Mathematical Physics MSc 1st Sem | Differential Equations | MSc Physics Full Course

Mathematical Physics Msc 1st Sem - Differential Equations - MSc Physics Full Course syllabus given below.

Unit-I: Differential Equations
Basic Ideas – Ordinary Differential Equations – Partial Differential Equations – Heat equation – Wave equation – Laplace equation – Boundary value problems – Method of Separation of Variables – Linear ordinary differential equations with constant coefficients and the Euler equation – Frobenius method of the series solution – Strum-Liouvllie problem – Orthogonal
eigenfunction expansions.

Unit-II: Special Functions
Beta, Gamma, Delta and Error functions – Bessel, Hermite, Legendre, Associated Legendre and Laguerre functions – Generating functions – Recurrence relations – Applications in physics.

Unit-III: Complex Variables
Introduction – Elements of analytic function theory – Cauchy-Riemann conditions – Singularities, poles and essential singularities – Cauchy’s integral theorem – Cauchy integral formula – Taylor, Maclaurin and Laurent series of complex functions – Residue theorem - Applications of Residue theorem.

Unit-IV: Fourier Transform
Introduction to Fourier analysis – Half range Fourier series – Harmonic analysis and applications – Forced oscillations – Finite and infinite Fourier transforms – Fourier sine and cosine transforms – Complex Fourier transforms – Fourier expansion and inversion formulas – Convolution theorem – Applications to solutions of partial differential equations.

Unit-V: Laplace Transforms
Laplace transforms – Inverse transforms – Linearity and Shifting theorems – Laplace transform of derivative of a function – Laplace transform of integral of a function – Unit step function – t-shifting– Short impulses – Dirac-delta function – Convolution – Integral equations – Application to solve differential equations.

Textbooks [1, 2]
Supplementary Readings [3, 4]

Recommended Books
[1] R K Jain and S R K Iyengar. Advanced Engineering Mathematics, 4th Edition. Narosa, 2014.
[2] K F Riley, P Hobson, and S J Bence. Mathematical Methods for Physics and Engineering. Cambridge University Press, 2006.
[3] Alan Jeffrey. Advanced Engineering Mathematics. Academic Press (Indian reprint), 2002.
[4] G B Arfken, H J Weber, and F E Harris. Mathematical Methods for Physicists: A Comprehensive Guide. Elsevier, 2012.