Weeks Weekly Lecture Topics Assignment No.& Type
1 Day 1 Module 1 : Introduction to Real Functions
Day 2 Module 2 : Limits: Definition and Properties
Day 3 Module 3 : Sequential Criterion for Limits
Day 4 Module 4 : Limit Theorems: Part I
Day 5 Assignment No. 1 MCQ
2 Day 1 Module 5 : Limit Theorems: Part II
Day 2 Module 6 : One sided Limits
Day 3 Module 7 : Infinite limits
Day 4 Module 8 : Limits at infinity
Day 5 Assignment No. 2 MCQ
3 Day 1 Module 9 : Continuous Functions
Day 2 Module 10 : Combinations of Continuous Functions
Day 3 Module 11 : Composition of Continuous Functions
Day 4 Module 12 : Continuous Functions on Intervals,
Boundedness theorem
Day 5 Assignment No. 3 MCQ
4 Day 1 Module 13 : Maximum Minimum Theorem
Day 2 Module 14 : Location of Roots Theorem
Day 3 Module 15 : Bolzano’s Intermediate Value Theorem
Day 4 Interaction based on the modules covered
Day 5 Assignment No. 4 MCQ
5 Day 1 Module 16 : Uniform Continuity
Day 2 Module 17 : Lipschitz Function
Day 3 Module 18 : Continuous Extension Theorem
Day 4 Module 19 : Approximations
Day 5 Assignment No. 5 MCQ
6 Day 1 Module 20 : Monotone Functions
Day 2 Module 21 : Inverse Functions
Day 3 Module 22 : Differentiability: Introduction to Derivatives
Day 4 Module 23: Tangent lines and Rates of Change
Day 5 Assignment No. 6 MCQ
7 Day 1 Module 24 : Chain Rule and Caratheodery’s theorem
Day 2 Module 25 : Derivatives of Inverse Functions
Day 3 Module 26 : Role of Derivatives in Real World
Day 4 Module 27: Differentials and Linear approximations
Day 5 Assignment No. 7 MCQ
8 Day 1 Module 28 : Extrema of Functions
Day 2 Module 29 : Rolle’s theorem & Mean Value Theorem
Day 3 Module 30 : Applications of Mean Value Theorem
Day 4 Interaction based on the modules covered
Day 5 Assignment No. 8 MCQ
9 Day 1 Module 31 : Intermediate Value Property, Darboux’s Theorem
Day 2 Module 32 : Increasing and Decreasing Functions
Day 3 Module 33: L’ Hôpital’s Rule
Day 4 Module 34 : Concavity and Inflection Points
Day 5 Assignment No. 9 MCQ
10 Day 1 Module 35 : Cauchy’s Mean Value Theorem
Day 2 Module 36 : Taylor’s theorem
Day 3 Module 37 : Applications of Taylor’s theorem, Newton’s Method
Day 4 Module 38 : Taylor’s Series
Day 5 Assignment No. 10 MCQ
11 Day 1 Module 39 : Maclaurin’s Series
Day 2 Module 40 : Applications of Taylor’s and Maclaurins’ series
Day 3 Module 41 : Partitions and Riemann Sums
Day 4 Module 42 : Properties of Riemann integrals
Day 5 Assignment No. 11 MCQ
12 Day 1 Module 43 : Existence of Riemann Integrals
Day 2 Module 44 : Riemann Integrable Functions
Day 3 Module 45 : Additivity Theorem
Day 4 Interaction based on the modules covered
Day 5 Assignment No. 12 MCQ
13 Day 1 Module 46 : Fundamental Theorem of Calculus
Day 2 Module 47 : Substitution Theorem
Day 3 Module 48 : Improper Integrals
Day 4 Interaction based on the modules covered
Day 5 Assignment No. 13 MCQ
14 Day 1 Module 49 : Applications of Improper Integrals
Day 2 Module 50 : Cauchy Principal Value and Tests for convergence
Day 3 Revision
Day 4
Day 5 Assignment No. 14 MCQ
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