Title: ODE (Code09050202)
B.Sc. Mathematics (Hons) – 2^{nd} 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 nonhomogeneous 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:
 D.A. Murray : Introductory Course in Differential Equations. Orient Longaman (India) . 1967
 A.R.Forsyth : A Treatise on Differential Equations, Machmillan and Co. Ltd. London
 E.A. Codington : Introduction to Differential Equations.
 S.L.Ross: Differential Equations, John Wiley & Sons
 B.Rai & D.P. Chaudhary : Ordinary Differential Equations; Narosa, Publishing House Pvt. Ltd