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)

    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 comprise the syllabus of the mid-term 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

  • 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

    Homework 13

    Homework 12

    Homework 11

    Homework 10

    Homework 9

    Homework 8

    Homework 7

    Homework 6

    Homework 5

    Homework 4

    Homework 3

    Homework 2

    Homework 1

  • Quiz solutions

    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 November 16, 2017