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:
Thomas' Calculus by George B. Thomas, Joel Hass, Christopher Heil, Maurice D. Weir
Understanding Analysis by Abbott Stephen
Class notes: https://web.iitd.ac.in/~sreenadh/teaching/mtl100/index.html
Evaluation structures:
Quiz 1: 15 Marks (20-24 Aug)
Minor: 25 marks (12-19 September)
Quiz 2: 15 Marks (22-26 October)
Major: 40 Marks (16 to 23 November)
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.)
Re-minor/ Re-exam: 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. The syllabus for the re-minor will cover material from the first lecture up to the last lecture before the re-minor date.