Syllabus Ordinary Differential Equations and Vector Calculus - (MA201BS) UNIT - I : First Order ODE Exact differential equations, Equations reducible to exact differential equations, linear and Bernoulli’s equations, Orthogonal Trajectories (only in Cartesian Coordinates). Applications : Newton’s law of cooling, Law of natural growth and decay. (Chapter - 1) UNIT - II : Ordinary Differential Equations of Higher Order Second order linear differential equations with constant coefficients : Non-Homogeneous terms of the type eax, sin ax, cos ax, polynomials in x, eax V(x) and x V(x), method of variation of parameters, Equations reducible to linear ODE with constant coefficients : Legendre’s equation, Cauchy-Euler equation. Applications : Electric Circuits. (Chapter - 2) UNIT - III : Laplace transforms Laplace Transforms : Laplace Transform of standard functions, First shifting theorem, Second shifting theorem, Unit step function, Dirac delta function, Laplace transforms of functions when they are multiplied and divided by ‘t’, Laplace transforms of derivatives and integrals of function, Evaluation of integrals by Laplace transforms, Laplace transform of periodic functions, Inverse Laplace transform by different methods, convolution theorem (without proof). Applications : solving Initial value problems by Laplace Transform method. (Chapter - 3) UNIT - IV : Vector Differentiation Vector point functions and scalar point functions, Gradient, Divergence and Curl, Directional derivatives, Tangent plane and normal line, Vector Identities, Scalar potential functions, Solenoidal and Irrotational vectors. (Chapter - 4) UNIT - V : Vector Integration Line, Surface and Volume Integrals, Theorems of Green, Gauss and Stokes (without proofs) and their applications. (Chapter - 5)
