Conics through four fixed points or touching four fixed lines.
The analysis of vector fields.
Limits and bounds of functions of a real variable.
Mean-value theorems and Taylor's theorem.
The Jacobian of \(n\) functions of \(n\) independent variables.
Partial differential equations.
Spherical harmonics or Fourier series.
Develop the formulae expressing the acceleration of a point in terms of its coordinates referred to moving rectangular axes. Use these formulae to find the equations of motion of a non-viscous fluid referred to cylindrical coordinates.
The application of conjugate functions to the solution of problems in electrostatics or current electricity.
State Kepler's three laws concerning the orbits of planets and shew how they are related to the theory of gravitation.