UM 101: Analysis and Linear Algebra I

Instructor: Arvind Ayyer
Office: X-15 (new wing)
Office hours: Thursdays, 5:00–6:00pm.
Phone number: (2293) 3215
Email: (First name) at iisc dot ac dot in
Class Timings: Monday, Wednesday and Friday -- 12:00–1:00pm.
Classroom: UG Lecture Hall
Textbook: Calculus Vol. 1 (Second edition)
by Tom M. Apostol
ISBN-13 - 9-788126-515196

Supplementary Text:
Linear Algebra and Its Applications (4th Edition)
by Gilbert Strang
ISBN-13 - 9-780030-105678
Tutorial timings: Thursday -- 9:30–10:30am.
Tutorial rooms: UG tutorial complex
Teaching Assistants:
Teaching Assistant Section Office Email (at iisc dot ac dot in) Office Hours
Surjadipta De Sarkar A (Room 1) N11 surjadiptade Tuesdays, 5-6pm
Shubham Rastogi B (Room 2) N04 shubhamr Mondays, 6-7pm
Pritam Ganguly C (Room 3) N04 pritamg Wednesdays, 6-7pm
Kartick Ghosh D (Room 4) N04 kartickghosh Saturdays, 4-5pm
Pabitra Barman - N03 pabitrab Fridays, 5:30-6:30pm
Pranab Sarkar - N03 pranabsarkar Saturdays, 11am-12pm

Course Description

One-variable calculus: Real and Complex numbers; Convergence of sequences and series;
Continuity, intermediate value theorem, existence of maxima and minima;
Differentiation, mean value theorem, Taylor series;
Integration, fundamental theorem of Calculus, improper integrals.
Linear Algebra: Vector spaces (over real and complex numbers), basis and dimension;
Linear Transformations and matrices.

Exams

All exams will be closed book, closed notes, and
no calculators or electronic devices are allowed.
No communication among the students will be tolerated.
There will be no make up exams.

The date for the midterm and final will be announced later.


Grading

Here are the weights for the homework and exams.
All marks will be posted online on Moodle.


Tentative Class Plan (Tutorial sessions are marked in green)

week date sections material covered homework and other notes
0 3/8 I 2.1-2.5 Review of basic set theory -
1 6/8 I 3.1-3.4 Real Line Homework 1 posted.
8/8 I 3.8-3.11 Upper bound, Supremum -
9/8 - Quiz 1 Moodle account set up
Solution posted
10/8 10.2-10.3 Sequences Homework 2 posted.
2 13/8 10.5-10.8 Series -
15/8 -

Holiday - Independence Day

-
16/8 - Quiz 2 -
17/8 10.11-10.14 Tests for convergence Homework 3 posted.
3 20/8 10.15-10.17 Ratio and root tests, Leibniz rule -
22/8 -

Holiday

-
23/8 - Quiz 3 -
24/8 -

Holiday

-
4 27/8 10.18-10.19 Absolute and conditional convergence -
29/8 3.1-3.2 Limit of a function
30/8 - -
31/8 3.3-3.5 Continuity -
5 3/9 3.7-3.9 Bolzano's theorem -
5/9 3.10-3.13 Intermediate value theorem
6/9 - -
9/9 3.16 Extreme value theorem -
6 10/9 4.2-4.4 Derivatives -
12/9 4.10-4.11 Chain rule
13/9 -

Holiday

-
14/9 4.13-4.14 Applications of derivatives -
7 17/9 4.16-4.18 Curve sketching -
19/9 7.1-7.3 Taylor's theorem
20/9 - -
21/9 -

Holiday

-
8 24/9 1.6-1.10 Areas of step functions -
26/9 1.12-1.16 Integrals of step functions -
27/9 - -
28/9 -

Midterm break - No class

-
9 1/10 -

First Midterm

-
3/10 -

Midterm break - No class

4/10 - -
5/10 1.17-1.20 Integrals of bounded functions -
10 8/10 -

Holiday

-
10/10 1.21-1.24 Integrals of monotonic functions
11/10 - -
12/10 1.25-1.27 Properties of integrals -
11 15/10 2.2-2.4 Applications of integration -
17/10 2.16-2.19 Applications of integration
18/10 - -
19/10 -

Holiday

-
12 22/10 3.17-3.20 Integration of continuous functions -
24/10 5.1-5.4 Fundamental theorems of calculus
25/10 - -
26/10 5.6-5.10 Techniques of integration -
13 29/10 6.3, 6.12-6.15
6.23, 7.5-7.6
Logarithmic and exponential functions
Partial fractions, Taylor series
-
31/10 15.2-15.4 Vector spaces
1/11 -

Second Midterm

-
2/11 15.6-15.8 Subspaces and bases -
14 5/11 15.10-15.11 Euclidean spaces -
7/11 -

Holiday

8/11 - -
9/11 16.1-16.2 Linear transformations -
15 12/11 16.3-16.5 Rank-nullity theorem -
14/11 16.6 Inverses of functions
15/11 - -
16/11 16.7-16.10 Matrix representations -
16 19/11 16.13-16.14 Vector space of matrices -
21/11 -

Holiday

22/11 - -
23/11 -

Holiday

-
17 26/11 16.15-16.17 Systems of equations -
28/11 16.18 Solving linear systems -
29/11 -
18 ?/12 -

Final Exam

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