Mathematical Methods MT 2009:

The course comprises of 20 lectures: four per week in weeks 1-4 and two per week in weeks 5-6.The course is divided into five parts, each of which is supported by a problem set. A collection paper for week 0 of HT 2010 will be available to tutors.

Recommended Books Some Lecture Notes
Small Format Lecture Notes

Part I:   Linear Algebra I  [Recommended Reading] [Problem Set I]
Euclidean Linear Vector Spaces; Real vs Complex Vector Spaces; Dual Vectors and Scalar Product; Linear Independence; Dimension; Bases; Different Bases and Orthogonality;

Part II:  Linear Algebra II  [Recommended Reading]  [Problem Set II]
Linear Operators;Matrices; Commutator; Functions of Operators; Matrix Representations of Linear Operators; Operations on Square Matrices; Change of Basis; Unitary and OrthogonalTransformations; Eigenvalues and Eigenvectors; Hermitian Matrices; Diagonalization of Hermitian Matrices; Jordan Normal Form; Simultaneous Diagonalization of Hermitian Matrices; Tensor Product of Vector Spaces;

Part III:  Fourier Methods and Generalized Functions
  [Recommended Reading]  [Problem Set III]
Fourier Series; Fourier Transforms as Limit of Fourier Series; Inverse Transform; Dirac Delta Function; Parseval's Theorem; Convolution;

Part IV: Ordinary Differential Equations
 [Recommended Reading]  [Problem Set IV]
Difference Equations; Differential Equations as limits of Matrix Equations; Boundary Conditions and
Eigenvalues; Green's Functions; Second order ODEs of Sturm-Liouville Type; Orthogonality of
Eigenfunctions; Legendre's Equation; Hermite's Equation; Eigenfunction Expansions;

Part V: Partial Differential Equations
  [Recommended Reading]  [Problem Set V]
Examples; Initial Conditions; Boundary Conditions; Separation of Variables; Use of Cartesian, Spherical Polar and Cylinder Coordinates;