My Notes

These are my college notes for courses taught in Nation Institute of Technology, Tiruchirappalli for mathematics. These include theory, problems and textbooks.

Table of contents

1. Matrices & Calculus - MAIR11
   1. Matrices
   2. Real analysis
   3. Functions in several variables

Matrices & Calculus - MAIR11

Matrices

Linear equations can be solved using matrices. You might be aware of how to use the Cramer’s rule to solve matrices of the form AX = B. But when the size of matrix is very large it not feasible even for the computers to get the solution. In this course we will be studying about the eigen values & eigen vectors, their different properties to make matrix operations easier, diagonalization of matrices & basic identification of quadratic forms using matrices.

• Lecture 1
• Lecture 2
• Lecture 3
• Lecture 4
• Lecture 5
• Lecture 6
• Lecture 7
• Lecture 8
• Lecture 9
• Lecture 10
• Lecture 11
• Lecture 12

Real analysis

Real analysis includes infinite series & their properties. In this course we will analyze the property of infinite series and methods to determine wether the infinite series is convergent or divergent using theorems & tests like monotonic convergence theorem, squeeze principle, comparision test, integral test, D’Alembert’s ratio test, cauchy’s root test, raabe’s test, logarithmic test, etc.

• Lecture 1
• Lecture 2
• Lecture 3
• Lecture 4
• Lecture 5
• Lecture 6
• Lecture 7

Functions in several variables

In engineering & physics, when we model practical problem we get functions & equations which depend on several variables. In this course we will discuss limits, continuity, partial differentiation, etc. of multivariable functions.

• Lecture 1
• Lecture 2
• Lecture 3

adding more soon…