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011

PX153 - mathematics for physicists

PX153 - 0 - mathematics for physicists

term 1

PX153 - A - vectors

PX153 - A1 - notation and geometrical representation

PX153 - A2 - cartesian coordinates and vector components

PX153 - A3 - position, velocity and acceleration vectors

PX153 - A4 - vector operations

PX153 - A5 - coordinate systems

PX153 - A6 - advanced vector operations

PX153 - A7 - reciprocal vectors

PX153 - B - complex numbers

B - complex numbers

PX153 - B1 - basic operations and the argand diagram

PX153 - B2 - polar representation

PX153 - B3 - de moivre's theorem

PX153 - B4 - application - first look at smh

PX153 - B5 - application - describing damped SHM

PX153 - B5.1 - underdamping

PX153 - B5.2 - overdamping

PX153 - B5.3 - critical damping

PX153 - C - first order ODEs

C - first order ODEs

PX153 - C1 - introduction and definitions

PX153 - C2 - construction of ODEs

PX153 - C3 - direct integration

PX153 - C4 - separation of variables

PX153 - C5 - substitution

PX153 - C6 - integrating factor

PX153 - D - second order ODEs

D - second order ODEs

PX153 - D1 - definitions

PX153 - D2 - solving 2nd order homogeneous ODEs

PX153 - D3 - reducing a non-linear ODE to a linear ODE

PX153 - E - second order inhomogeneous ODEs

E - second order inhomogeneous ODEs

PX153 - E1 - recap and introduction

PX153 - E2 - method of undetermined coefficients

PX153 - E3 - driven damped simple harmonic motion

PX153 - E4 - method of variation of parameters

PX153 - F - series

PX153 - F1 - taylor series

PX153 - F2 - convergence of a series

PX153 - F3 - estimating the sum of a series

PX155 - F4 - power series and taylor series revisited

PX153 - G - functions of many variables, calculus

G - calculus of functions of many variables

PX153 - G1 - partital differentiation

PX153 - G2 - the total differential, and exact and inexact differentials

PX153 - G3 - partial differential equations

PX153 - G4 - taylor expansion of a function of two variables

PX153 - G5 - critical points of a function of two variables

PX153 - H - gradients of scalar functions of many variables

H - gradient of a scalar function

PX153 - H1 - directional derivative and gradient vector of scalar functions

PX153 - H2 - visualising variability of a scalar function - contours

PX153 - H3 - gradients of functions of three variables

PX153 - H4 - application of gradient in physics - the potential of a conservative force

PX153 - H5 - coordinate systems revisited

PX153 - H6 - gradient operator

term 2

PX153 - I - integration

I - integration

PX153 - I1 - introduction

PX153 - I10 - conservative fields

PX153 - I11 - surface integrals

PX153 - I2 - multiple integrals

PX153 - I3 - domain of integration

PX153 - I4 - non-rectangular domain of integration

PX153 - I5 - summary of integrals in 3D

PX153 - I6 - volume integrals

PX153 - I7 - other coordinate systems

PX153 - I8 - summary of multidimensional integrals

PX153 - I9 - line integrals

PX153 - J - fourier series

J - fourier series

PX153 - J1 - introduction

PX153 - J10 - examples

PX153 - J2 - convergence

PX153 - J3 - proofs and derivations

PX153 - J4 - periodic extensions

PX153 - J5 - symmetric and antisymmetric functions

PX153 - J6 - parseval's theorem

PX153 - J7 - general interval

PX153 - J8 - sine and cosine series

PX153 - J9 - overshoot and gibbs phenomenon

PX153 - K - linear algebra

K - linear algebra

PX153 - K0 - outline

PX153 - K1 - terminology of matrices

PX153 - K10 - special matrices

PX153 - K11 - matrix operation on vectors

PX153 - K12 - eigenvectors and eigenvalues

PX153 - K13 - additional properties

PX153 - K14 - basis changes and similarity transformations

PX153 - K15 - similarity transformation

PX153 - K16 - diagonalization

PX153 - K17 - properties of diagonalization

PX153 - K2 - matrix operations

PX153 - K3 - solving simultaneous equations

PX153 - K4 - row-reduced echelon form (gaussian elimination)

PX153 - K5 - trace and determinants

PX153 - K6 - properties of determinants

PX153 - K7 - matrix inverse

PX153 - K8 - properties of matrix inverses

PX153 - K9 - LU decomposition method

review before exam

PX154 - physics foundations

PX154 - 0 - physics foundations

PX154 - A - dimensional analysis

A - dimensional analysis

PX154 - A1 - dimensional analysis

PX154 - A2 - dimensions

PX154 - A3 - applying dimensional analysis

PX154 - B - thermal physics

B - thermal physics

PX154 - B1 - heat and temperature

PX154 - B2 - thermal expansion

PX154 - B3 - heat capacity

PX154 - B4 - heat transfer mechanisms

PX154 - C - thermal physics 2

C - thermal physics 2

PX154 - C1 - ideal gas equation of state

PX154 - C10 - heat capacity of solids

PX154 - C2 - pV diagrams

PX154 - C3 - a real gas equation of state

PX154 - C4 - pV diagrams 2

PX154 - C5 - phase diagrams

PX154 - C6 - kinetic-molecular model of the ideal gas

PX154 - C7 - maxwell-boltzmann distribution

PX154 - C8 - collisions between molecules

PX154 - C9 - heat capacity of the ideal gas

PX154 - D - the first law of thermodynamic

D - the first law of thermodynamics

PX154 - D1 - introduction

PX154 - D2 - the first law

PX154 - D3 - work and the pV diagram

PX154 - D4a - isobars

PX154 - D4b - isochore

PX154 - D4c - isotherm

PX154 - D4d - interlude

PX154 - D4e - adiabat

PX154 - D5 - summary of processes

PX154 - E - the second law of thermodynamics

E - the second law of thermodynamics

PX154 - E1 - work done along different paths in the pV diagram

PX154 - E2 - heat engine cycles and the pV diagram

PX154 - E3 - the second law of thermodynamics

PX154 - E4 - the carnot cycle

PX154 - E5 - reversible and irreversible processes

PX154 - E6a - introduction to entropy

PX154 - E6b - quantitative definition of entropy

PX154 - E6c - adiabatic processes

PX154 - F - waves

PX154 - F1a - concepts and definitions

PX154 - F1b - the wave function

PX154 - F1c - propagation

PX154 - F2 - the wave equation

PX154 - F3a - principle of superposition

PX154 - F3b - beats

PX154 - F4 - wave groups and group velocity

PX154 - G - mechanical waves

G - mechanical waves

PX154 - G1a - waves on a taut string

PX154 - G1b - transfer of power by the wave

PX154 - G2 - longitudinal waves along a bar (1D)

PX154 - G3 - shear waves

PX154 - G4 - three dimensional solids - bulk waves

PX154 - G5 - waves in bulk gases - sound waves

PX154 - G6 - the doppler effect

PX154 - H - waves at boundaries

H - waves at boundaries

PX154 - H1 - fixed and free ends

PX154 - H2 - two strings joined together - transmission and reflection

PX154 - H3 - standing waves and normal modes

PX154 - I - light

PX154 - I1 - the nature of light

PX154 - I2 - polarization

PX154 - I3 - polarized and unpolarized light

PX154 - I4 - propagation of light

PX154 - I5 - snell's law

PX154 - I6 - transmission and reflection coefficients for light

review before exam

PX155 - classical mechanics and special relativity

PX155 - 0 - classical mechanics and special relativity

classical mechanics

PX155 - A - foundations of classical mechanics

A - foundations of classical mechanics

PX155 - A1 - newton's first law

PX155 - A2 - newton's second law

PX155 - A3 - newton's third law

PX155 - A4 - scalars and vectors

PX155 - A5 - static and dynamic friction

PX155 - A6 - block on a slope

PX155 - A7 - gravitational force

PX155 - B - systems of particles, accelerations

B - systems of particles and acceleration

PX155 - B1 - systems of particles I

PX155 - B2 - continuous bodies

PX155 - B3 - forces out of balance

PX155 - B4 - equations of motion

PX155 - C - work and energy

C - work and energy

PX155 - C1 - work and kinetic energy

PX155 - C2 - conservative forces, potential energy

PX155 - C3 - gravitational potential energy

PX155 - C4 - using energy conservation

PX155 - C5 - power

PX155 - D - simple harmonic motion

D - simple harmonic motion

PX155 - D1 & D2 - oscillations & mass on a spring

PX155 - D10 - pendulums and SHM

PX155 - D3 - solving the SHM equation

PX155 - D4 - initial conditions

PX155 - D5 - energy and SHM

PX155 - D6 - SHM and complex exponentials

PX155 - D7 - damped oscillations

PX155 - D8 - 3 regimes of damping

PX155 - D9 - driven damped simple harmonic motion

PX155 - E - circular motion, rotation of bodies

E - circular motion, rotation of bodies

PX155 - E1 - circular motion

PX155 - E10 - systems of particles III

PX155 - E11 - moment of inertia for continuous rigid bodies

PX155 - E12 - example of moments of intertia

PX155 - E13 - cylinder rolling down a slope

PX155 - E14 - parallel axis theorem

PX155 - E15 - the compound pendulum

PX155 - E16 - using conservation of momentum

PX155 - E2 - angular velocity vector

PX155 - E3 - circular motion and rolling

PX155 - E4 - centripetal acceleration

PX155 - E5 - moments

PX155 - E6 - system of particles II

PX155 - E7 - back to levers

PX155 - E8 - angular momentum of a particle moving in a circle

PX155 - E9 - orbital angular momentum

PX155 - F - collisions

PX155 - F1 - collisions in 1D

PX155 - F2 - collisions in 3D

PX155 - classical mechanics - summary

special relativity

PX155 - G - foundations of special relativity

G - foundations of special relativity

PX155 - G1 - gallilean transforms

PX155 - G2 - galilean invariance and light

PX155 - G3 - the postulates of special relativity

PX155 - G4 - relativity of simultaneity

PX155 - G5 - coordinate transforms

PX155 - H - the lorentz transformations

H - the lorentz transformation

PX155 - H1 - lorentz transformation

PX155 - H2 - length contraction

PX155 - H3 - time dilation

PX155 - H4 - relativistic doppler effect - seeing vs observing

PX155 - H5 - the twin paradox

PX155 - H6 - relativistic velocity addition

PX155 - I - relativistic momentum mass and energy

I - relativistic momentum, mass, and energy

PX155 - I1 - momentum

PX155 - I2 - relativistic momentum

PX155 - I3 - causality

PX155 - I4 - light cones

PX155 - I5 - relativistic kinetic energy

PX155 - I6 - mass, energy, and momentum

PX155 - I7 - massless particles

PX155 - I8 - particle accelerators

PX155 - I9 - how far could you go

review before exam

PX156 - quantum phenomena

PX156 - 0 - quantum phenomena

PX156A - quantum phenomena

PX156 - A - light

PX156 - A1 - background

PX156 - A2 - blackbody radiation and laws

PX156 - A3a - blackbody models

PX156 - A3b - planck's function

PX156 - A3c - boltzmann distribution

PX156 - A4 - the photoelectric effect

PX156 - A5 - the compton effect

PX156 - B - atomic stucture

B - atomic structure

PX156 - B1 - atoms and atomic spectra

PX156 - B2 - bohr's model

PX156 - B3 - de broglie hypothesis

PX156 - B4 - classical vs quantum

PX156 - C - quantum mechanics

C - quantum mechanics

PX156 - C1 - the schrodinger equation

PX156 - C2 - matter waves

PX156 - C3 - wave packets

PX156 - C4 - gaussian distribution

PX156 - C5 - top-hat distribution

PX156 - C6 - the uncertainty principle

PX156 - D - time independent schrodinger equation

D - time independent schrödinger equation

PX156 - D1 - time independent schrödinger equation

PX156 - D2 - infinite potential well

PX156 - D3 - finite potential well

PX156 - D4 - classical and quantum particle

PX156 - D5 - the finite potential barrier

PX156 - D6 - rutherford scattering experiment

PX156 - D7 - alpha decay of nuclei

PX156B - particle physics

PX156 - E - introduction

E - introduction

PX156 - E1 - guides

PX156 - E2 - forces

PX156 - E3 - unification

PX156 - E4 - units

PX156 - E5 - scales

PX156 - F - the particle zoo

F - the particle zoo

PX156 - F1 - quantum number

PX156 - F2 - categorization

PX156 - F3 - leptons

PX156 - F4 - quarks

PX156 - F5 - quark combinations

PX156 - F6 - conservation of quantum numbers in interactions

PX156 - G - feynmann diagrams

E - feynmann diagrams

PX156 - G1 - introduction

PX156 - G2 - interactions

PX156 - G3 - basic rules

PX156 - G4 - strategies of drawing a feynmann diagram

PX156 - G5 - virtual particles

PX156 - H - aspects of the forces

H - aspects of the forces

PX156 - H1 - the electromagnetic force

PX156 - H2 - the strong force

PX156 - H3 - the weak force

PX156 - I - symmetries

PX156 - I1 - symmetries

PX156 - I2 - continuous symmetries

PX156 - I3 - discrete symmetries

PX156 - I4 - internal symmetries

PX156 - J - particle decays & relativistic kinematics

J - particle decays & relativistic kinematics

PX156 - J1 - decays

PX156 - J2 - decay channels

PX156 - J3 - relativistic invariants

PX156 - J4 - two body collisions

PX156 - J5 - natural sources of particles

PX156 - K - accelerators & detectors

K - accelerators & detectors

PX156 - K1 - introduction

PX156 - K2 - linear accelerator

PX156 - K3 - cyclotron

PX156 - K4 - synchrotron

PX156 - K5 - detectors

PX156 - K6 - detector design

review before exam

PX157 - electricity and magnetism

PX157 - 0 - electricity and magnetism

PX157 - A - coulomb's law

A - coulomb's law

PX157 - A1 - introduction

PX157 - A2 - coulomb's law

PX157 - A3 - principle of super position

PX157 - B - electric fields

I - field

PX157 - B1 - introduction

PX157 - B2a - electric field from a continuous distribution

PX157 - B2b - electric field from an infinite line of charge

PX157 - B3 - electrical dipoles

PX157 - B4a - electric flux

PX157 - B4b - electric flux from an arbitrary surface

PX157 - B5a - gauss's law

PX157 - B5b - electric field from a uniformly charged sphere

PX157 - B5c - electric field from an infinite line of charge

PX157 - B5d - electric field from an infinite plane of charge

PX157 - B6a - conductors

PX157 - B6b - electric field around a conductor

PX157 - B6c - faraday cage

II - potentials

PX157 - B7a - electric potential energy

PX157 - B7b - potential energy and potential of two point charges

PX157 - B7c - electric potential

PX157 - B8a - calculating potentials

PX157 - B8b - potential of a point charge

PX157 - B8c - potential of a ring of charges

PX157 - B8d - potential of an infinite line of charge

PX157 - B8e - potential difference between two oppositely charged plates

PX157 - B8f - potential of an ideal electric dipole

PX157 - B9 - potential gradients

III - properties

PX157 - B10 - capacitors

PX157 - B11 - field energy

PX157 - B12a - dielectrics

PX157 - B12b - relative permittivity

PX157 - B13a - current

PX157 - B13b - resistance

PX157 - B13c - electromotive force

IV - circuits

PX157 - B14a - circuits - kirchhoff's rules

PX157 - B14b - circuits - maxwell loops

PX157 - B14c - circuits - RC circuit

B - electric fields

PX157 - C - magnetic fields

C - magnetic fields

PX157 - C10a - classification of materials

PX157 - C10b - diamagnetic materials

PX157 - C10c - paramagnetic materials

PX157 - C10d - ferromagnetic materials

PX157 - C10e - working of a magnet

PX157 - C1a - the lorentz force

PX157 - C1b - magnetic flux

PX157 - C1c - a charge in a magnetic field

PX157 - C2 - force of current loops

PX157 - C3a - the biot-savart law

PX157 - C3b - the biot-savart law applied to a wire

PX157 - C3c - magnetic field of a straight wire

PX157 - C3d - forces between two current loops

PX157 - C4a - ampere's law

PX157 - C4b - magnetic field of an infinite straight wire

PX157 - C4c - magnetic field on a long cylindrical conductor

PX157 - C4d - magnetic field on a long cylindrical wire with a hole

PX157 - C8 - solenoid

PX157 - C9 - magnetic dipole moment

PX157 - D - induction

PX157 - D1a - faraday's law

PX157 - D1b - a moving crossbar

PX157 - D1c - lenz's law

PX157 - D1d - motional emf

PX157 - D1e - a rotating conducting rod in a magnetic field

PX157 - D1f - a falling magnet in a pipe

PX157 - D2 - induced electric fields

PX157 - D3a - inductors

PX157 - D3b - faraday's law for solenoid or inductor

PX157 - D3c - magnetic field energy

PX157 - D3d - inductors in series

PX157 - D3e - inductors in parallel

PX157 - D4 - transformer

PX157 - Dx1 - displacement current

PX157 - Dx2 - maxwell's equations

PX157 - E - AC circuits

E - AC circuits

PX157 - E1 - complex representation

PX157 - E2 - complex impedences

PX157 - E3 - kirchhoff's laws for AC circuits

PX157 - E4a - LRC circuits 1

PX157 - E4b - LRC circuits 2

PX157 - E4c - LRC circuits 3

PX157 - E4d - solving as an ODE

PX157 - E5 - AC power

review before exam

PX158 - astronomy

PX158 - 0 - astronomy

problem sheets

PX158 - A - introduction

A - introduction

PX158 - A1 - introduction

PX158 - B - the celestial sphere

B - the celestial sphere

PX158 - B1 - introduction

PX158 - B2 - maximum altitude

PX158 - B3 - measuring time

PX158 - C - angles and parallax

C - angles and parallax

PX158 - C1 - parallax

PX158 - C2 - proper motion

PX158 - D - fluxes and magnitudes

D - fluxes and magnitudes

PX158 - D1 - luminosity and flux

PX158 - D2 - brightness and magnitudes

PX158 - E - telescopes

PX158 - E1 - introduction

PX158 - E2 - extended objects

PX158 - F - blackbody and colours

F - black bodies and colours

PX158 - F1 - black body radiation

PX158 - F2 - luminosity-temperature-radius of stars

PX158 - F3 - colours

PX158 - G - astronomical masses

G - astronomical masses

PX158 - G1 - two masses in a mutual circular orbit

PX158 - G2 - spectroscopic binaries

PX158 - G3 - gravitational lensing

PX158 - H - the solar system and exoplantes

H - the solar system and exoplanets

PX158 - H1 - introduction

PX158 - H2 - temperature of solar system bodies

PX158 - H3 - planets

PX158 - H4 - exoplanets

PX158 - I - stars

PX158 - I1 - hertzprung-russell diagram

PX158 - I2 - stellar classes

PX158 - I3 - theoretician's H-R diagram

PX158 - I4 - star clusters

PX158 - I5a - pressure at the centre of stars

PX158 - I5b - temperature at the centre of stars

PX158 - I6a - stellar evolution

PX158 - I6b - mass-luminosity relationship

PX158 - I6c - evolution of a sun-like star

PX158 - I6d - stars by masses

PX158 - I7a - white dwarfs

PX158 - I7b - neutron stars

PX158 - I7c - chandrashekhar limit

PX158 - I7d - blackholes

PX158 - J - galaxies

PX158 - J1 - introduction

PX158 - J2 - types of galaxies

PX158 - J3 - weighing galaxies

PX158 - J4 - central blackholes

PX158 - K - the universe

K - the universe

PX158 - K1 - hubble's law

PX158 - K2 - the age of the universe

PX158 - K3 - cosmic microwave background

PX158 - K4 - the big bang theory

PX158 - K5 - density of the universe

review before exam

012

PX262 - quantum mechanics

term 1

A - recap

PX262 - A1 - photoelectric effect

PX262 - A2 - compton scattering

PX262 - A3 - line spectra

PX262 - A4 - bohr's model

PX262 - A5 - debroglie waves

PX262 - A6 - wave-particle duality

PX262 - A7 - the uncertainty principle

B - introduction

B - introduction

PX262 - B1 - schrödinger equation

PX262 - B2 - time-independent schrödinger equation

PX262 - B3 - boundary conditions

PX262 - B4 - particle in an infinite square well

PX262 - B5 - quantum tunnelling

PX262 - B6 - 1D harmonic oscillator

C - the basic postulates

C - the basic postulates

PX262 - C10 - the basic postulates

PX262 - C1a - the wavefunction

PX262 - C1b - postulate 1

PX262 - C1c - example problem

PX262 - C2a - the dynamical variables

PX262 - C2b - momentum & position operator

PX262 - C2c - postulates 2 & 3

PX262 - C3 - orthonormality

PX262 - C4 - probability distributions

PX262 - C4b - postulate 4

PX262 - C4c - continuous eigenvalues

PX262 - C5 - expectation value

PX262 - C6a - commutation relations

PX262 - C6b - compatibility of operators

PX262 - C7a - the uncertainty principle

PX262 - C8 - postulate 5

PX262 - C9a - degeneracy

PX262 - C9b - schmidt orthogonalization

PX262 - C9c - compatibility of measurements

D - ladder operators and angular momentum

D - ladder operators and angular momentum

PX262 - D1 - ladder operators

PX262 - E1a - angular momentum operators

PX262 - E1b - compatibility

PX262 - E2 - eigenvalues and eigenfunctions

F - 3D systems

PX262 - F1 - the schrödinger equation in 3D

PX262 - F2a - particle in an infinite potential well

PX262 - F2b - degeneracy

PX262 - F3 - 3D harmonic oscillator

PX262 - F4 - separation in spherical polar coordinates

PX262 - F5 - particle in a spherical potential well

PX262 - F6 - hydrogenic atom

PX262 - F7 - properties of hydrogen-like atoms

G - additional interactions

G - additional interactions

PX262 - G1 - particle with angular momentum in magnetic field

PX262 - G2a - stern-gerlach experiment

PX262 - G2b - spin

PX262 - G3 - matrix representation

PX262 - G4 - pauli spin matrices

PX262 - G5 - multielectron atoms

PX262 - G6a - interactions of moments

PX262 - G6b - spin-orbit coupling

PX262 - G6c - zeeman effect

PX262 - G7a- pure spin-orbit coupling

PX262 - G7b - strong-field zeeman effect

PX262 - G7c - weak-field zeeman effect

PX262 - G8 - photon emission from atoms

term 2

H - free electron model

H - free electron model

PX262 - H1 - current

PX262 - H2 - quantum mechanics and many particles

PX262 - H3 - free electron model (1D)

PX262 - H4 - free electron model (3D)

PX262 - H5 - metals in a magnetic field

I - nuclear matter

I - nuclear matter

PX262 - I1 - nuclear matter and the liquid drop model

PX262 - I2 - implications for nature of nuclear forces

PX262 - I3 - liquid drop model of nucleus

J - atoms and molecules

J - atoms and molecules

PX262 - J1 - electrons in atoms and molecules

PX262 - J2 - electronic configurations

PX262 - J3 - molecules

PX262 - J4 - interacting electrons and nuclei in matter

PX262 - J5 - density functional theory

K - crystalline solids

K - crystalline solids

PX262 - K1 - electrons in crystalline solids

PX262 - K2 - reciprocal lattice and reciprocal space

PX262 - K3 - wavevector space and brillouin zone

PX262 - K4 - electrons in crystalline solids

PX262 - K5 - block wavefunctions, electronic energy bands and gaps

PX262 - K6 - energy gaps

L - semiconductors

L - semiconductors

PX262 - L1 - introduction to semiconductors

PX262 - L2 - n- and p-type semiconductors

PX262 - L3 - p-n junction

M - basic postulates revisited

M - basic principles revisited

PX262 - M1 - introduction to spin

PX262 - M2 - recap

PX262 - M3 - dirac notation

N - relativity and quantum mechanics

N - relativity and quantum mechanics

PX262 - N1 - klein-gordon equation

PX262 - N2 - dirac equation

PX262 - N3 - prediction of antiparticles

PX262 - 0 - quantum mechanics

PX275 - mathematical methods

PX275 - 0 - mathematical methods

term 1

A - differentiation

1 - introduction A1 & A2

PX275 - A1a - partial differentiation

PX275 - A1b - total differentiation

PX275 - A2 - exact and inexact differentials

PX275 - A2a - inexact differentials

PX275 - A2b - testing for exact differentials

PX275 - A2c- maxwell's thermodynamic relation

2 - advanced A3, A4 & A5

PX275 - A3a - the chain rule

PX275 - A3b - example

PX275 - A3c - change of variables and coordinate system

PX275 - A3e - chain rule additional

PX275 - A4a - directional derivatives

PX275 - A4c - the laplacian

PX275 - A5 - lagrange multipliers

PX275 - A5b - definition using gradient

A - differentiation

B - coordinate systems and integration

B1 - coordinate systems

B1 - coordinate systems

PX275 - B1a - cylindrical polar coordinates

PX275 - B1b - cylindrical polar basis vectors

PX275 - B1c - cylindrical polar representation

PX275 - B1d - time derivatives

PX275 - B1e - spherical polar coordinates

PX275 - B1f - spherical basis vectors

PX275 - B1g - spherical polar representation

B2-4 - integration

B2-4 - integration

PX275 - B2 - multiple integration

PX275 - B2a - 1D integrals in 2D and 3D

PX275 - B2b - simple examples of line integrals

PX275 - B3 - jacobian

PX275 - B3a - hyperbolic coordinates

PX275 - B4a - surface of revolution

PX275 - B4b - example - a cone

PX275 - B4c - example - a torus

PX275 - B4d - volumes of revolution

PX275 - B4e - pappus's first theorem

B - coordinate systems and integration

C - vector calculus

C - vector calculus

PX275 - C1a - gradient or gra

PX275 - C1b - divergence or div

PX275 - C1c - interpretation of div

PX275 - C1d - curl

PX275 - C1e - examples of curl

PX275 - C1f - example of curl II

PX275 - C1g - interpretation of curl

PX275 - C2a - grad squared

PX275 - C2b - examples of using the laplacian

D - vector integration

D1-2

PX275 - D1 - vector displacements

PX275 - D2a - line integrals with fields

PX275 - D2b - conservative vector fields

D3 - green's theorem

PX275 - D3a - green's theorem in the plane

PX275 - D3b - proof of green's theorem

PX275 - D3c - application of green's theorem

PX275 - D3d - area of an ellipse

PX275 - D3e - divergence theorem in 2D

PX275 - D3f - physical significance of the divergence theorem

PX275 - D3g - the physical significance of green's theorem in the plane

D4 - vector surface area

PX275 - D4a - flux of a vector field through a loop

PX275 - D4b - the vector surface area and element

PX275 - D4c - total vector surface area

PX275 - D4d - comments

D - vector integration

E - stoke's theorem and the divergence theorem

E - stokes' theorem and the divergence theorem

PX275 - E1a - stokes' theorem

PX275 - E1b - examples

PX275 - E2a - divergence theorem

PX275 - E2b - dirac delta

PX275 - E2c - example

PX275 - E2d - scalar fields

F - tensors and summation conventions

F - tensors and summation conventions

PX275 - F1 - tensors

PX275 - F2 - summation conventions

PX275 - F3 - levi-civita symbol

term 2

G - partial differential equations

G - partial differential equations

PX275 - G1 - functions of a single variable

PX275 - G10 - plane waves

PX275 - G11a - schrödinger equation

PX275 - G2 - functions of a multiple variables

PX275 - G3a - diffusion equation

PX275 - G3b - heat equation

PX275 - G4 - wave equation

PX275 - G5 - method of separation of variables

PX275 - G6 - boundary and initial conditions

PX275 - G7 - dirac delta function

PX275 - G8 - complex exponential form of solution in 3D

PX275 - G9 - orthogonality relations

PX275 -G11b - other examples

H - fourier series and transforms

H - fourier series and transforms

PX275 - H1 - complex fourier series

PX275 - H10 - FT and PDEs

PX275 - H11 - FT in data analysis

PX275 - H2 - calculating coefficients

PX275 - H3 - fourier transforms

PX275 - H4 - example of fourier transform

PX275 - H5 - parseval's theorem

PX275 - H6 - fourier transforms in the time domain

PX275 - H7a - convolutions

PX275 - H7b - examples of convolutions

PX275 - H8 - multidimensional convolutions

PX275 - H9 - FT and differential equations

I - optics

PX275 - I0 - introduction to waves

PX275 - I1 - diffraction and interference

PX275 - I2 - huygen's principle and point sources

PX275 - I3 - point sources in 3D

PX275 - I4 - key geometry

PX275 - I5 - different path lengths

PX275 - I6a - square aperture

PX275 - I6b - rectangular aperture

PX275 - I6c - multiple slits

PX275 - I6d - circular aperture

PX275 - I7 - rayleigh criterion for resolution

PX275 - I8 - optical elements in instruments

PX275 - formula sheet

PX282 - stars and solar system

PX282 - 0 - stars & solar system

term 1 - stars

A - introduction

A - introduction

PX282 - A0 - hydrostatic equilibrium

PX282 - A1 - a star

PX282 - A10 - real spectra

PX282 - A2 - hertzsprung-russel diagrams

PX282 - A3 - luminosity and flux

PX282 - A4 - parallax and parsecs

PX282 - A5 - astrophysical observations

PX282 - A6 - magnitudes, band passes, colours

PX282 - A7 - inside a star

PX282 - A8 - solid angle

PX282 - A9 - connection to luminosity

B - spectral classification

B - stellar spectroscopy and classification

PX282 - B1 - spectral classification

PX282 - B2 - typical spectral lines

PX282 - B3 - spectral lines and classes

C - stellar atmosphere

C1-4 - boltzmann-saha

PX282 - C1 - the physics of line strength

PX282 - C2a - the boltzmann equation

PX282 - C2b - an alternate form

PX282 - C3 - the saha equation

PX282 - C4 - the boltzmann-saha equation

C10-13 - radiative transfer

PX282 - C10a - radiative transfer equation

PX282 - C10b - understanding the radiative transfer equation

PX282 - C11 - radiation pressure

PX282 - C12 - temperature structure

PX282 - C13 - limb darkening

C5-8 - stellar atmospheres

PX282 - C5 - definitions

PX282 - C6a - radiation-matter interactions

PX282 - C6b - intensity after absorption

PX282 - C7 - mean free path

PX282 - C8 - optical depth

C9 - sources of opacity

PX282 - C9a - sources of opacity

PX282 - C9b - bound-bound absorption

PX282 - C9c - bound-free absorption

PX282 - C9d - free-free absorption

PX282 - C9e - scattering

PX282 - C9f - deionized hydrogen

PX282 - C9g - combined opacity

C - stellar atmospheres

D - stellar structure and interiors

D - solar structure and interiors

PX282 - D1 - stellar interiors

PX282 - D2 - energy generation and transport

PX282 - D2b - radiation

PX282 - D2c - convection

PX282 - D3 - equations of state

PX282 - D4 - virial theorem - energy in stars

PX282 - D5 - energy sources and timescales

PX282 - D6 - nuclear binding energies

PX282 - D7 - PP1 fusion chain

E - stellar evolution

E - stellar evolution

PX282 - E1a - star formation

PX282 - E1b - initial mass function

PX282 - E2 - protostar

PX282 - E3 - main sequence

PX282 - E4 - turnoff points and stellar clusters

PX282 - E5a - post-main sequence evolution

PX282 - E5b - red giant branch (RGB)

PX282 - E5c - helium flash

PX282 - E5d - horizontal branch

PX282 - E5e - asymptotic giant branch (AGB)

PX282 - E5f - post AGB

PX282 - E6 - higher mass stars

PX282 - E7 - remnants

PX282 - E8 - supernova Ia

F - binary stars and fundamental parameters

F - binary stars and fundamental parameters

PX282 - F1 - binary stars

PX285 - F2 - visual binaries

PX285 - F3 - spectroscopic binaries

PX285 - F4 - eclipsing binaries

term 2 - solar system

G - the sun

PX282 - G1 - fundamental properties

PX282 - G2 - internal structure

PX282 - G3 - sunspots

PX282 - G4 - solar atmosphere

PX282 - G5 - solar activity cycle

H - introduction to the planets

H - introduction to the planets

PX282 - H1 - planets

PX282 - H2 - spectrum of a planet

I - planetary motion

I - planetary motion

PX282 - I1 - models

PX282 - I2 - kepler's laws

PX282 - I3 - newtons' laws

PX282 - I4 - energy in orbits

PX282 - I5 - two body problem

PX282 - I6a - three body problem I

PX282 - I6b - three body problem II

PX283 - I7 - tides

J - terrestrial planets

J - terrestrial planets

PX282 - J1 - mercury

PX282 - J2 - venus

PX282 - J3 - earth

PX282 - J4 - mars

PX282 - J5 - interiors

PX282 - J6 - surfaces

PX282 - J7a - atmospheres

PX282 - J7b - greenhouse effect

PX282 - J7c - earth and venus

PX282 - J7d - atmospheric escape

PX282 - J8 - orbits

PX282 - J9 - moons

K - giant planets

K - giant planets

PX282 - K1 - composition

PX282 - K2a - interiors of gas giants

PX282 - K2b - interiors of ice giants

PX282 - K3 - internal heat

PX282 - K4 - atmosphere

PX282 - K5 - moons

L - formation of solar system

L - formation of solar system

PX282 - L1 - nebular hypothesis

PX282 - L2 - core accretion

M - habitability

M - habitability and extraterrestrial life

PX282 - M1 - requirements for life

PX282 - M2 - possible environments for life

PX284 - SMETO

part 1 - statistical mechanics

A - probability

A - probability

PX284 - A1 - discrete probability distributions

PX284 - A2 - continuous probability distributions

PX284 - A3 - the bernoulli trial

PX284 - A4 - bayes' theorem

B - introduction

B - introduction

PX284 - B0 - approaches to thermal physics

PX284 - B1 - the system

PX284 - B2 - microstates and macrostates

PX284 - B3 - assumptions

PX284 - B4 - ensembles

C - entropy and temperature

C - entropy and temperature

PX284 - C1a - boltzmann entropy formula

PX284 - C1b - combining systems

PX284 - C1c - isothermal expansion

PX284 - C1d - second law

PX284 - C2 - temperature

PX284 - C3 - boltzmann distribution

PX284 - C4 - measuring entropy

PX284 - C5 - general definition of entropy

D - equipartition theorem

D - equipartition theorem

PX284 - D1 - equipartition theorem

PX284 - D2 - applications of the equipartition theorem

E - single-particle partition function

E - single-particle partition function

PX284 - E0 - solving problems in statistical mechanics

PX284 - E1a - functions of state

PX284 - E1a -internal energy

PX284 - E1b - entropy

PX284 - E1c - helmholtz free energy

PX284 - E1d - others

PX284 - E2 - two-level system (revisited)

PX284 - E3 - harmonic oscillator in 1D

PX284 - E4 - degeneracy

PX284 - E5b - combining partition functions

PX284 - E5b - harmonic oscillator in 3D

PX284 - E5c - spin-half paramagnet

F - connection between thermodynamics and statistical mechanics

F - connection between thermodynamics and statistical mechanics

PX284 - F1 - isolated system or microcanonical ensemble

PX284 - F2a - systems with fixed T and V or canonical ensemble

PX284 - F2b - aside on lagrange multipliers

G - fluctuations

G - fluctuations

PX284 - G1 - energy deviation

PX284 - G2 - large systems

H - gases

PX284 - H0 - introduction

PX284 - H1 - density of states (DOS)

PX284 - H2 - single-particle partition function

PX284 - H3 - distinguishability

PX284 - H4 - ideal gas

PX284 - H5 - gibbs paradox

I - chemical potential

I - chemical potential

PX284 - I1 - definition

PX284 - I2 - significance

PX284 - I3 - grand canonical ensemble

PX284 - I4 - conservation laws

J - photons

PX284 - J1 - blackbody radiation

PX284 - J2 - statistical mechanics of photons

PX284 - J3 - cosmic microwave background

K - phonons

PX284 - K1 - einstein model

PX284 - K2 - debye model

L - exchange symmetry

L - exchange symmetry

PX284 - L1 - exchange symmetry

PX284 - L2 - pauli exclusion principle

PX284 - L3 - distribution functions

M - fermions

PX284 - M1 - electron gas

PX284 - M2 - fermi energy

PX284 - M3 - degeneracy pressure

PX284 - M4 - heat capacity

PX284 - M5 - neutron stars

N - bosons

PX284 - N1 - recap

PX284 - N2 - boson gases

PX284 - N3 - bose-einstein condensation

part 2 - electromagnetic theory

PX284 - 0 - statistical mechanics, electromagnetic theory & optics

O - introduction to EMT

O - introduction to EMT

PX284 - O1 - required maths

PX284 - O2 - electric and magnetic fields

PX284 - O3 - charge

PX284 - O4 - maxwell's equations in differential form

PX284 - O5 - electrostatics

PX284 - Ox - maxwell's equations in free space

P - EM waves

P - electromagnetic waves in free space

PX284 - P1 - introduction to EM waves

PX284 - P2 - energy in EM fields

PX284 - P3 - flux in EM waves

Q - maxwell's equations in matter

PX284 - Q1a - polarization

PX284 - Q1b - polarization of a slab

PX284 - Q2 - magnetization

PX284 - Q3 - maxwell's equations in matter

PX284 - Q4 - boundary conditions

Q - maxwell's equations in matter

R - dielectrics

PX284 - R1 - waves in dielectrics

PX284 - R2 - poynting vector

R - dielectrics

S - EM waves at boundaries

PX284 - S1 - snell's law

PX284 - S2a - fresnel relations

PX284 - S2b - brewster's angle

PX284 - S2c - total internal reflection

PX284 - S3a - conductors

PX284 - S3b - reflections on boundaries with metals

S - EM waves at boundaries

T - geometric optics

PX284 - T1 - wavefronts and rays

PX284 - T2 - fermat's principle

PX284 - T3a - imaging

PX284 - T3b - spherical surface using intersecting cords theorem

PX284 - T3c - spherical surface using trigonometric properties

PX284 - T4 - thin lens

PX284 - T5 - principal rays

PX284 - T6 - images

PX284 - T7 - telescopes

T - geometric optics

U - wave optics

PX284 - U1- resolution

PX284 - U2 - thin film interference

PX284 - U3 - fabry-perot interferometry

U - wave optics

PX285 - hamiltonian mechanics & fluid dynamics

PX285 - 0 - hamiltonian mechanics & fluid dynamics

term 1 - hamiltonian mechanics

A - introduction

A - introduction

PX285 - A1 - newton's laws

PX285 - A2a - conservation laws

PX285 - A2b - angular momentum

B - variational principles

B - variational principles

PX285 - B1 - variational principles

PX285 - B2 - fermat's law in optics

PX285 - B3 - newtonian mechanics - the principle of least action

C - calculus of variations

C - calculus of variations

PX285 - C1 - the euler-lagrange equation

PX285 - C2 - coordinate change

PX285 - C3 - newton's second law

PX285 - C4 - simple pendulum

PX285 - C5 - a roller-coaster

PX285 - C6a - multi-coordinate problems

PX285 - C6b - a particle in a cartesian plane

PX285 - C6c - two particles in 1D

PX285 - C6d - two particles in 3D

D - the hamiltonian

D - the hamiltonian

PX285 - D1 - the hamiltonian

PX285 - D2 - a constant of the motion

PX285 - D3 - the conservation of energy

PX285 - D4 - roller-coaster revisited

E - conservation laws and symmetries

E - conservation laws and symmetries

PX285 - E1 - noether's theorem

PX285 - E2 - translation of space

PX285 - E3 - translation in time

PX285 - E4 - rotation of space

F - hamilton's equations

F - hamilton's equations

PX285 - F1 - hamilton's equations

PX285 - F2 - phase space

PX285 - F3a - particle in 1D

PX285 - F3b - pendulum

PX285 - F4 - gyroscope

PX285 - F5 - central forces - particle approaching the sun

G - normal modes and small oscillations

G - normal modes and small oscillations

PX285 - G1 - inertia tensor

PX285 - G2 - stiffness matrix

PX285 - G3 - derivation from examples

PX285 - G4 - attached particles on springs

PX285 - G5 - non-diagonal inertia matrix

PX285 - G6 - summary

PX285 - G7 - example

PX285 - G8 - diatomic molecule

PX285 - G9 - triatomic molecule

term 2 - fluid dynamics

H - introduction to fluids

H - introduction to fluids

PX285 - H1 - fluids

PX285 - H2 - fluid approach

PX285 - H3 - mechanical perspective of fluids

PX285 - H4 - newton's law of viscosity

PX285 - H5 - fluid element

PX285 - H6a - stream line

PX285 - H6b - example of a flow

PX285 - H6c - example in a cylinder

PX285 - H7 - quantifying the effects of viscosity

I - navier-stokes equation

I - navier-stokes equation

PX285 - I1 - conservation of mass

PX285 - I2a - conservation of momentum

PX285 - I2b - advective derivative

PX285 - I3 - pressure equation

PX285 - I4 - core equations

PX285 - I5 - initial and boundary conditions

J - some approximate solutions

J - some approximate solutions

PX285 - J1a - bernoulli's principle from conservation of energy

PX285 - J1b - bernoulli's principle from navier-stokes equation

PX285 - J2 - hydrostatic limit and archimedes' principle

PX285 - J3 - water drain

PX285 - J4 - venturi pipe

PX285 - J5 - stagnation point

PX285 - J6 - pitot pipe

PX285 - J7- surface waves

PX285 - J8 - aerofoil

K - circulation and vorticity

K - circulation and vorticity

PX285 - K1 - vorticity

PX285 - K2 - kelvin's circulation theorem

L - potential flows

L - potential flows

PX285 - L1 - potential flows

PX285 - L2 - potential dipole

PX285 - L3 - potential flows involving cylinders and aerofoils

PX285 - L4a - lift and circulation - magnus effect

PX285 - L4b - aerofoil

PX285 - L5a - vortex lines

PX285 - L5b - interacting vortex lines

PX285 - L6 - potential flow over a wing

PX285 - L7 - boundary layers

PX285 - L8 - aerofoil lift

M - turbulence and drag

PX284 - M1 - turbulence

013

A - small angle scattering

A - small angle scattering

A1 - introduction

A10 - invariant calculation

A2 - structural significance

A3 - form factor

A4 - structure factor

A5 - neutron radiation

A7 - correlation function theory

A8 - neutron polarization

A9 - guinier approximation

B - python

1 - OOP

B3 - decorators

B5 - inheritance

B6 - operator overloading

2 - additional

B10 - list comprehension

B13 - decorators

B14 - variable scopes and lookup

B16 - data classes

B17 - unittest framework

B18 - pytest framework

B7 - type hints

B9 - args and kwargs

C - error statistics

C - error statistics

C1 - method of least squares

C2 - reduced-chi squared

D - git

D11 - advanced workflows

D2 - branching and merging

D4 - relative refs

D5 - reversing changes

D6 - cherry-picking and interactive rebasing

D7 - tag and describe

D9 - basic git workflow

E - PyQt

E1 - getting started with PyQT

E2 - signals, slots and events

E5 - toolbars and menus - QAction

E6 - dialogs and alerts

E7 - multiwindow

F - mathematics

F - mathematics

F1 - maximum entropy principle

F2 - bessel functions

F3 - hankel transforms

G - programming practices

G - programming practices

G1 - command line

H - probability

A - probability on events

A - probability on events

A1 - sample space and events

A2 - probability defined on events

A3 - conditional probabilities

A4 - independent events

A5 - law of total probability

A6 - bayes' law

Ax1- probability with combinatorics

B - discrete random variables

B - discrete random variables

B1 - introduction

B2 - common discrete random variables

B3 - multiple random variables and join probabilities

C - expectation

C - expectation

C1 - expectation of a discrete random variable

C2 - linearity of expectation

C3 - conditional expectation

C4 - computing expectations via conditioning

C5 - simpson's paradox

D - variance, higher moments, and random sums

D - variance, higher moments, and random sums

D1 - higher moments

H - probability

I - group theory

A - introduction to groups

A - introduction to groups

A1 - definition of a group

A2 - elementary properties of a group

A3 - important groups

A4 - symmetries of a square

A6 - subgroup tests

B - cyclic groups

B - cyclic groups

B1 - definition of a cyclic group

C - permutation group

C - permutation groups

C1 - permutation and symmetry

C2 - symmetry groups

C4 - properties

C5 - transposition

D - isomorphism

D - isomorphism

D1 - group isomorphism

D2 - properties

D3 - automorphism

D4 - cayley's theorem

E - cosets and lagrange's theorem

E - cosets and lagrange's theorem

E2 - lagrange's theorem

E3 - application of cosets to permutation groups

F - external direct product

F - external direct products

F1 - definition

F2 - properties

F3 - groups of units modulo n

G - normal subgroups and factor groups

G - normal subgroups and factor groups

G1 - normal subgroups

G2 - normal subgroup test

G3 - factor groups

G4 - applications of factor groups

G5 - cauchy's theorem for abelian groups

I - group theory

J - ML

0 - prerequisites

0 - prerequisites and ML basics

02 - cloud computing

04 - machine learning basics

05 - training, validation, and testing

06 - overfitting, underfitting, and regularisation

07 - classification metrics

08 - regression metrics

10 - production ML and the model lifecycle

11 - LLM fundamentals

12 - embeddings, vector search and RAG

A - microsoft stack

A - Microsoft stack and AML fundamentals

A1 - Azure's resource hierarchy

A10 - architecture design

A11 - Azure networking and private endpoints

A12 - registries and cross-workspace asset sharing

A2 - Entra ID, RBAC & managed identities

A3 - CLI & bicep

A4 - architecture

A5 - ML compute

A6 - datastores & data assets

A7 - environments

A9 - SDK, CLI & YAML

B - MLflow

B1 - experiment tracking

B2 - models, signatures and registration

B3 - model lifecycle

B4 - feature retrieval specifications

B5 - responsible AI

C - pipelines & hyperparameter tuning

C - pipelines & hyperparameter turning

C1 - pipelines & components

C2 - sweep jobs & hyperparameter tuning

C3 - building a complete pipeline

D - deployment and MLOps

D - deployment and MLOps

D1 - online vs batch endpoints

D2 - managed online deployments

D3 - batch endpoints and batch inference

D4 - monitoring, drift & model performance

E - GitHub Actions & production CI

E - GitHub Actions & production CI, CD

E1 - CI, CD for ML systems

E2 - workload identity federation

E3 - promotion across environments

F - Microsoft Foundry

F - Microsoft Foundry

F1 - architecture

F2 - models and deployment

F3 - prompting, RAG & fine-tuning

F4 - agents & tool use

F5 - GenAI evaluation and production

F6 - Foundry development options, PTUs

F7 - prompt lifecycle

G - production RAG & GenAIOps

G - production RAG & GenAIOps

G1 - Azure AI search & RAG architecture

G2 - chunking, embeddings and indexing

G4 - retrieval evaluation

G5 - tracing, monitoring and safety

G6 - GenAI evaluation

G7 - advanced RAG

G8 - the complete GenAIOps lifecycle

H - optimisation

H - optimisation

H1 - model optimisation

H2 - advanced fine-tuning

H3 - synthetic data

I - Python SDK v2 sytax

I - Python SDK v2 syntax

I1 - authentication, connection and jobs

X - machine learning process

X - machine learning process

X1 - defining the problem

X2 - getting and preparing the data

X3 - training a model

X4 - integrating the model

X5 - monitoring the model

PX390 - scientific computing

A - C foundations

A - C foundations

A1 - hello world

A2 - variables and data types

A3 - debugging and standard IO

A5 - decision making

A7 - conditionals and loops

A9 - derived data types

B - numerical methods

B - numerical methods

B1 - representing continuous functions and derivatives

B10 - numerical integration

B11 - numerical integration of ODEs

B12 - varying diffusion coefficients

B2 - convergence

B3 - local truncation error

B4 - discretising heat equation PDEs

B5 - implicit methods

B6a - advection equation

B6b - finite difference

B6c - upwinding

B7 - boundary conditions

B8 - 2D boundary value problem

B9 - numerical differentiation

x - working with vonneumann

x1 - code for difference schemes comparison

x2 - code for transforming indices

x3 - compactly storing banded matrices

PX390 - 0 - scientific computing

014

019

PX447 - quantum computation and simulation

A - introduction

A - computation theory

A1 - computation

A2 - circuit models

B - quantum computation

B - quantum computation

B1 - postulates

B3 - quantum computation

PX447 - 0 - quantum computation and simulation

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PX156 - A3b - planck's function

energy is quantized:

E_{n} = n h f

where, $n \in Z$ , $h =$ planck's constant

average energy:

⟨ E ⟩ = \frac{h f}{\exp (\frac{h f}{k_{B} T}) - 1}

Connected Pages

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PX156 - 0 - quantum phenomena

PX156 - C2 - matter waves