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
*Polar coordinates

Unit – 2: Differential Calculus – II

Taylor’s Theorems
Maclaurin’s Theorems
Expansion of function of several variables
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
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
and their physical interpretations
Vector identities
Directional derivatives
Line,Surface and Volume integrals
Applications of Green’s, Stoke’s and Gauss divergence theorems

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