This is an online topic wise solutions & notes on Engineering Mathematics for BTech First Year students.

##### Unit – 1: Differential Calculus – I

Leibnitz’s theorem

Partial derivatives

Euler’s theorem for homogeneous functions

Total derivatives

Change of variables

Curve tracing

*Cartesian

*Polar coordinates

##### Unit – 2: Differential Calculus – II

Taylor’s Theorems

Maclaurin’s Theorems

Expansion of function of several variables

Jacobian

Approximation of errors

Extrema of functions of several variables

Lagrange’s method of multipliers ( Simple applications)

##### Unit – 3: Linear Algebra

Inverse of a matrix by elementary transformations

Rank of a matrix ( Echelon & Normal form)

Linear dependence

Consistency of linear system of equations and their solution

Characteristic equation

Eigen values

Eigen vectors

Cayley-Hamilton Theorem

A brief introduction to Vector Spaces

Subspaces

Rank & Nullity

Linear transformations

##### Unit – 4: Multiple Integrals

Double and triple integrals

Change of order of integration

Change of variables

Application of integration to lengths

Volumes and Surface areas – Cartesian and Polar coordinates

Beta functions

Gamma functions

Dirichlet’s integral and applications

##### Unit – 5: Vector Calculus

Point function

Gradient

Divergence

Curl

and their physical interpretations

Vector identities

Directional derivatives

Line,Surface and Volume integrals

Applications of Green’s, Stoke’s and Gauss divergence theorems