Sample lecture schedule
(based on 25 lectures each of duration 75 minutes)
- Lecture 1:
Probability 1 –
Probability Distributions
- Lecture 2:
Probability 2 –
Generating Functions and the Central Limit Theorem
- Lecture 3:
Probability 3 –
Stochastic Processes
- Lecture 4:
Complex Variables 1 –
Analytic Functions
- Lecture 5:
Complex Variables 2 –
Complex Integrals
- Lecture 6:
Complex Variables 3 –
Residues and Contour Integration
- Lecture 7:
Complex Variables 4 –
Contour Integration
- Lecture 8:
Asymptotic Expansions
- Lecture 9:
Group Theory 1 –
Definitions, examples, applications
- Lecture 10:
Group Theory 2 –
Representations and Properties
- Lecture 11:
Group Theory 3 –
Characters, Product Reps and Clebsch-Gordan coefficients
- Lecture 12:
Group Theory 4 –
Irreducible Representations and Irreducible Tensors, Wigner-Eckart
- Lecture 13:
Fourier Transforms and
Delta Functions
- Lecture 14:
Convolution, Correlation, and Power Spectrum Density
- Lecture 15:
ODEs 1 – Exact Solutions
- Lecture 16:
ODEs 2 – Series Solutions – Legendre polynomials and functions
- Lecture 17:
ODEs 3 – Series Solutions – Frobenius method and Bessel functions
- Lecture 18:
ODEs 4 – Qualitative Methods
- Lecture 19:
ODEs 5 – Qualitative Methods and
Numerical Methods
- Lecture 20:
Green's Functions (1D)
- Lecture 21:
Eigenfunctions and
Orthogonal Functions
- Lecture 22:
Sturm-Liouville Theory
- Lecture 23:
PDEs 1 – Separation of Variables
and Cylindrical Coordinates
(Bessel)
- Lecture 24:
PDE 2 – Spherical Coordinates
(Legendre and Spherical Harmonics)
- Lecture 25:
PDE 3–
Green's Functions and Boundary Problems in 3D
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