Advanced Mathematical Physics

Advanced Mathematical Physics MTH

MTH2132 Intermediate Mathematical Physics

3 hours One requisite

1 Curvilinear coordinates / Orthogonal coordinates in r3 / Differential vector operators / Special coordinate systems / Circular cylinder coordinates / Spherical polar coordinates

2 Group theory / Introduction to group theory / Generators of continuous groups / Homogeneous lorentz group / Lorentz covariance of maxwell’s equations / Discrete groups / Differential forms

3 Tensor analysis / Cartesian tensors / Tensor notation and operations / Inertia tensor / Kronecker delta and levi-civita symbol / Pseudovectors and pseudotensors / More about applications / Curvilinear coordinates / Vector operators in orthogonal curvilinear coordinates / Non-cartesian tensors

4 Complex variables / Functions of a complex variable / The cauchy–riemann relations / Power series in a complex variable / Some elementary functions / Multivalued functions and branch cuts / Singularities and zeros of complex functions / Conformal transformations / Complex integrals / Cauchy’s theorem / Cauchy’s integral formula / Taylor and laurent series / Residue theorem / Definite integrals using contour integration / Applications of complex variables / Complex potentials / Applications of conformal transformations / Location of zeros / Summation of series / Inverse laplace transform / Stokes’ equation and airy integrals / Wkb methods

5 Numerical methods / Interpolation / Curve fitting / Examples

1.1 Mapped to: K1

Identify tensors to generalize scalars, vectors and matrices to higher dimensions.

Teaching Strategy Lectures