ENGINEERING MATHEMATICS

Course Curriculum

Chapter 1: MATRICES

Lecture 1: Introduction to Sets, vectors & Matrices

Lecture 2: Vectors

Lecture 3: Algebraic operations on Vectors

Lecture 4: Triple Product

Lecture 5: Dependent Vectors

Lecture 6: Orthogonal & Orthonormal Vectors

Lecture 7: Normalizing Vector & Projection of Vectors

Lecture 8: Matrices

Lecture 9: Types of Matrices – 1

Lecture 10: Types of Matrices – 2

Lecture 11: Solving System of Linear equations

Lecture 12: Row Operations and Equivalent Systems

Lecture 13: Gaussian Elimination or Row Reduction method

Lecture 14: Echelon Form of a Matrix

Lecture 15: Rank of a matrix by Echelon form

Lecture 16: Rank of a matrix using Normal Form

Lecture 17: Invertible Matrices – 1

Lecture 18: Theorems on Invertible Matrices

Lecture 19: Inverse of a matrix using Gauss-Jordan method

Lecture 20: Homogeneous and non homogeneous linear systems

Chapter 2: Eigen values and Eigen vectors

Lecture 1: Matrix Eigenvalues

Lecture 2: Finding Eigenvalues and Eigenvectors

Lecture 3: Cayley-Hamilton Theorem

Lecture 4: Cayley-Hamilton Theorem-2

Lecture 5: Gram Schmidt method

Lecture 6: Gram Schmidt method – 2

Lecture 7: Diagonalization

Lecture 8: Matrix Decomposition

Chapter 3: Sequences & Series

Lecture 1: Sequence

Lecture 2: Convergence & Divergence

Lecture 3: Convergence & Divergence – 2

Lecture 4: Series

Lecture 5: Numerical Series

Lecture 6: Tests for Convergence and Divergence

Lecture 7: Tests for Convergence and Divergence – 2

Lecture 8: D'Alembert's Ratio Test

Lecture 9: D'Alembert's Ratio Test – 2

Lecture 10: Raabe’s Test

Lecture 11: Raabe’s Test – 2

Lecture 12: Cauchy’s Integral test

Lecture 13: Cauchy’s root test

Lecture 14: Cauchy’s root test – 2

Lecture 15: Logarithmic Test

Lecture 16: Logarithmic Test – 2

Lecture 17: Alternating series test

Chapter 4: Calculus

Lecture 1: Basics

Lecture 2: Mean value theorem

Lecture 3: Lagrange’s Mean Value Theorem

Lecture 4: Cauchy’s Mean Value Theorem

Lecture 5: Generalized mean value theorems: Taylor series

Lecture 6: Taylor’s Theorem-2

Lecture 7: Applications of definite integrals