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Title: ORDINARY DIFFERENTIAL EQUATIONS (Code-09050202) | B.Sc. (Hons) Mathematics | 2nd semester

Title: ORDINARY DIFFERENTIAL EQUATIONS  (Code-09050202)

B.Sc. (Hons) Mathematics – 2nd semester

S.No. Topic Domain Hours as per UGC
 

 

 

1

·         Geometrical meaning of DE
·         Exact DE, Integrating factors
·         First order higher degree equations solvable for x,y,p .
·         Lagrange’s equations
·         Clairaut’s equations
·         Equations reducible to Clairaut’s form
·         Singular solutions
 

 

 

Must know

 

 

 

15

 

 

 

 

2

·         Orthogonal trajectories in cartesian coordinates and polar coordinates
·         Self orthogonal family of curves
·         Linear DE with constant coefficients
·         Homogeneous linear ODE
·         Equations reducible to homogeneous
 

 

 

 

Must know

 

 

 

 

15

 

 

 

 

 

3

·         Linear DE of second order: Reduction to normal form
·         Transformation of the equation by changing the dependent variable/independent variable
·         Solution by operators of non-homogeneous linear DE
·         Reduction of order of a DE
·         Method of variations of parameters
·         Method of undetermined coefficients
 

 

 

Must know

 

 

 

 

15

 

 

4

·         Ordinary simultaneous DE
·         Solution of simultaneous DE involving operators x (d/dx) or t (d/dt) etc.
·         Simultaneous equation of the form dx/P=dy/Q=dz/R .
·         Total DE
·         Condition for Pdx+Qdy=Rdz=0 to be exact.
·         General method of solving Pdx+Qdy+Rdz=0 by taking one variable constant.
·         Method of auxiliary equations

·

 

 

Nice to know

 

 

Books Recommended :

  1. E.A. Codington : Introduction to Differential Equations.
  2. S.L.Ross: Differential Equations, John Wiley & Sons
  3. 3.B.Rai & D.P. Chaudhary : Ordinary Differential Equations; Narosa, Publishing House p.vt. Ltd.