Course Syllabus
This syllabus outlines the modules of Engineering Mathematics – I.
- Elementary transformations and Rank of Matrix
- Rank by using Echelon and Normal form of Matrices
- Linear dependence and independence of vectors in $R^n$ space
- Consistency of System of Linear Equations
- Eigenvalues and Eigenvectors, Cayley-Hamilton Theorem
- Similarity of Matrices and Diagonalization of Square Matrices
- Quadratic Form, Canonical Form of Matrices
- Higher order derivatives; Successive differentiation and Leibnitz’s Theorem
- Mean Value Theorems (Rolle’s; Lagrange’s; Cauchy)
- Indeterminate Forms; L’ Hopital Rule
- Tangents and Normal of Algebraic and Polar Curves, Curvature
- Partial differentiations; Euler’s theorems
- Limit, Continuity and differentiability of functions of Several Variables
- Taylor’s theorem with various forms of remainders, Maclaurin's theorem
- Maxima and Minima for functions of several variables; Lagrange’s Multiplier Method
- Differentiation under the integral sign; Leibnitz’s rule
- Double integral; Change the order of integration; polar co-ordinates
- Triple Integral; Spherical Polar and Cylindrical polar co-ordinates
- Beta; Gamma; Elliptic integral; General Properties and related problems
- Scalar and vector valued functions; Concepts of gradient, divergence and curl
- Geometrical and physical significance; tangent plane; directional derivative
- Line, surface and volume integrals
- Statement of Green’s, Stokes’ and Gauss divergence theorems