# IIT Delhi MTL1001 Mathematics I Calculus: Syllabus and Practice

> Study guide for IIT Delhi MTL1001 Mathematics I (Calculus), 2025 curriculum: sequences, series, one variable calculus and multivariable calculus in one course.

Source: https://practicecalculus.com/courses/iit-delhi-mtl1001
Updated: 2026-11-08

## At a glance

- **Course code:** MTL1001 Mathematics I Calculus
- **Curriculum:** IIT Delhi curriculum, 2025 onwards
- **Credits:** 4 credits (L-T-P 3-1-0)
- **Offered by:** Department of Mathematics
- **Prerequisites:** None listed in the course template
- **Covers:** Real sequences and series, limits, continuity, mean value theorems, Taylor series, Riemann integral, improper integrals, beta and gamma functions, partial derivatives, Lagrange multipliers, double and triple integrals, surface integrals
- **Next course:** [MTL1002 Mathematics II](/courses/iit-delhi-mtl1002), linear algebra and differential equations
- **Practice here:** [Calculus 1](/learn/calculus-1), [sequences and series](/learn/calculus-2/sequences-and-series/sequences) and [Calculus 3](/learn/calculus-3)

## Key takeaways

- MTL1001 Mathematics I Calculus is the first mathematics course in the IIT Delhi curriculum that applies from 2025 onwards.
- It is a 4 credit course with 3 lectures and 1 tutorial a week, offered by the Department of Mathematics.
- It starts with the completeness of the real numbers and convergence of sequences and series before any differentiation.
- It covers single variable and multivariable calculus in one semester, ending with surface integrals.
- Its partner course is MTL1002 Mathematics II Linear Algebra and Differential Equations.

**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

| MTL1001 topic | Practice | Read |
| --- | --- | --- |
| Sequences and convergence | [Sequences](/learn/calculus-2/sequences-and-series/sequences) | [Convergence tests](/blog/convergence-tests) |
| Series and partial sums | [Series and partial sums](/learn/calculus-2/sequences-and-series/series-and-partial-sums) | [Geometric series](/blog/geometric-series) |
| Comparison tests | [Comparison tests](/learn/calculus-2/sequences-and-series/comparison-tests) | [nth term test](/rules/nth-term-test) |
| Ratio and root tests | [Ratio and root tests](/learn/calculus-2/sequences-and-series/ratio-and-root-tests) | [Ratio test](/rules/ratio-test) |
| Alternating series and Leibniz test | [Alternating series](/learn/calculus-2/sequences-and-series/alternating-series) | [Alternating series test](/rules/alternating-series-test) |
| Limits and continuity | [Continuity](/learn/calculus-1/limits/continuity) | [Continuity](/blog/continuity) |
| Mean value theorems | [Linear approximation and the MVT](/learn/calculus-1/applications-of-derivatives/linear-approximation-and-mvt) | [Mean value theorem](/theorems/mean-value-theorem), [Rolle's theorem](/theorems/rolles-theorem) |
| Taylor's theorem and power series | [Power series and radius](/learn/calculus-2/power-series-parametric-polar/power-series-and-radius) | [Taylor's theorem](/theorems/taylors-theorem), [power series](/blog/power-series) |
| Maxima and minima | [Absolute extrema](/learn/calculus-1/applications-of-derivatives/absolute-extrema) | [Optimization problems](/blog/optimization-problems) |
| Riemann integral and fundamental theorems | [Riemann sums](/learn/calculus-1/integrals/riemann-sums) | [Fundamental Theorem of Calculus](/blog/fundamental-theorem-of-calculus) |
| Improper integrals | [Infinite limits of integration](/learn/calculus-2/improper-integrals-and-applications/infinite-limits-of-integration) | [Improper integrals](/blog/improper-integrals) |
| Partial and directional derivatives | [Gradient and directional derivatives](/learn/calculus-3/partial-derivatives/gradient-and-directional-derivatives) | [Partial derivatives](/blog/partial-derivatives) |
| Chain rule in several variables | [Multivariable chain rule](/learn/calculus-3/partial-derivatives/multivariable-chain-rule) | [Partial derivatives practice](/practice-problems/partial-derivatives) |
| Lagrange multipliers | [Lagrange multipliers](/learn/calculus-3/partial-derivatives/lagrange-multipliers) | [Lagrange multipliers](/blog/lagrange-multipliers) |
| Double and triple integrals | [Iterated integrals](/learn/calculus-3/multiple-integrals/iterated-integrals) | [Double integrals](/blog/double-integrals) |
| Jacobians and coordinate systems | [Change of variables](/learn/calculus-3/multiple-integrals/change-of-variables) | [Cylindrical and spherical](/learn/calculus-3/multiple-integrals/cylindrical-spherical) |
| Surface integrals | [Surface integrals and flux](/learn/calculus-3/vector-calculus/surface-integrals-and-flux) | [Divergence theorem](/theorems/divergence-theorem) |

## 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 $x = t^2$,

$$\int_0^\infty e^{-t^2}\,dt = \frac{1}{2}\Gamma\left(\tfrac{1}{2}\right) = \frac{\sqrt{\pi}}{2}$$

**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](/learn/calculus-2/sequences-and-series/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](/practice) and the [formula sheet](/formulas), and read [how to prepare for a calculus exam](/blog/how-to-prepare-for-a-calculus-exam) before minors and majors.

## Frequently asked questions

### What is MTL1001 at IIT Delhi?

MTL1001 Mathematics I Calculus is the first year calculus course in IIT Delhi's curriculum for 2025 onwards. It is offered by the Department of Mathematics for 4 credits (3 lectures and 1 tutorial a week) and covers sequences and series, one variable differential and integral calculus, and multivariable differential and integral calculus.

### Is MTL1001 the same as MTL100?

MTL1001 is the course code in IIT Delhi's curriculum for 2025 onwards. Earlier batches studied calculus under the older code MTL100. Check the curriculum for your entry year to see which code applies to you.

### Does MTL1001 cover vector calculus theorems?

The course template ends multivariable integral calculus with surface integrals and applications to area, volume and surface. Green's, Stokes' and Gauss' theorems are not named in the MTL1001 template.

### How hard is IIT Delhi MTL1001?

It is fast and more rigorous than school calculus. The first weeks on completeness, Cauchy sequences and convergence tests surprise many students, so start practising series early and keep up with the weekly tutorial.