The main topics in this course are Differentiation and Integration. The focus will be divided equally between the computational aspects and on the understanding of limits and convergence via rigorous proofs. This is a compulsory course for first-year BSMS students.
Announcements:
On October 22 and October 24, no new topic will be introduced. Tutors will take classes. They will discuss some problems.
There will be classes on November 1 and November 8.
There will not be any quiz on October 13.
Tutorial will be as per schedule.
Quiz 5 will be taken on October 24.
There will not be any tutorial and quiz on October 20 as it will be a diwali vacation.
There will be tutorial on October 22 when assignment 7 will be discussed. Tutorial timing 8.45-9.45 am.
On October 24, assignment 8 will be discussed. Tutorial timing 8.45-9.45 am.
Prerequisites
None
Lectures
Wednesdays and Fridays: 8:45-9:45am in NLH
Saturdays before mid-semester exam: 12-1pm in NLH
Tutorials
The class will be divided into eight groups. These groups will have tutorials at one of two possible slots in LHC 105, 106, 107, 108:
Monday 10-11:30am (Groups B1, B2, B5.1)
Monday 5-6:30pm (Groups B3, B4, B5.2)
Changing tutorial groups is not permitted.
Instructor
(First Half) Tejas Kalelkar, Email: tejas@iiserpune.ac.in
(Second Half) Debargha Banerjee, Email: debargha@iiserpune.ac.in
Teaching Assistants
Antara Manik, Email: antara.manik@students.iiserpune.ac.in
Ayon Roy, Email: ayon.roy@students.iiserpune.ac.in
Gaurav Kumar, Email: gaurav.kumar@students.iiserpune.ac.in
Mohammed Sharukh, Email: mohd.sharukh@acads.iiserpune.ac.in
Nishtha Sharma, Email: nishtha.sharma@acads.iiserpune.ac.in
Sourav Ghosh, Email: sourav.ghosh@students.iiserpune.ac.in
Textbook
Calculus, by Thomas (15th edition in SI units)
Calculus, by Spivak
Homework
Weekly homework assignments will be uploaded on the Google Classroom page for this course by Saturday evening. These do not need to be submitted and will not be graded.
Tests
A short test will be taken at the beginning of each tutorial session based on the homework assignment of the previous week.
Exams
There will be one mid-semester exam and one final exam.
Grading
The final score is calculated as follows:
Weekly tests (40%)
Mid-semester exam (30%)
End-semester exam (30%)
The two lowest weekly-test scores will be dropped before calculation, but no further relaxations will be made for sickness, emergencies, institute events etc.
Course Content
The following is just an approximate schedule to aim for, and will invariably differ from the actual pace followed in class:
Week 1 (Aug 18)
Notations, functions and their graphs
Combining functions and their graphs
Trigonometric, exponential and logarithmic functions
Interpreting the graph of a function
Week 2 (Aug 25) - Saturday extra class
Convergence and Divergence of sequences
Calculating limits of sequences
Commonly occurring limits, Recursive definitions, Bounded monotonic sequences
Week 3 (Sep 1) - Eid Holiday on Friday, Saturday extra class
Limit of a function and limit laws
Precise definition of a limit
One-sided limits
Week 4 (Sep 8) - Saturday extra class
Continuity
Tangents and the derivative at a point
Derivative as a function
Week 5 (Sep 15) - Saturday extra class
Differentiation rules
Derivatives of trigonometric, inverse and logarithmic functions
Chain Rule
Week 6 (Sep 22) - Exam begins on Saturday
Derivative as a rate of change
Revision
Week 7 (Sep 29)
Mid-semester Exams
Classes resume from October 8.
Week 8 (Oct 6)
1. October 8:Extreme values of functions on closed intervals, Rolle's theorem.
2. October 10: Mean Value Theorem, Monotonic functions and first derivative test.
Week 9 (Oct 13)
Area and Estimating with finite sums
Sigma notation and limits of finite sums
Definite integral
Week 10 (Oct 20)
On October 22 and October 24, no new topic will be introduced. Tutors will take classes. They will discuss some problems.
Week 11 (Oct 27)
Fundamental theorem of calculus
Indefinite integrals and substitution method
Area between curves (class on Saturday 1st November)
Week 12 (Nov 3) - Guru Nanak Jayanti Holiday on Wednesday
Basic integration formulas (Nov 5)
Integration by parts (class on Saturday 8th November)
Week 13 (Nov 10)
Trigonometric integrals
Trigonometric substitutions
Integration of rational functions by partial fractions
Week 14 (Nov 17)
Improper integrals
Revision
If there is time:
Inverse function and their derivatives, logarithm and exponential functions
Numerical integration
All the best!