Course Description. The main aim of this course is to provide a rigorous introduction to the formal mathematical theory underlying calculus, followed by a brief introduction to linear algebra. UM 101 will also act as a course in proof-writing, which involves converting hazy mathematical intuition into clear and logical arguments. The best way to engage with this material is through extensive problem-solving.

Broadly speaking, we will cover the topics listed here. However, to keep track of the precise syllabus, see the calendar at the bottom of this page. It will be updated on a weekly basis.

Textbook. Tom M. Apostol, Calculus, Volume 1, 2nd edition, Wiley, India Edition, 2001
Instructor. Purvi Gupta
Office. L-25 (Math)
Email. purvigupta 		Tutors
  • Geethika Sebastian (✉geethikas)
  • Manpreet Singh (✉manpreets)
TAs
  • Agniva Chatterjee (✉agnivac)
  • Arpita Mal (✉arpitamal)
  • Manoj Kumar (✉manojkumar1)
  • Shraddha Srivastava (✉sshraddha)
  • Subhajit Das (✉subhajitdas)
Lecture timings. MWF 11:00 am - 12:00 pm.
Lecture room. F12, Old Physics Building
Tutorials Thursdays, 11 am - 12 pm
Section Location Instructor
A F12, OPB Geethika
B F8A, OPB Manpreet
C G02, OPB Agniva
D G20, OPB Arpita
E G21, OPB Subhajit
Office hours will be held

by in during for
Purvi L25 (Math) M 5:30-6:30 pm the entire class
Shraddha N24 (Math) F 5:00-6:00 pm the entire class
Manoj R 24 (Math) W 5:30-6:30 pm the entire class
        


by in during for
Geethika L18 (Math) W 5:30-6:30 pm Section A
Manpreet N11 (Math) Tu 5:30-6:30 pm Section B
Agniva X22 (Math) Tu 5:30-6:30 pm Section C
Arpita N28 (Math) Th 5:00-6:00 pm Section D
Subhajit LH 2 (Math) W 5:30-6:30 pm Section E
HW Assignments. A list of problems will be posted here (almost) every Thursday. These are not meant for submission, but only for self-study. You are expected to work on these problems on your own (this is not a team sport) before the subsequent tutorial, where (1) the TA will moderate a discussion on this problem set, and (2) you will answer a written based on it. The TA will not be helpful if they perceive any lack of preparation.
Evaluation Scheme.  
Course materials. You will be added to the UM 101 MS Teams page, where you can access your grades and other course materials.
Course Calendar. Topics and assignments will be updated here. Tutorials are highlighted in pink.

         
Lec.# Date Topics Sections Assignments, etc.
Week 1
1. 17/10 Introduction; Peano sets I 2.1- 2.5
2. 19/10 The ZFC axioms
20/10 No tutorial this week HW 1 (solutions)
3. 21/10 Natural numbers
Week 2
24/10 Holiday
4. 26/10 Peano addition and multiplication
27/10 Tutorial 1 + Quiz 1 HW 2 (solutions)
5. 28/10 fields, ordered sets & ordered fields I 3.2-3.5
Week 3
6. 31/10 $\mathbb R$, bounded sets, supremum and the l.u.b property I 3.8-3.9
7. 2/11 Sequences: definition of convergence, examples 10.2
3/11 Tutorial 2 + Quiz 2 HW 3 (solutions)
8. 4/11 Sequences continued 10.3-10.4
Week 4
9. 7/11 Series: definition of convergence, examples 10.5-10.9
10. 9/11 Series: convergence tests 10.11-10.12, 10.14-10.16
10/11 Tutorial 3 + Quiz 3 HW 4 (solutions)
11. 11/11 Series: absolute convergence, Leibniz's test 10.17-10.18
Week 5
12. 14/11 Limit of a function, examples 3.2
13. 16/11 Basic limit theorems 3.4-3.6
Tutorial 4 + Quiz 4 HW 5 (solutions)
14. 18/11 Continuity: definitions, examples, compositions 3.3, 3.7-3.8
Week 6
15. 21/11 The intermediate value theorem 3.10-3.11
16. 23/11 The extreme value theorem 3.16
24/11 Tutorial 5 + Quiz 5 HW 6 (solutions)
17. 25/11 Derivatives: definition, examples 4.2-4.4
Week 7
18. 28/11 Algebra of derivatives 4.5-4.6
19. 30/11 Invertible functions: monotoncitiy & continuity 3.12-3.13
1/12 Tutorial 6 + Quiz 6 No HW will be posted
2/12 Review Session
Week 809/12 Midterm Examination (Solutions)
Week 9
20. 12/12 Differentiability of inverse & compositions, inverse trig. functions 4.10, 6.20-21
21. 14/12 Local extrema 4.13-15
15/12 Tutorial 7 + No Quiz HW 7 (solutions)
23. 16/12 The mean value theorem 4.13-15
Week 10
23. 19/12 The first derivative test 4.16-17
24. 21/12 Higher derivatives, Taylor's theorem
22/12 Tutorial 8 + Quiz 7
25. 23/12 Derivative: concluding remarks HW 8 (solutions)
Week 11
26. 26/12 Intervals, partitions, step functions 1.8-13, 1.15
27. 28/12 Definition of Riemann integrability 1.16-17
25. 29/12 Riemann integrability of monotone functions 1.21-26 HW 9 (solutions)
30/12 No class
Week 12
29. 02/01 Integrability of continuous functions 3.17-20
30. 04/01 The first FTOC 5.1-2
05/01 Tutorial 9 + Quiz 8 HW 10 (solutions)
31. 06/01 Primitives; the second FTOC 5.3
Week 13
32. 09/01 FTOC II continued; integration by substitution
33. 11/01 Logarithm & exponentiation 6.2-3, 6.5, 6.7, 6.12, 6.14-16
12/01 Tutorial 10+ Quiz 9 HW 11
34. 13/01 An intro. to linear algebra; vector spaces 15.2
Week 14
35. 16/01 Examples of vector spaces 15.3
36. 18/01 Basic properties of vector spaces; subspaces 15.4-5
19/01 Tutorial 11+ Quiz 10
37. 20/01 Spanning sets 15.6 HW 12
Week 14
38. 23/01 Linear independence 15.7
39. 25/01 Bases 15.8
26/01 No tutorial HW 13
40. 27/01 Dimension 15.8-9
Week 15
41. 30/01 Linear transformations 16.1
42. 01/02 Matrix representations; L(V,W) as a v.s., null and range spaces 16.10, 16.2-16.5
02/02 Tutorial 12+Quiz 11 HW 13 will be posted
40. 03/02 End of classes!