Lecture notes

The lecture notes on this page cover all or parts of physics1 classes taught/lectures delivered across various levels and institutions. Some may be updated and/or improved over time and their latest versions will be linked to from this page for anyone interested in using them for either reference or learning.

Thoughts, criticisms and suggestions for improvement are always welcome. Please feel free to get in touch with me via e-mail anytime. Find a simple list below; a detailed list is available further down the page.

Quick list

Below is simply a list of lecture notes without their contents for those who know what they are looking for or those who want to blindly dive in.

  1. Small oscillations (postgraduate)
  2. Fields due to moving charges (postgraduate)
  3. Radiating electrodynamic systems (postgraduate)
  4. Nuclear Magnetic Resonance (postgraduate) (Under way)
  5. X-ray diffraction: techniques and mathematical tools (postgraduate)
  6. Mechanics (IAL – AS)
  7. Materials (IAL – AS)
  8. Statistics (IAL – AS)

1. Graduate physics

1.1. Advanced classical mechanics

1.1.1. Small oscillations (Download)

  1. Introductory notes
  2. Equilibria
    1. Stable
    2. Unstable
    3. Neutral
  3. Building the Lagrangian
    1. Potential energy
    2. Kinetic energy
    3. Lagrangian and equation of motion
    4. Understanding the general Lagrangian
  4. The eigenvalue problem
    1. The eigenvalue equation
    2. Characteristics of the eigenvector
    3. Solving the eigenvalue equation
  5. Normal coördinates and normal modes
  6. Example systems
    1. Vibrations of a particle pair
    2. Linear, triatomic molecules (general case)
    3. Linear, triatomic molecules of equal mass

1.2. Advanced classical electrodynamics

1.2.1. Fields due to moving charges (Download)

  1. Review of prerequisite topics
  2. Retarded time and potential
    1. Relativistic effects
    2. Spatial derivatives
    3. Proof of time dependence
  3. Liénard-Wiechert potentials
    1. Derivation
    2. Understanding the \textbf{r}\cdot \textbf{v}(t_r) term
  4. Fields due to a moving point charge
    1. Arbitrary motion
    2. Observations on the LW fields
    3. V and A at a constant velocity
    4. E and B at a constant velocity
    5. Notes on the constant velocity case

1.2.2. Radiating electrodynamic systems (Download)

  1. Oscillating electric dipoles
    1. Potentials in the far field region
    2. Fields in the radiation zone
    3. Poynting vector and the power of radiation
  2. Radiation from point charges
    1. Power (Larmor formula)
    2. Liénard’s generalisation of Larmor’s formula
  3. Implications of the relativistic Larmor formula
    1. Radiation energy loss in linear accelerators
    2. Bremsstrahlung
  4. Reactive forces
    1. The Abraham-Lorentz formula
    2. Observations on the Abraham-Lorentz formula

1.3. Spectroscopy

1.3.1. Nuclear magnetic resonance (Download)

  1. Spin-field interactions
    1. Magnetons
    2. Energy levels
    3. Larmor precession
    4. Population
  2. Perturbations
    1. Time evolution of spin
  3. Relaxation
    1. Rate of magnetisation
    2. Spin-Lattice relaxation
    3. Chemical shift
    4. (In progress: please check back later)

1.4. X-ray diffraction

1.3.1. Techniques and mathematical tools

  1. The basics
    1. Definitions
    2. Real lattice, Miller indices and Miller planes
    3. Bragg and Laue equations
  2. The reciprocal lattice
    1. (In progress: please check back later)

2. International Advanced Level

2.1. Physics for AS

2.1.1. Mechanics (Download)

  1. Velocity, displacement, acceleration
  2. Reading graphs
    1. Interpretation: lines, slopes, areas
    2. Position-time and velocity-time graphs
  3. SUVAT equations (of motion)
  4. Vector operations (matrix representation is not discussed)
    1. Addition
    2. Dot and cross products
    3. Resolution of vectors
  5. Newton’s laws of motion
    1. The first law
    2. Mass and inertia
    3. Friction
    4. The second law
    5. Weight
    6. The third law
  6. Projectiles
    1. Vertical throws
    2. Plotting coördinates
    3. Calculating travel time
    4. Calculating range
    5. Calculating the maximum height
  7. Work
  8. Energy
    1. Laws of conservation of energy
    2. Kinetic and potential energy
  9. Power and efficiency

2.1.2. Materials (Download)

  1. Static fluids
    1. Mass and volume
    2. Density
    3. Upthrust
    4. Archimedes’ principle
  2. The mathematics of static fluids
    1. Pressure in a fluid
    2. Buoyant force
    3. Cases of submersion
  3. Pascal’s law
  4. Fluid dynamics
    1. Types of flow
    2. Viscosity
    3. Coefficient of viscosity and Poiseuille’s law
    4. Viscous drag and Stokes’ law
    5. Terminal velocity
  5. Material strength
    1. Hooke’s law
    2. Stress and strain
    3. Young’s modulus
    4. Expanding and compressing forces
  6. Errors in experimentation
    1. Types of errors
    2. Error propagation
  7. The nature of materials (qualitative discussion)
  8. Measuring strength, hardness etc. (qualitative discussion)

2.2 Mathematics and statistics for AS

2.2.1 Statistics S1 (Download)

  1. Mathematical models
    1. What are mathematical models?
    2. Stages of modelling
  2. Organising data
    1. Types of variables
    2. Frequencies
    3. Variable grouping
  3. Measuring data
    1. Weights and means
    2. Median
    3. Mode
    4. Interpolating the median
  4. Representing data with codes
  5. Dispersions (In progress, please check back for updates)

Have a nice day.

  1. ‘Physics’ used as an umbrella term: some mathematics and statistics classes are included as well.
Also: read essays in the journal