Weeks Weekly Lecture Topics (Module Titles) Assignment
1
Day 1 Module 1 : Introduction to Real Functions No. 1 MCQ
Day 2 Module 2 : Limits: Definition and Properties
Day 3 Module 3 : Sequential Criterion for Limits
Day 4 Interaction based on the three modules covered
Day 5 Assignment
2
Day 1 Module 4 : Limit Theorems: Part I
Day 2 Module 5 : Limit Theorems: Part II
Day 3 Module 6 : One sided Limits
Day 4 Interaction based on the three modules covered
Day 5 Assignment
3
Day 1 Module 7 : Infinite limits
Day 2 Module 8 : Limits at infinity
Day 3 Module 9 : Continuous Functions
Day 4 Interaction based on the three modules covered
Day 5 Assignment
4
Day 1 Module 10 : Combinations of Continuous Functions
Day 2 Module 11 : Composition of Continuous Functions
Day 3 Module 12 : Continuous Functions on Intervals, Boundedness theorem
Day 4 Interaction based on the three modules covered
Day 5 Assignment
5
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
Day 5 Assignment
6
Day 1 Module 16 : Uniform Continuity
Day 2 Module 17 : Lipschitz Function
Day 3 Module 18 : Continuous Extension Theorem
Day 4 Interaction based on the three modules covered
Day 5 Assignment
7
Day 1 Module 19 : Approximations No.
Day 2 Module 20 : Monotone Functions
Day 3 Module 21 : Inverse Functions
Day 4 Interaction based on the three modules covered
Day 5 Assignment
8
Day 1 Module 22 : Differentiability: Introduction to Derivatives
Day 2 Module 23: Tangent lines and Rates of Change
Day 3 Module 24 : Chain Rule and Caratheodery’s theorem
Day 4 Interaction based on the three modules covered
Day 5 Assignment
9
Day 1 Module 25 : Derivatives of Inverse Functions
Day 2 Module 26 : Role of Derivatives in Real World
Day 3 Module 27: Differentials and Linear approximations
Day 4 Interaction based on the three modules covered
Day 5 Assignment
10
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
Day 5 Assignment
11
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 Interaction based on the three modules covered
Day 5 Assignment
12
Day 1 Module 34 : Concavity and Inflection Points
Day 2 Module 35 : Cauchy’s Mean Value Theorem
Day 3 Module 36 : Taylor’s theorem
Day 4 Interaction based on the three modules covered
Day 5 Assignment
13
Day 1 Module 37 : Applications of Taylor’s theorem, Newton’s Method No. 13 MCQ
Day 2 Module 38 : Taylor’s Series
Day 3 Module 39 : Maclaurin’s Series
Day 4 Interaction based on the three modules covered
Day 5 Assignment
14
Day 1 Module 40 : Applications of Taylor’s and Maclaurins’ series
Day 2 Module 41 : Partitions and Riemann Sums
Day 3 Module 42 : Properties of Riemann integrals
Day 4
Day 5 Assignment
15
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 three modules covered
Day 5 Assignment
16
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 three modules covered
Day 5 Assignment
17
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
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