Gautam Bharali                Department of Mathematics                  Indian Institute of Science                  Bangalore 560012
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### TEACHING: AUTUMN SEMESTER, 2017

#### UM 101: UNDERGRADUATE ANALYSIS & LINEAR ALGEBRA

• Meeting times

Lectures: Tuesday, Friday 9:30–10:30 a.m., Wednesday 8:30–9:30 a.m.

Tutorials: Thursday 9:30–10:30 a.m.

• Textbook

Tom M. Apostol, Calculus, Vol. 1, 2nd edition, Wiley, India Edition, 2001

• Tutorials (replace «...» by gmail.com in the addresses below)

GROUP A

Tutor: Kriti Sehgal (kritisehgal01@«...»), Location: Tutorial Room 1

Office hour: Saturdays, 2:00 to 3:00 p.m.

GROUP B

Tutor: Sahil Gehlawat (sahil.gehlawat@«...»), Location: Tutorial Room 2

Office hour: Thursdays, 6:00 to 7:00 p.m.

GROUP C

Tutor: Mayuresh Mahadeo Londhe (mayureshwar99@«...»), Location: Tutorial Room 3

Office hour: Thursdays, 5:30 to 6:30 p.m.

GROUP D

Tutor: Nidhi Rathi (nidhirathi11@«...»), Location: Main Lecture Hall, UG Lecture Hall Complex

Office hour: Mondays, 6:30 to 7:30 p.m.

• Documents

Handout no. 1: Course information

• Syllabus (tentative: the list below will grow as the semester progresses the topics below comprise the syllabus of the final exam)

All numbers refer to sections in the textbook.

Your lecture notes will cover all the material (except for a few topics assigned for self-study) in the syllabus. The chapters listed below provide more extensive explanations, and lots of exercises for you to work on.

Basic set theory: I.2.1–I.2.5

The real line: I.3.1–I.3.4, I.3.8–I.3.10, I.3.12

Sequences and convergence: 10.2–10.4

Infinite series and their convergence: 10.5–10.9

Convergence tests for non-negative series: 10.11, 10.12, 10.14, and the criterion for summability of the pth powers

Absolute and conditional convergence: 10.18, 10.20

The ratio and root tests: 10.15, 10.16, 10.20

Leibniz's Rule: 10.17, 10.20

The limit of a function: 3.1, 3.2, 3.4, 3.5

The sign-preservation property: 3.9, 3.11

Continuity: 3.3, 3.6

The topics above comprised the syllabus of the mid-term examination. They will also be a part of the syllabus of the final examination.

Bolzano's Theorem, the intermediate-value theorem, and applications: 3.9–3.11

The extreme-value theorem: 3.16

Differential calculus: 4.2–4.7, 4.9

Points of absolute/global and relative/local extremum: 4.13–4.16

The chain rule and its applications: 4.10–4.12, excluding the discussion on "implicit differentiation"

The mean-value theorem and its applications: 4.14–4.17, excluding the discussion on convexity

Inverse functions and their derivatives: 3.13, 6.20–6.22

Integration, motivation, step functions: 1.8–1.13, 1.15

Integration: 1.16, 1.17, 1.21, 1.24

Uniform continuity

Integrability of continuous functions: 3.18

The first and second Fundamental Theorems of Calculus: 5.1, 5.3, 5.5

The substitution rule: 5.7, 5.8

Integration by parts: 5.9, excluding Theorem 5.5. Note: Section 5.10 is for self-study, as you have seen most of the problems in them in high school. For help and solved examples, see Section 5.9

The logarithm and the exponential functions: 6.3, 6.7, 6.12, 6.15, 6.16

Vector spaces and subspaces: 15.2, 15.3, 15.5, 15.6

Linear independence and bases: 15.7–15.9

Linear transformations: 16.1, 16.2, 16.4

The Rank-Nullity Theorem: 16.3, 16.4

Matrix representations of linear transformations: 16.10

Composition of linear transformations, matrices, invertibility of matrices: 16.5, 16. 15, 16.16

One-to-one linear transformations: 16.7

• Announcements

Oct. 16: We shall have two make-up lectures to compensate for classes that have been lost to holidays. They shall be held on October 28 and November 11. They will be held at the usual venue; time: 10:30-11:30 a.m.

Sep. 15: The mid-term examination is scheduled for September 27 at 9:30 a.m.

Sep. 4: Office hours of all UM101 TAs have been announced. Note that the instructor's office hour is still available, and will continue to be scheduled 6:00 to 7:00 p.m. on Fridays.

Aug. 20: The first tutorial session of the course will be on Thursday, August 10.

• Homework assignments

• Quiz solutions

The solution to Quiz 9

The solution to Quiz 8

The solution to Quiz 7

The solution to Quiz 6

The solution to Quiz 5

The solution to Quiz 4

The solution to Quiz 3

The solution to Quiz 2

The solution to Quiz 1

### TEACHING: LAST 5 YEARS

• UNDERGRADUATE ANALYSIS & LINEAR ALGEBRA (UM101)  [Autumn 2013, Autumn 2015]

• MULTIVARIABLE CALCULUS & COMPLEX VARIABLES (UM202)  [Spring 2015]

• ANALYSIS–II: MEASURE AND INTEGRATION (MA222)  [Spring 2012, Spring 2017 ]

• COMPLEX ANALYSIS (MA224)  [ Spring 2016 ]

• TOPICS IN COMPLEX ANALYSIS (MA324)  [Spring 2014]

• INTRODUCTION TO SEVERAL COMPLEX VARIABLES (MA328-329)  [experimentally as a "topics course" (MA329) in Autumn 2014 ]

• INTRODUCTION TO COMPLEX DYNAMICS (MA380)  [ Autumn 2016 ]

Page last updated on December 1, 2017