Unit 3: Laplace Transform
Laplace transforms of standard function, periodic
functions, Unit step function, Transforms of
derivatives and integrals. Differentiation and
integration of transforms, Linearity property,
Inverse Laplace transform, Shifting theorems,
Convolution. Application to solve differential
and integral equations ( initial value problem).,,,,,,,,Unit 6 : Vectors:
Vector algebra, product of vectors, vector
differentiation, vector differential operator, gradient,
directional derivatives, divergence, curl, line
integral, double integral, green’s theorem.,,,,,,,,Unit 1: Ordinary Differential Equation
Differential equation of first order. Linear
differential equation of second order (homogeneous
and nonhomogeneous case). Cauchy, Euler’s
equation, Application of first order differential
equations (mixture problem, Newton’s law of
cooling, orthogonal trajectory).,,,,,,,,,,,,,riemann integration CALCULUS of functions in one variable,,,,,,,,,,,taylor and mclaurin seriea
Unit 3: Laplace Transform
Laplace transforms of standard function, periodic
functions, Unit step function, Transforms of
derivatives and integrals. Differentiation and
integration of transforms, Linearity property,
Inverse Laplace transform, Shifting theorems,
Convolution. Application to solve differential
and integral equations ( initial value problem).,,,,,,,,Unit 6 : Vectors:
Vector algebra, product of vectors, vector
differentiation, vector differential operator, gradient,
directional derivatives, divergence, curl, line
integral, double integral, green’s theorem.,,,,,,,,Unit 1: Ordinary Differential Equation
Differential equation of first order. Linear
differential equation of second order (homogeneous
and nonhomogeneous case). Cauchy, Euler’s
equation, Application of first order differential
equations (mixture problem, Newton’s law of
cooling, orthogonal trajectory).,,,,,,,,,,,,,riemann integration CALCULUS of functions in one variable,,,,,,,,,,,taylor and mclaurin seriea
