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Title: ODE (Code-09050202)

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

S.No. Content of the topics Learning      Objectives Teaching Guidelines Methodology Time (Hours)
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

Student will be able to study  limit, Continuity & differentiability of function Lecture should be effective so that student will be able to grasp the topics easily Assignment/  seminar/       Class tests/  Presentation 14
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

Student will be able to study of Asymptotes, Curvature and Points of infixion Lecture should be effective so that student will be able to grasp the topics easily Assignment/  seminar/       Class tests/  Presentation 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

 

 

Student will be able to trace the curves & study Reduction formulae , Rectification Lecture should be effective so that student will be able to grasp the topics easily Assignment/  seminar/       Class tests/  Presentation 8
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

Student will be able to find the area and Volumes  of curves Lecture should be effective so that student will be able to grasp the topics easily Assignment/  seminar/       Class tests/  Presentation 8

 

Books Recommended:

  1. D.A. Murray : Introductory Course in Differential Equations. Orient Longaman (India) . 1967
  2. A.R.Forsyth : A Treatise on Differential Equations, Machmillan and Co. Ltd. London
  3. E.A. Codington : Introduction to Differential Equations.
  4. S.L.Ross: Differential Equations, John Wiley & Sons
  5. B.Rai & D.P. Chaudhary : Ordinary Differential Equations; Narosa, Publishing House Pvt. Ltd
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