Page 249 - FINAL_HANDBOOK_20252026
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Faculty of Science Handbook, Academic Session 2025/2026
Hamiltonian, Hamilton’s equation of Continuous 40%
motion, phase space, Liouville’s theorem, Assessment:
Poisson bracket ); Special theory of
relativity (Einstein’s postulates, Lorentz SIF2028 MATHEMATICAL METHOD III (4
transformation, length contraction, time CREDITS)
dilation, covariant formulation, four
vectors, relativistic dynamics, lagrange and Fourier Series and Transformation Series:
Hamiltonian formulation for relativistic Periodic functions, Fourier series, average
mechanics), Capita Selecta. value of a function, Fourier coefficient,
Dirichlet condition, complex form of
Assessment Method: Fourier Series, general interval, even and
Summative 60% odd functions, Parseval theorem. Fourier
Assessment: transformation and Parserval Theorem.
Continuous 40% Laplace Transforms, Solution of differential
Assessment: equations by Laplace transforms, Dirac
Delta Function, Laplace transform of a
SIF2027 OPTICS (3 CREDITS) delta function; Fourier transform of a delta
function
Nature of light: brief history; Wave-particle Special Functions: Factorial functions,
duality; The electromagnetic spectrum; Gamma functions, Beta functions,
Radiometry & Photometry; Black body relationship between Beta and Gamma
radiation; Optical radiation sources. functions, error functions, asymptotic
Matrix methods in paraxial optics; ABCD series, Stirling formula and elliptical
matrix; Reflection in plane mirrors and integrals.
refraction through plane surfaces; Series Solution for Differential Equations:
Reflection and refraction at spherical Legendre equations, Leibnitz rule,
surface; thin lenses, cylindrical lenses, thick Rodriguez formula, generating functions
lenses; prisms. for Legendre polynomial, orthogonal
Wave equation; Harmonic waveforms: functions, orthogonalization and
plane, spherical, and cylindrical; normalization of Legendre polynomials,
Electromagnetic waves; superposition; Legendre series, Associate Legendre
two-beam interference & two slit (Young) function, Frobenius method, Bessel
interference; Interference in dielectric equation, second solution of Bessel
films, multiple-beam interference; Optical equation, recurrence relationship, general
interferometry: Michelson interferometer, differential equation with Bessel function
Fabry-Perot Interferometer. as a solution, orthogonalization of Bessel
Huygen-Fresnel principle; Fraunhofer function, Hermite function, Laguerre
diffraction: diffraction from single slit, function, step operator.
multiple slits-diffraction grating. Partial Differential Equation: Separation of
Polarized light; Polarization by selective variables method applied to partial
absorption, reflection, scattering, differential equation; applications to
birefringence & dichroism; Jones vectors Laplace equation, steady state
and matrices; Fresnel equations. Fresnel temperature in a square plate, Schrödinger
diffraction & Fresnel lens equation, heat and diffusion equation.
Wave equation, vibrating string, steady
Assessment Method: state temperature in a cylinder, steady
Summative 60% state temperature in a sphere, Poisson
Assessment: equation.
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