# BITS Pilani MATH F111 Mathematics I: Syllabus, Topics and Practice

> Study guide for BITS Pilani MATH F111 Mathematics I: functions, limits, derivatives, integrals, conics, polar, series, partial derivatives and vector calculus.

Source: https://practicecalculus.com/courses/bits-pilani-math-f111
Updated: 2026-11-08

## At a glance

- **Course code:** MATH F111 Mathematics I
- **Source:** BITS Pilani Bulletin 2025-2026
- **Units:** 3 units (3 lecture, 0 practical/project)
- **Semester:** First year, first semester where it appears in a semester-wise pattern (for example B.E. Robotics and Industrial Automation)
- **Prerequisites:** Not stated in the course description
- **Covers:** Functions and graphs, limits and continuity, applications of derivatives and integrals, conics, polar coordinates, sequences and series, Maclaurin and Taylor series, partial derivatives, vector calculus with Green, Gauss and Stokes
- **Next course:** MATH F112 Mathematics II (complex variables and linear algebra)
- **Practice here:** [Calculus 1](/learn/calculus-1), [Calculus 2](/learn/calculus-2) and [Calculus 3](/learn/calculus-3)

## Key takeaways

- MATH F111 Mathematics I is a 3 unit BITS Pilani foundation course in calculus, described in the Bulletin 2025-26.
- It runs from functions and limits through series and partial derivatives to the theorems of Green, Gauss and Stokes.
- In the 2025-26 bulletin most B.E. programmes list MATH F101 Multivariable Calculus instead; MATH F111 still appears in the B.E. Robotics and Industrial Automation pattern.
- Its partner course is MATH F112 Mathematics II, which covers complex variables and linear algebra.

**MATH F111 Mathematics I** is the long standing first year calculus course at **BITS Pilani**, described in the official **Bulletin 2025-2026** as a 3 unit foundation course. It covers single variable calculus, conics and polar coordinates, series, partial derivatives and vector calculus. This guide follows the bulletin's course description and links every topic to free practice.

## MATH F111 or MATH F101?

In the 2025-26 bulletin, most B.E. semester-wise patterns put [MATH F101 Multivariable Calculus](/courses/bits-pilani-math-f101) in the first semester, and a bulletin note for the BITS-Iowa State 2+2 programme says MATH F111 is replaced by MATH F101. MATH F111 is still listed in the course descriptions and in the B.E. Robotics and Industrial Automation pattern, where it sits in the first semester with MATH F112 Mathematics II in the second. If you are unsure which applies to you, check the semester-wise pattern for your programme and year of admission.

| | MATH F111 Mathematics I | MATH F101 Multivariable Calculus |
| --- | --- | --- |
| Units | 3 | 3 |
| One variable calculus | Functions, limits, derivatives, integrals | Not listed |
| Conics | Yes | No |
| Polar coordinates | Yes | Yes, with integrals |
| Sequences, series, Taylor series | Yes | Yes |
| Partial derivatives and vector calculus | Yes | Yes, plus multiple integrals |
| Next course | MATH F112 Mathematics II | MATH F102 Linear Algebra and Complex Variables |

## What MATH F111 covers

The bulletin's description lists, in order:

- functions and graphs;
- limit and continuity;
- applications of the derivative and the integral;
- conics;
- polar coordinates;
- convergence of sequences and series;
- Maclaurin and Taylor series;
- partial derivatives;
- vector calculus in $\mathbb{R}^n$ and vector analysis;
- the theorems of Green, Gauss and Stokes.

No prerequisite is stated, so the course builds on Class 12 mathematics.

## MATH F111 topic map

| MATH F111 topic | Practice | Read |
| --- | --- | --- |
| Functions and graphs | [Function notation](/learn/calculus-1/functions-warmup/function-notation) | [Exponential functions](/functions/exponential-functions), [rational functions](/functions/rational-functions) |
| Limit and continuity | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [How to evaluate limits](/blog/how-to-evaluate-limits) |
| Applications of the derivative | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization) | [Optimization problems](/blog/optimization-problems), [related rates](/blog/related-rates) |
| Applications of the integral | [Volumes with disks](/learn/calculus-1/applications-of-integrals/volumes-disks) | [Area between curves](/blog/area-between-curves) |
| Conics and parametric curves | [Parametric curves](/learn/calculus-2/power-series-parametric-polar/parametric-curves) | [Quadratic function](/functions/quadratic-function) |
| Polar coordinates | [Polar coordinates](/learn/calculus-2/power-series-parametric-polar/polar-coordinates) | [Parametric and polar practice](/practice-problems/parametric-and-polar) |
| Sequences and series | [Series and partial sums](/learn/calculus-2/sequences-and-series/series-and-partial-sums) | [Convergence tests](/blog/convergence-tests) |
| Maclaurin and Taylor series | [Taylor polynomials](/learn/calculus-2/power-series-parametric-polar/taylor-polynomials) | [Taylor series](/blog/taylor-series) |
| Partial derivatives | [Partial derivatives](/learn/calculus-3/partial-derivatives/partial-derivatives) | [Partial derivatives](/blog/partial-derivatives) |
| Vectors in space | [Vectors and length](/learn/calculus-3/vectors-and-space/vectors-and-length) | [Vectors, dot and cross product](/blog/vectors-dot-and-cross-product) |
| Vector analysis | [Curl and divergence](/learn/calculus-3/vector-calculus/curl-and-divergence) | [Gradient and directional derivatives](/blog/gradient-and-directional-derivatives) |
| Green, Gauss and Stokes | [Green's theorem](/learn/calculus-3/vector-calculus/greens-theorem) | [Green's theorem](/theorems/greens-theorem), [Stokes' theorem](/theorems/stokes-theorem) |

## Example problems at the MATH F111 level

These are original practice problems, not past BITS papers.

**1. Optimisation.** A rectangle has perimeter 20. Its area $A = x(10 - x)$ has $A'(x) = 10 - 2x = 0$ at $x = 5$, so the largest area is $25$, a square.

**2. A Maclaurin series.**

$$e^{x} = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots, \quad\text{so}\quad e^{-x^2} = 1 - x^2 + \frac{x^4}{2} - \cdots$$

**3. A conic.** The ellipse $\frac{x^2}{25} + \frac{y^2}{9} = 1$ has $a = 5$, $b = 3$ and $c = \sqrt{25 - 9} = 4$, so its foci are $(\pm 4, 0)$ and its eccentricity is $\frac{4}{5}$.

## How to do well in MATH F111

- **Do not coast through the first weeks.** One variable calculus goes quickly, and the course soon moves to series and several variables.
- **Practise series tests until choosing one is automatic,** with [choosing a test](/learn/calculus-2/sequences-and-series/choosing-a-test).
- **Draw pictures for vector calculus.** Orientation and boundaries decide the sign of the answer in Green's and Stokes' theorems.
- **Study in short daily sessions** with [practice](/practice) and the [formula sheet](/formulas), and see [how to prepare for a calculus exam](/blog/how-to-prepare-for-a-calculus-exam).

## Frequently asked questions

### What is MATH F111 at BITS Pilani?

MATH F111 Mathematics I is a 3 unit calculus course in the BITS Pilani Bulletin. Its description lists functions and graphs; limit and continuity; applications of derivative and integral; conics; polar coordinates; convergence of sequences and series; Maclaurin and Taylor series; partial derivatives; vector calculus in R^n; vector analysis; and the theorems of Green, Gauss and Stokes.

### Has MATH F111 been replaced by MATH F101?

In the 2025-26 bulletin, most B.E. semester-wise patterns list MATH F101 Multivariable Calculus in the first semester, and the bulletin's BITS-Iowa State note says MATH F111 is replaced by MATH F101. MATH F111 is still listed in the B.E. Robotics and Industrial Automation pattern and in the course descriptions, so check the pattern for your programme and year of admission.

### What comes after MATH F111?

MATH F112 Mathematics II follows in the second semester. The bulletin describes it as complex numbers, analytic functions, Cauchy's theorems, elementary functions, series expansions, the calculus of residues, vector spaces, basis and dimension, linear transformations and row reduction.

### How should I prepare for MATH F111?

Review Class 12 limits, derivatives and integrals, since the course moves through them quickly and spends most of its time on series and several variable calculus. Daily short practice works better than cramming before the comprehensive exam.