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### Title-Ordinary Differential Equations (Code-09010202)

 S.N Unit Content of the topics Learning objects Teaching Guidelines Methodology Time (Hrs) 1 one 1.       Geometrical meaning of DE, 2.       Exact DE, Integrating factors, 3.       First order higher degree equations solvable for x,y,p, 4.       Lagrange’s equations, 5.       Clairaut’s equations, 6.       Equations reducible to Clairaut’s form, 7.       Singular solutions Students will be able to   1.       Geometrical meaning of DE. 2.       First order higher degree equations solvable for x,y,p. 3.       Lagrange’s equations 4.       Clairaut’s equations Lecture should be effective so that student can grasp the topics easily. 1. Lecture. 2.  Seminar. 3. Discussion/Interaction with Students. 4. Assignment. 5.  Discussion on Assignment. 6. Evaluation of Assignment. 15 2 Two 1.      Orthogonal trajectories in cartesian coordinates and polar coordinates, 2.      Self orthogonal family of curves, 3.      Linear DE with constant coefficients, 4.      Homogeneous linear ODE, 5.      Equations reducible to homogeneous, 6.      Linear DE of second order: Reduction to normal form, 7.      Transformation of the equation by changing the dependent variable/independent variable, 8.      Solution by operators of non-homogeneous linear DE Students will be able to 1.   Orthogonal trajectories 2.   Linear DE with constant coefficients. 3.   Homogeneous linear ODE. Transformation of the equation 4.   Method of variations of parameters Lecture should be effective so that student can grasp the topics easily. 1.    Lecture. 2.     Seminar. 3.    Discussion/Interaction with Students. 4.    Assignment. 5.    Discussion on Assignment. 6.    Evaluation of Assignment 15 3 Three 1.      Ordinary simultaneous DE, 2.      Solution of simultaneous DE involving operators x (d/dx) or t (d/dt) etc., 3.      Simultaneous equation of the form dx/P=dy/Q=dz/R , 4.      Total DE, 5.      Condition for Pdx+Qdy=Rdz=0 to be exact, 6.      General method of solving Pdx+Qdy+Rdz=0 by taking one variable constant, 7.      Method of auxiliary equations To make students familiar with Ordinary simultaneous DE, Solution of simultaneous DE involving operators x (d/dx) or t (d/dt) etc. General method of solving Pdx+Qdy+Rdz=0 by taking one variable constant. Lecture should be effective so that student can grasp the topics easily. 1.    Lecture. 2.    Seminar. 3.    Discussion/Interaction with Students. 4.    Assignment. 5.    Discussion on Assignment. 6.    Evaluation of Assignment 15