


Mathematical Methods II, PHAS0009
 Course Outline and Lecture Notes (Table of Contents)
Chapter1:
Differential Vector Operators 
 Scalar and Vector Fields
 Partial Derivatives of Fields
 Directional Derivative and Gradient
 The Total Differential of Fields
 Divergence and Curl of Vector Fields
 Product Rules
 2nd Order Variations of Fields, Laplace Operator

Chapter2:
Multidimensional Integration

 Line Integrals
 Area Integrals
 Polar Coordinates
 Volume Integrals
 Cylindrical and Spherical Coordinates
 Surface Integrals
 Gauss's Divergence Theorem
 Stokes's Theorem

Chapter3:
Ordinary Differential
Equations (ODEs)

 Examples of ODEs in Physics
 Fixing the Arbitrary Constants
 Separable FirstOrder ODEs
 Linear FirstOrder ODEs
 Perfect Differential Method
 SecondOrder Linear ODEs with Constant Coefficients

Chapter4:
Linear Alegbra

 Formal Definition of Complex Vector Spaces
 Linear Dependence and Independence of Vectors
 Matrices and linear transformations
 Matrix addition and multiplication
 Determinants
 Trace of a matrix
 Properties of matrices (symmetric, hermitian, unitary)
 Inverse of a matrix
 Solving coupled linear equations
 Eigenvalues and Eigenvectors
 Matrix Diagonalisation
 Quadratic Forms

 Books recommended as core/background reading
 Mathematical Methods in the Physical Sciences, Mary L. Boas, John Wiley & Sons
 Mathematical Methods for Physics and Engineering: A Comprehensive Guide,
K.F. Riley, M.P. Hobson, S.J. Bence, Cambridge University Press



