# Applied Maths - I

Below is the syllabus for Applied Maths-I:-

## UNIT-I

Linear Algebra:
The rank of a matrix, elementary transformations, elementary matrices, Gauss Jordon method to find inverse using elementary transformations, the normal form of a matrix, linear dependence and independence of vectors, consistency of the linear system of equations, linear and orthogonal transformations, eigenvalues and eigenvectors, properties of eigenvalues, Cayley – Hamilton theorem and its applications, diagonalization of matrices, quadratic forms.

## UNIT–II

Differential Calculus I:

Successive differentiation, Leibnitz theorem, and applications, Taylor’s and Maclaurin’s series (single variable), Expansion of functions, Asymptotes (Cartesian and Polar Co-ord.), Curve Tracing (for standard curves, Cartesian and Polar).

## UNIT–III

Differential Calculus II:

Concept of limit and continuity of a function of two and three variables, Partial derivatives, variable treated as constant, Euler’s theorem on Homogeneous functions, total derivative, differentiation of an implicit function, chain rue, change of variable, Jacobian, Taylor’s, and Maclaurin’s series (two variables). Maxima and minima of a function of two variables, Lagrange’s method of undetermined multipliers.

## UNIT-IV

Integral Calculus:

Application of single integration to find the volume and surface areas of solid of revolution, Double integrals, Change of the order of integration, Areas enclosed by plane curves, Triple integrals, Volume of solids, Change of variables.

## TEXTBOOKS:

1. E. Kreyszig, Advanced Engineering Mathematics, Wiley India

## REFERENCE BOOKS:

1. G. B. Thomas, R. L. Finney, Calculus and Analytic Geometry, Pearson Education.
2. B. V. Ramana, Engineering Mathematics, Tata McGraw Hill
3. Michael D. Greenberg, Advanced Engineering Mathematics, Pearson Education, Prentice-Hall.