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
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
Divergence and Curl and Their Physical Interpretations
Vector Identities
Directional Derivatives
Line, Surface and Volume Integrals
Applications of Green’s, Stoke’s And Gauss Divergence Theorems (Without Proofs)

Share Button
error: Content is protected !!