IDC205 Differential Equations for Scientists
IDC205: Differential equations for scientists
- [Cr:2, Lc:2, Tt:0, Lb:0]
- Meaning of a differential equation and its solution, examples, families of curves, orthogonal trajectories.
- First order equations: Homogeneous, exact, linear, Bernoulli, Riccati and Clairaut equations, equations reducible to first order equations.
- Second and higher order linear equations, linear equations with constant coefficients, general solution of homogeneous equations, operator method for finding a particular solution, vibra- tions in mechanical and electrical systems. Power series method: Legendre, Hermite, Bessel and hypergeometric equation.
- Special functions: Legendre, Hermite and Chebychev polynomials, Bessel functions and appli- cations.
- Earl A. Coddington, An Introduction to Ordinary Differential Equations, Dover Publications (1989).
- Ravi P. Agarwal and Donal O’Regan, Ordinary and Partial Differential Equations, Springer (2008).
- Shepley L. Ross, Differential Equations, Wiley (1984).
- George F. Simmons, Differential Equations with Applications and Historical Notes, Tata McGraw-Hill Publishing Company (1978).
IDC201 Astronomy and Astrophysics
IDC201: Astronomy and astrophysics
- [Cr:2, Lc:2, Tt:0, Lb:0]
- Tools: The EM spectrum, Telescopes. Resolution and sensitivity of various direct measurements (time, angle, flux at various wavelengths, velocities). Important spectral lines. Inferring distances and masses, abundances, and energetics.
- Objects: Solar system, stars, clusters. The Milky Way.Interstellar matter (cold clouds, molecular clouds, HII regions, supernova remnants). Groups of galaxies. Large scale structure. CMBR.
- Physical processes and models: Newtonian gravity and binary orbits. Estimates of pressures and temperatures. Physical conditions in planets, the sun and stars. Mass-radius relation for cold objects. Basic dynamics of star clusters and galaxies. Newtonian cosmology. A physical introduction to relativistic gravity and its applications to the universe and compact objects.
- Microscopic radiation processes for atoms, molecules and free electrons. Optically thick and thin regimes. Formation of line / continuum spectra in various objects (stellar atmospheres, interstellar clouds, high energy electrons).
- Nuclear and particle processes: Stellar nucleosynthesis and energy generation. Cosmic ray processes and particle acceleration. Early universe and light element production. Other proposed particle processes (baryogenesis, dark matter candidates).
- F.H.Shu, Physical Universe: An Introduction to Astronomy, University Science Books (1982).
- K.D.Abhyankar, Astrophysics: Stars and Galaxies, Tata McGraw Hill (2002).
- S.A. Gregory and M.Zeilik, Introductory Astronomy and Astrophysics, 04th edition, Brooks Cole (1997).
- A.Unsold, B.Baschek and W.D.Brewer, The New Cosmos: An Introduction to Astronomy and Astrophysics, 05th edition, Springer (2005).
- T.P.Snow, The dynamic universe: An introduction to Astronomy, West publishing company (1991).