# MTH101A

## Contents |

## Course Details

**MTH101(Mathematics I)** is a compulsory course for all the undergraduate students of IITK in their first years of study.
This course is conducted by Department of Mathematics and Statistics,IITK but is compulsory for all departments. The objective of this course is the cover to a wide range of mathematical concepts at the fundamental level.This is one of the pre-requisites for the most of the other mathematics courses.

## Course Content

- Real number system : Completeness axiom, density of rationals (irrationals) in R
- Convergence of a sequence, Sandwich theorem, Monotone sequences
- Cauchy criterion, Subsequence, Every bounded sequence has a convergent subsequence,convergence of a sequence satisfying Cauchy criterion
- Limits and Continuity of functions, Boundedness of a continuous function,Cauchy mean value theorem, L’Hospital rule.
- Fixed point iteration method,Newton’s method,Increasing and decreasing functions, Convexity, Second derivative test for

max and min, Point of inflection, curve sketching

- Ratio test, Root test,Leibniz’s theorem ,Power series, Radius of convergence,Introduction to Riemann integration, Integrability, Fundamental Theorems of calculus, Riemann Sum
- Volumes by Shell and Washer methods, Length of a curve,Differentiability,The method of Lagrange multipliers,Double integral, Fubini’s theorem, Volumes and Areas.

## Lecture

This is an 11 credit course with 9 credit for lectures and 2 credits for tutorial. This means 3 lectures are held(3 credits per lecture) weekly, 50 minutes each.

## Tutorial

The remaining 2 credits of the 11 are for tutorial. A single tutorial is held per week for 50 minutes. Tutorials are held in smaller groups of students for assignment discussion and doubt solving. These give the students a better opportunity to interact with the faculty on one to one basis, and thus are an intergral part of the course

## Exam

In this coursethere are three types of exam. Quiz,mid-sem, and end-sem. Basically two quizes in this course are held, one before mid-sem and one after it. The weightages of various exams depend on the instructor, but roughly can be estimated to Quiz - 20% ,Mid Sem -30% ,End Sem -50 %

## Class size and structure

Its compulsory course for each and every student of first year approx 800