Vectors and Elementary linear algebra – Linear vector space and matrices – Determinants, trace and special matrices – Linear first order differential equations – First and second order linear differential equations – Second Order DEs and Introduction to power series – Introduction to harmonic oscillators – Hermite polynomials – Quantum mechanics of harmonic oscillators – Coordinate transformations from cartesian to spherical coordinates – Quantum mechanics of hydrogen atom – Particle in a One dimensional box – Particle in a two dimensional box – Particle on a ring

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