IIT Delhi MTL1001 Mathematics I Calculus: Syllabus and Practice

MTL1001 Mathematics I Calculus is the first year calculus course at the Indian Institute of Technology Delhi (IIT Delhi) in the institute's curriculum for 2025 onwards. It is a 4 credit course with 3 lectures and 1 tutorial a week, offered by the Department of Mathematics. This guide follows the official MTL1001 course template on the IIT Delhi curriculum site and maps every topic to free practice.

Earlier batches took calculus under the older code MTL100, so check which curriculum applies to your entry year.

What MTL1001 covers

The course template lists six blocks:

• Sequences of real numbers: the real number system and its completeness property, the Archimedean property, sequences and convergence, Cauchy sequences, and limit superior and inferior.
• Infinite series: absolute and conditional convergence, alternating series, and the comparison, Cauchy condensation, ratio, root and Leibniz tests.
• Differential calculus: limits, continuity, differentiability, mean value theorems, Taylor's theorem, Taylor series, power series, and maxima and minima.
• Integral calculus: the Riemann integral and its properties, the fundamental theorems, improper integrals of the first and second kind, and the beta and gamma functions.
• Multivariable differential calculus: limits and continuity in several variables, partial and directional derivatives, differentiability, the chain rule, the gradient, Taylor's theorem, maxima and minima in two variables, and Lagrange multipliers.
• Multivariable integral calculus: double and triple integrals, Jacobians and change of variables, polar, spherical and cylindrical coordinates, surface integrals, and applications to area, volume and surface.

The listed outcomes stress rigour as well as technique: appreciating the role of completeness, building problem solving skills with limits, derivatives and integrals, and modelling problems such as optimisation and area or volume calculations.

MTL1001 topic map

Example problems at the MTL1001 level

These are original practice problems.

1. Cauchy condensation. \sum \frac{1}{n(\ln n)^p} converges exactly when \sum 2^k \cdot \frac{1}{2^k (k\ln 2)^p} = \sum \frac{1}{(k\ln 2)^p} does, that is, when p > 1.

2. A gamma integral. With x = t^2,

3. A Jacobian. Under u = x + y, v = x - y, \left|\frac{\partial(x, y)}{\partial(u, v)}\right| = \frac{1}{2}, so dx\,dy = \frac{1}{2}\,du\,dv.

How to do well in MTL1001

• Take the first weeks seriously. Completeness and Cauchy sequences come first, and the series tests depend on them.
• Practise convergence tests until you can choose one quickly. The choosing a test lesson trains exactly that.
• Use the tutorial hour to check your written arguments, not just your answers.
• Study a little every day with practice and the formula sheet, and read how to prepare for a calculus exam before minors and majors.