## Applied Maths - II

Below is the syllabus for Applied Maths – II:-

## UNIT-I

Theory of Equations: Introduction, formation of equations, Relation between roots and coefficient, Reciprocal Equations, Transformation of equations.
Integral Calculus: Beta and Gamma functions, Evaluation of integrals by Leibnitz’s rule (Differentiation under the Integral sign).

## UNIT–II

Laplace Transforms and its applications: Laplace transforms: Basic concept, Existence conditions, transform of elementary functions, Properties of Laplace transforms, transform of derivatives and integrals, multiplication and division property, Evaluation of integrals by Laplace transforms Dirac’s Delta function, Application to linear differential equations and simultaneous linear differential equations with constant coefficients.

## UNIT–III

Ordinary Differential Equations and its applications: Exact differential equations, Equations reducible to exact differential equations, Applications of differential equations of first order and first degree to simple electric circuits, Newton’s law of cooling, heat flow and orthogonal trajectories.
Linear differential equations of second and higher order, complete solution, complementary function and particular integral, method of variation of parameters and method of undetermined coefficient to find the particular integral, Cauchy’s and Legendre’s linear equations, simultaneous linear equations with constant coefficients.

## UNIT-IV

Vector Calculus: Differentiation of Vectors, Scalar and vector point functions, Gradient of a scalar field and directional derivative, divergence and Curl of a vector field and their physical interpretation, line integrals, surface integral, volume integral, Green’s theorem in the plane, Stoke’s Theorem, Gauss Divergence Theorem (without proof) and their applications.

## REFERENCE BOOKS:

1. E. Kreyszig, Advance Engineering Mathematics, Wiley India.
2. G. B. Thomas, R. L. Finney, Calculus and Analytic Geometry, Pearson Education.
3. B. V. Ramana, Engineering Mathematics, Tata McGraw Hill
4. Michael  D. Greenberg, Advanced Engineering Mathematics, Pearson Education, Prentice Hall.
Below is the link to download Applied Maths – II notes.