# Teaching

## M303-Differential Equations

Semester:
Aims and objectives:

To obtain a basic understanding of Ordinary Differential Equations. An introduction to Partial Differential Equations will be given if time permits.

Syllabus:

Classifications of Differential Equations: origin and applications, family of curves, isoclines. First order equations: separation of variable, exactequation, integrating factor, Bernoulli equation, separable equation, homogeneous equations, orthogonal trajectories, Picard’s existence and uniqueness theorems. Second order equations: variation of parameter, annihilator methods. Series solution: power series solutions about regular and singular points. Method of Frobenius, Bessel’s equation and Legendre equations. Wronskian determinant, Phase portrait analysis for 2nd order system, comparison and maximum principles for 2nd order equations. Linear system: general properties, fundamental matrix solution, constant coefficient system, asymptotic behavior, exact and adjoint equation, oscillatory equations, Green’s function. Sturm-Liouville theory. Partial Differential Equations: Classification of PDE, method of separation of variables.

Mode of evaluation:
Absolute

To Be Announced

School of Mathematical Sciences

NISERPO- Bhimpur-PadanpurVia- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

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