IDC205: Differential equations for scientists

Course Outline

• 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 applications.

Recommended Reading

• Earl A. Coddington, An Introduction to Ordinary Differential Equations, Dover Publications (1989).
• Ravi P. Agarwal and Donald 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).