Asteroid Defense

 

Electronics

Arduino Network Sensors

 

 

 

 

Supplementals

 

Asymptote Source Files

 

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