Mathematical Physics

The mathematical toolkit a working physicist actually uses.

Syllabus

  1. Vectors, Tensors & Linear Algebra

    1. Vector Calculus & Index Notation
    2. Curvilinear Coordinates & the Field Operators
    3. Linear Algebra for Physics
    4. Tensors & Transformations

  2. Complex Analysis

    1. Analytic Functions & the Cauchy-Riemann Equations
    2. Contour Integration & Cauchy's Theorem
    3. The Residue Theorem & Real Integrals

  3. Differential Equations & Special Functions

    1. ODEs & Series Solutions
    2. Sturm-Liouville Theory & Orthogonal Functions
    3. The Special Functions

  4. Transforms, PDEs & Green's Functions

    1. The Calculus of Variations
    2. Fourier Series & the Fourier Transform
    3. PDEs & Separation of Variables
    4. Green's Functions