Advanced · Physics (Calculus-Based)

Advanced Physics Syllabus

Unlock Physics (Calculus-Based) · $39

Block A

General Physics and Classical Mechanics

1. Vector Calculus for Physics (Gradient, Divergence and Curl)

2. Kinematics in Cartesian, Polar and Spherical Coordinates

3. Dynamics in Differential Form (Variable Mass, Drag Forces)

4. Work and Potential Energy as a Gradient in Conservative Force Fields

5. Centre of Mass and Momentum of a System of Particles

6. Rigid-Body Dynamics in 3D and the Moment of Inertia Tensor

7. Euler's Equations for a Rigid Body and Gyroscopes

8. Kinematics in Non-Inertial Reference Frames

9. Fictitious Forces: the Coriolis and Centrifugal Forces

10. Motion in Central Force Fields and the Effective Potential

11. The Two-Body Problem, Reduced Mass and Keplerian Orbits

12. Particle Scattering and the Cross Section (Rutherford)

13. Relativistic Collisions and the Four-Momentum

14. Nonlinear Dynamics and an Introduction to Chaos Theory

15. Continuum Mechanics and Elasticity

Block B

Analytical Mechanics and Thermodynamics

1. Constraints, Generalised Coordinates and Virtual Work

2. D'Alembert's Principle and the Derivation of the Lagrange Equations

3. Lagrange Equations of the Second Kind and Their Applications

4. Noether's Theorem and Conservation Laws

5. The Hamiltonian and Hamilton's Canonical Equations

6. Canonical Transformations and Poisson Brackets

7. The Hamilton-Jacobi Equation

8. Phenomenological Thermodynamics: the First and Second Laws

9. Thermodynamic Cycles and Carnot's Theorem

10. Thermodynamic Potentials (Internal Energy, Enthalpy, Helmholtz and Gibbs Energy)

11. Maxwell Relations in Thermodynamics

12. Phase Transitions and the Clausius-Clapeyron Equation

13. Introduction to Statistical Physics: Microstates and Macrostates

14. The Microcanonical and Canonical Ensembles (the Boltzmann Distribution)

15. Quantum Statistics (Bose-Einstein and Fermi-Dirac)

Block C

Electromagnetism and Electrodynamics

1. Rigorous Electrostatics: Potential and the Multipole Expansion

2. The Laplace and Poisson Equations (Method of Images, Separation of Variables)

3. Dielectrics, Polarisation and the Electric Displacement Field

4. Steady Currents and the Continuity Equation

5. Magnetostatics, the Biot-Savart Law and the Vector Potential

6. Magnetic Media, Magnetisation and the Magnetic Field Strength

7. Electrodynamics, the Displacement Current and the Full Maxwell Equations

8. Poynting's Theorem and the Momentum of the Electromagnetic Field

9. The Electromagnetic Wave Equation, Plane Waves and Polarisation

10. Reflection and Refraction of Electromagnetic Waves (the Fresnel Equations)

11. Waveguides and Resonant Cavities

12. Retarded Lienard-Wiechert Potentials

13. Radiation from Electric and Magnetic Dipoles

14. Radiation from Point Charges (the Larmor Formula)

15. The Relativistic Formulation of Electrodynamics (the Field Tensor)

Block D

Quantum Mechanics and Modern Physics

1. The Crisis of Classical Physics and the Origins of Quantum Mechanics

2. Postulates of Quantum Mechanics, Wave Functions and the Born Interpretation

3. The Schrodinger Equation (Time-Dependent and Time-Independent)

4. Mathematical Formalism: Hilbert Space and Hermitian Operators

5. Commutation Relations and the Heisenberg Uncertainty Principle

6. The One-Dimensional Potential Well and Quantum Tunnelling

7. The Harmonic Oscillator in the Algebraic Approach (Ladder Operators)

8. Angular Momentum Operators and Spherical Harmonics

9. The Hydrogen Atom: Full Solution of the Schrodinger Equation

10. Spin and the Pauli Matrices

11. Addition of Angular Momenta and Clebsch-Gordan Coefficients

12. Time-Independent and Time-Dependent Perturbation Theory

13. Identical Particles: Fermions, Bosons and the Pauli Exclusion Principle

14. Introduction to Solid State Physics: the Band Theory of Conduction

15. Introduction to the Standard Model and Elementary Particles