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2B24 Atomic and Molecular Physics (UCL lecture notes)

**Mathematical Methods I** (substitute Lecture Notes)

Overview

Introductory material

Differentiation

Integration

Series

Fourier Analysis

Complex Numbers

Sample problems and solutions

**Mathematical Methods II** (substitute Lecture Notes)

Complex Numbers

Coordinates

Hyperbolic Functions

Differential Equations

Fourier Analysis 2

Vectors

Vector Fields

Maxwell's Equations

Line Integrals

Multiple Integrals

Matrices

Matrix Determinants

Eigenvalues and Eigenvectors

Eigenvalues

Ch 6 only for more on Eigenvalues and Eigenvectors

MT3LectureNotes (more on Matrices, vectors and operators)

Extra book:

Elementary Linear Algebra - K. Matthews

2112 (2B12) **Nebulae to Stars** (Astrophysics)

Interstellar Clouds:

Physical conditions. Heating and cooling processes. Line broadening (natural, thermal, turbulent).

Line transfer, curve of growth, abundances.

Photoionized Nebulae:

Physical conditions. Heating and cooling processes; collisional excitation of emission lines. Ionization equilibrium. Absorption & emission coefficients, and the source function. Free-free radio continuum, and radiative transfer.

Stellar Atmospheres:

Radiation transport. Moments of the radiation field. Saha-Boltzmann equation. Local Thermodynamic
Equilibrium.

Stellar Interiors:

Equation of state. Hydrostatic equilibrium. Radiation pressure, Eddington limit. Virial theorem,
stellar timescales.

Nuclear Processes:

PP chain. CNO cycle. 3- processes and later stages of burning. Neutron capture, *r* and *s* processes.

Supernovae.

Suggested Reading

The Physics of the Interstellar Medium (J.E. Dyson & D.A. Williams, IoP Publishing)

Astrophysics I: Stars (R. Bowers & T. Deeming, Jones & Bartlett)

2246 **Mathematical Methods III**

Part 1 - Preliminaries

Part 2

Part 3

Part 4

Part 5

Part 6

Part 7

Harmonic Oscillator - (HO)

**Extra books**:

Statistical Physics Problem book - Y. Galperin

Mathematical Methods of Engineering Analysis

Some extra material on Tensor Calculus: (Tensors are not covered in the main maths modules above)

Introduction To Tensor Calulus - Dullemond & Peeters

Introduction to Tensor Calculus for GR - E. Birtschinger (MIT)

Introduction to Tensor Calculus - A. Smirnov

UCL Physics BSc course modules

QMUL Physics and Astrophysics MSc course outlines

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