NOC:Advanced Engineering Mathematics (2023)

Lecture 1 - Introduction on functions of a single variable

Lecture 2 - Basic definitions

Lecture 3 - Mean value Theorems

Lecture 4 - Extremum of function of single variable

Lecture 5 - Examples

Lecture 6 - Introduction on functions of two variable

Lecture 7 - Basic definitions

Lecture 8 - Partial differentiation

Lecture 9 - Extremum of function of two variable

Lecture 10 - Examples

Lecture 11 - Convergence and divergence test

Lecture 12 - Beta function, Gamma function

Lecture 13 - Differentiation under integral sign

Lecture 14 - Line integral, integration in R^2 (Double integral)

Lecture 15 - Examples

Lecture 16 - Double integral

Lecture 17 - Integration in R3

Lecture 18 - Triple integral

Lecture 19 - Examples

Lecture 20 - Introduction to Differential equation

Lecture 21 - Exact form

Lecture 22 - Second order differential equation

Lecture 23 - Iterative method (bisection and fixed point)

Lecture 24 - Newton-Raphson, Jacobi and Gauss-Seidel method

Lecture 25 - Finite difference method

Lecture 26 - Newton's forward and backward interpolation

Lecture 27 - Numerical integration

Lecture 28 - Vector space and Subspace

Lecture 29 - Basis and dimension

Lecture 30 - Rank of a matrix

Lecture 31 - Gauss-Elimination Method

Lecture 32 - Linear Transformation

Lecture 33 - Examples

Lecture 34 - Matrix Representation

Lecture 35 - Eigenvalues and Eigenvectors

Lecture 36 - Cayley-Hamilton Theorem

Lecture 37 - Diagonalisation of a Matrix

Lecture 38 - Examples and applications

Lecture 39 - Types of matrices

Lecture 40 - Equivalent Matrices and Elementary Matrices

Lecture 41 - Introduction to the vector function

Lecture 42 - Differentiation and integration of the vector function

Lecture 43 - Partial differentiation of vector function

Lecture 44 - Directional derivative of a vector function

Lecture 45 - Examples on directional derivative, tangent plane and normal

Lecture 46 - Divergence and curl of a vector function

Lecture 47 - Application to mechanics of vector calculus

Lecture 48 - Serret-Frenet formula and more applications to mechanics

Lecture 49 - Examples on finding unit vectors, curvature and torsion

Lecture 50 - Application of vector calculus to the particle dynamics

Lecture 51 - Line integral of vector function

Lecture 52 - Surface integral of vector function

Lecture 53 - Volume integral of vector function and Gauss Divergence Theorem

Lecture 54 - Green's theorem and Stoke's theorem

Lecture 55 - Verification and application of Divergencen theorem, Green's theorem and Stoke's theorem

Lecture 56 - Basic properties of a complex valued function

Lecture 57 - Analytic Complex valued function

Lecture 58 - Complex Integration and theorems

Lecture 59 - Application of Cauchy's integral formula

Lecture 60 - Regular and Singular point of a complex valued function