Mathematical Principles in Physics 1

2020–21–A

Course topics

  1. Introduction to scalars and vectors: operations with scalars and vectors, scalar product, vector product, vector equations, indices, Einstein summation convention, kronecker delta, Levi-Civita symbol.
  2. Introduction to functions: types, continuity, limits, derivatives, integrals, integration methods, taylor series, remainder.
  3. Functions with scalar input and vector output: curves, tangent, normal, velocity, acceleration, curvature, torsion. Frenet-Serret basis and kinematics.
  4. Functions with vector input and scalar output: extrema, contours, gradient, directional derivative, tangent space.
  5. Multiple integrals
  6. Functions with vector input and vector output: conservative fields, rotational fields, divergence, curl, line integral, surface integral, Stokes and Gauss
  7. Differential equations: damped harmonic oscillator with driving
  8. Rotations: scalars, vectors, tensors
  9. Curvilinear coordinates

University course catalogue: 203.1.1141