MTL100

Course Syllabus:  Review of Limit, Continuity and Differentiability, uniform continuity, Mean Value Theorems and applications, Taylor’s Theorem, maxima and minima, Sequences and series, limsup, liminf, convergence of sequences and series of real numbers, absolute and conditional convergence. Reimann Integral, fundamental theorem of integral calculus, applications of definite integrals, improper integrals, beta and gamma functions. Functions of several variables, limit and continuity, partial derivatives and differentiability, gradient, directional derivatives, chain rule, Taylor’s theorem, maxima and minima and method of Lagrange Multipliers. Double and triple integration, Jacobian and change of variables formula. Parametrization of curves and surfaces, vector fields, divergence and curl, Line integrals, Green’s theorem, surface integral, Gauss and Stokes theorems with applications. 

Reference Books:

1. Thomas' Calculus by George B. Thomas, Joel Hass, Christopher Heil, Maurice D. Weir

2. Understanding Analysis by Abbott Stephen 

3. Elementary Analysis: The Theory of Calculus by Kenneth A. Ross

4. Calculus, Volume 2 by Tom M. Apostol

Class notes: https://web.iitd.ac.in/~sreenadh/teaching/mtl100/index.html

Evaluation structures:

1. Quiz 1: 15 Marks (23 Aug)

2. Minor: 25 marks (17 September)

3. Quiz 2: 15 Marks (16 October)

4. Major: 40 Marks (22 November)

5. Attendance in Tutorials: 5 Marks (12: 5 Mark, 11: 4 Marks, 10: 3 Marks, 9: 2 Marks, 8: 1 Marks, less than 8 attendances: 0 Marks.)

Attendance in Lectures: 75% is mandatory.  If a student’s attendance is less than 75%, the student will be awarded one grade less than the actual grade that he/she has earned.

6. Re-minor/ Re-exam (23 October): There will be only one re-minor/re-exam exam at the end of October. If a student misses the minor exam due to medical reasons (prior to viewing the question paper), they will be eligible to take the re-minor. Similarly, if a student misses a quiz and/or minor exam due to medical reasons (prior to viewing the question paper), their marks will be adjusted during the re-minor exam, likely by including additional questions. 

Lecture 1, Lecture 2, Lecture 3, Lecture 4, Lecture 5, Lecture 6,  Lecture 7 Lecture 8 Lecture 9 Lecture 10 Lecture 11 Lecture 12 Lecture 13 Lecture 14 Lecture 15 Lecture 16 Lecture 17 Lecture 18 Lecture 19 Lecture 20 Lecture 21 Multi-variable (Lecture 22-28) Lecture 29 Lecture 30 Lecture 31 Lecture 34 Lecture 35

 Tutorial 1  Practice Problem 1 Tutorial 2 Quiz 1 Tutorial 3 Minor Tutorial 4 Tutorial Sheet 5 Quiz 2 Tutorial Sheet 6 Major

Class and Tutorial Schedule (Group-wise)