# Engg Mathematics -1

Unit – 1: Differential Calculus – I

Leibnitz’s Theorem
Partial Derivatives
Euler’s Theorem for Homogeneous Functions
Total Derivatives
Change of Variables
Curve Tracing: Cartesian and Polar Coordinates

Unit – 2: Differential Calculus – II

Taylor’s And McLaurin’s Theorems
Expansion of Function of Several Variables
Jacobean
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 and 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 and Gamma Functions
Dirichlet’s Integral and Applications

Unit – 5: Vector Calculus

Point Function