Syllabus
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Course Code: BMAT20 2 Course Name: Differential Equations |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Basic concepts and genesis of ordinary differential equations, Order and degree of a differential equation, Differential equations of first order and first degree, Equations in which variables are separable, Homogeneous equations, equations reducible to homogeneous, Linear differential equations and equations reducible to linear form. Exact differential equations, Integrating factor. First order higher degree equations solvable for x, y and p. Clairaut’s form and singular solutions. Orthogonal trajectories of one-parameter families of curves in a plane. | |
| 2 | Solutions of homogeneous linear ordinary differential equations of second order with constant coefficients, linear non-homogeneous differential equations. Linear differential equation of second order with variable coefficients. Method of reduction of order, method of undetermined coefficients, method of variation of parameters. Cauchy-Euler equation. | |
| 3 | Solution of simultaneous differential equations, total differential equations. Genesis of Partial differential equations (PDE), Concept of linear and non-linear PDEs. Complete solution, general solution and singular solution of a PDE. Linear PDE of first order. Lagrange’s method for PDEs of the form: P(x,y,z) p + Q(x,y,z) q = R(x,y,z), where p=∂z/∂x and q=∂z/∂y. | |
| 4 | Second Order Partial Differential Equations with Constant Coefficients. Integral surfaces passing through a given curve. Surfaces orthogonal to a given system of surfaces. Compatible systems of first order equations. Charpit’s method, Special types of first order PDEs, Jacobi’s method. Solutions of second order linear partial differential equations (homogeneous and non-homogeneous) with constant coefficients. Solution of PDEs with variable coefficients reducible to equations with constant coefficients. | |
