# Engineering Mathematics for BTech First Year

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

Point function