- #1

- 30

- 0

## Main Question or Discussion Point

Hi Guys I am new here...I need a favour from you guys...Here's my background first...I'm seventeen years old and somewhat obsessed with Physics and Math as I am sure most people on this forum are...

As a kid I had a teacher who came to teach me advanced math thought it was a good idea to help me grow my interests blah blah...So for a 17 year old I have a really strong Math background (high end calc, diff geometry, number theory blah blah)...However my Physics background has always been far more self study...Over the last 2 years this is the work that I have done and the subject material I have covered...I'll be going to college next year...and I am curious as to how advanced this is...I know its not high school physics but I would like to know exactly where I stand... I figure there must be some people like me here...SO yeah like the title says...just tell me the level of my work so I know...Cheers. Thanks in advance!

Fluid Dynamics : Consistency Equations (Navier-Stokes, Euler), Linear

Hyperbolic Systems, Convective and Diffusive analysis for systems in 1-D and 2-

D, Finite Difference Operations - Point, Matrix, Pade's formula, Stability and

Consistency of Flow by Fourier stability analysis, Vortex, Turbulence of Flow,

Differential Geometry in Physics: Vectors and Curves, Differential Forms - 1

forms, Tensors, Exterior derivatives, Hodge-* Operator, Connections - Frames,

Curvilinear coordinates, Covariant Derivatives, Theory Of Surfaces - Flux,

Manifolds, Fundamental Theorems

Electromagnetic : Integral and Differential Calculus of Vector Fields,

Electromagnetic Theory - Maxwell, Vector Potentials, Principle of Least Action,

Solutions to Maxwell's equations of Free Space and Currents Charges,

Waveguides - Transmission Lines, Cut Off, Cavity Resonators, Alternating

Currents, Lorentz Transformations for fields, EM Mass, Internal Crystal

Geometry, AC Circuits, Reactance, Susceptance

Semiconductors: Junction Diodes, Transistors, Characteristics, Light based

devices, Amplifiers, Oscillators.

Quantum Theory: Introduction and History of the Quantum Theory, Wave-

Particle Duality, Probability Amplitudes, Spin One and Spin Half Mechanics,

Time-Dependence of Amplitude, Hamiltonian Matrices, Schrödinger Equation in

Quantum and Classical Contexts, Hyperfine Splitting in H-Atom, Heisenberg's

Uncertainty Principle

Relativity: Introduction to theory of Relativity, Special Relativity, Relativistic

Effects on Radiation, Relativistic Effects on Matter - Time Dilation etc.,

Geometry of Space time, Dynamics in 4-D, Unifying Electromagnetism and

relativity

Mechanics: Translational and Rotational Kinematics, 2D and 3D Mechanics,

Forces, Energy, Transients, Resonance, Oscillations, Wave mechanics,

Gravitational Field, Elasticity, Molecular Forces and Solid Materials

Optics: Introduction to Geometrical ray optics, Hygens principle, Freunhofer/Fresnel diffraction, Interference, YDSE, Single slit, Multiple slits, Polarisation, Wave-Particle duality of light

This isnt quite exhaustive but I think is a bulk of what I have done...Tell me if you need any more detail. Thanks!!

As a kid I had a teacher who came to teach me advanced math thought it was a good idea to help me grow my interests blah blah...So for a 17 year old I have a really strong Math background (high end calc, diff geometry, number theory blah blah)...However my Physics background has always been far more self study...Over the last 2 years this is the work that I have done and the subject material I have covered...I'll be going to college next year...and I am curious as to how advanced this is...I know its not high school physics but I would like to know exactly where I stand... I figure there must be some people like me here...SO yeah like the title says...just tell me the level of my work so I know...Cheers. Thanks in advance!

Fluid Dynamics : Consistency Equations (Navier-Stokes, Euler), Linear

Hyperbolic Systems, Convective and Diffusive analysis for systems in 1-D and 2-

D, Finite Difference Operations - Point, Matrix, Pade's formula, Stability and

Consistency of Flow by Fourier stability analysis, Vortex, Turbulence of Flow,

Differential Geometry in Physics: Vectors and Curves, Differential Forms - 1

forms, Tensors, Exterior derivatives, Hodge-* Operator, Connections - Frames,

Curvilinear coordinates, Covariant Derivatives, Theory Of Surfaces - Flux,

Manifolds, Fundamental Theorems

Electromagnetic : Integral and Differential Calculus of Vector Fields,

Electromagnetic Theory - Maxwell, Vector Potentials, Principle of Least Action,

Solutions to Maxwell's equations of Free Space and Currents Charges,

Waveguides - Transmission Lines, Cut Off, Cavity Resonators, Alternating

Currents, Lorentz Transformations for fields, EM Mass, Internal Crystal

Geometry, AC Circuits, Reactance, Susceptance

Semiconductors: Junction Diodes, Transistors, Characteristics, Light based

devices, Amplifiers, Oscillators.

Quantum Theory: Introduction and History of the Quantum Theory, Wave-

Particle Duality, Probability Amplitudes, Spin One and Spin Half Mechanics,

Time-Dependence of Amplitude, Hamiltonian Matrices, Schrödinger Equation in

Quantum and Classical Contexts, Hyperfine Splitting in H-Atom, Heisenberg's

Uncertainty Principle

Relativity: Introduction to theory of Relativity, Special Relativity, Relativistic

Effects on Radiation, Relativistic Effects on Matter - Time Dilation etc.,

Geometry of Space time, Dynamics in 4-D, Unifying Electromagnetism and

relativity

Mechanics: Translational and Rotational Kinematics, 2D and 3D Mechanics,

Forces, Energy, Transients, Resonance, Oscillations, Wave mechanics,

Gravitational Field, Elasticity, Molecular Forces and Solid Materials

Optics: Introduction to Geometrical ray optics, Hygens principle, Freunhofer/Fresnel diffraction, Interference, YDSE, Single slit, Multiple slits, Polarisation, Wave-Particle duality of light

This isnt quite exhaustive but I think is a bulk of what I have done...Tell me if you need any more detail. Thanks!!