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|
· 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|
- 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