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BITS Pilani

BITS Pilani MATH F101 Multivariable Calculus: Syllabus and Practice

Study guide for BITS Pilani MATH F101 Multivariable Calculus (Bulletin 2025-26): series, polar coordinates, partial derivatives and vector calculus.

BITS Pilani Updated 3 min read

At a glance

Course code
MATH F101 Multivariable Calculus
Source
BITS Pilani Bulletin 2025-2026
Units
3 units (3 lecture, 0 practical/project)
Semester
First year, first semester for most B.E. programmes
Prerequisites
Not stated in the course description
Covers
Sequences and series, Taylor series, polar coordinates and integrals, functions of several variables, partial derivatives, multiple integrals, vector calculus with Green, Gauss and Stokes
Next course
MATH F102 Linear Algebra and Complex Variables in the second semester
Practice here
Sequences and series, power series and polar and Calculus 3

Try it yourself

For $a_n = 6n$, find the partial sum $S_4 = a_1 + a_2 + a_3 + a_4$.
S_4 = 6 + 12 + 18 + 24
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On this page
  1. Where MATH F101 fits
  2. What MATH F101 covers
  3. MATH F101 topic map
  4. Example problems at the MATH F101 level
  5. How to do well in MATH F101

MATH F101 Multivariable Calculus is the first semester calculus course for most B.E. programmes at BITS Pilani in the Bulletin 2025-2026, the official handbook of courses and semester-wise patterns. It is a 3 unit course, and it covers series, Taylor series, polar coordinates, several variable calculus and vector calculus in one semester. This guide follows the bulletin's course description and maps each topic to free practice.

Where MATH F101 fits

The 2025-26 semester-wise patterns for B.E. programmes such as Computer Science, Mechanical, Electrical and Electronics, Electronics and Communication, Chemical and Civil list MATH F101 in the first year, first semester. The second semester has MATH F113 Probability and Statistics and MATH F102 Linear Algebra and Complex Variables. MATH F211 Mathematics III (differential equations) follows in the second year.

The bulletin also notes that MATH F111 Mathematics I is replaced by MATH F101 Multivariable Calculus in the BITS-Iowa State 2+2 programme. The B.E. Robotics and Industrial Automation pattern still lists MATH F111, so check the pattern for your own programme.

Course Units Semester (most B.E. programmes) Focus
MATH F101 Multivariable Calculus 3 Year 1, Semester 1 Series, Taylor series, polar, several variables, vector calculus
MATH F113 Probability and Statistics 3 Year 1, Semester 2 Probability and statistics
MATH F102 Linear Algebra and Complex Variables 3 Year 1, Semester 2 Linear algebra and complex analysis
MATH F211 Mathematics III 3 Year 2 Differential equations and Laplace transforms

What MATH F101 covers

According to the bulletin, the course covers:

  • convergence of sequences and series of real numbers;
  • Taylor series of functions;
  • polar coordinates and applications involving integrals;
  • functions of several variables;
  • partial derivatives and applications;
  • multiple integrals and applications;
  • vector calculus and applications, including the theorems of Green, Gauss and Stokes.

The bulletin does not state a prerequisite, so the course assumes Class 12 calculus.

MATH F101 topic map

MATH F101 topic Practice Read
Sequences Sequences Convergence tests
Series and convergence tests Choosing a test Convergence tests practice
Geometric and p-series Integral test and p-series Geometric series formula
Taylor series Maclaurin series Taylor series, Taylor's theorem
Polar coordinates Polar coordinates Parametric and polar practice
Area in polar coordinates Polar area Arctangent
Functions of several variables Functions of several variables Partial derivatives
Partial derivatives and applications Lagrange multipliers Lagrange multipliers
Gradient and tangent planes Gradient and directional derivatives Gradient and directional derivatives
Multiple integrals Iterated integrals Double integrals
Applications of multiple integrals Triple integrals Double integrals practice
Vector fields and line integrals Line integrals of vector fields Vectors, dot and cross product
Green's theorem Green's theorem Green's theorem
Gauss and Stokes Stokes and divergence theorems Divergence theorem, Stokes' theorem

Example problems at the MATH F101 level

These are original practice problems, not past BITS papers.

1. Ratio test. For \sum \frac{n^2}{3^n}, \frac{a_{n+1}}{a_n} = \frac{(n + 1)^2}{3n^2} \to \frac{1}{3} < 1, so the series converges.

2. Area in polar coordinates. The area inside the cardioid r = 1 + \cos\theta is

\frac{1}{2}\int_0^{2\pi}(1 + \cos\theta)^2\,d\theta = \frac{1}{2}\left(2\pi + 0 + \pi\right) = \frac{3\pi}{2}

3. Divergence theorem. For \mathbf{F} = \langle x, y, z \rangle over the unit ball, \nabla \cdot \mathbf{F} = 3, so the outward flux is 3 \cdot \frac{4\pi}{3} = 4\pi.

How to do well in MATH F101

  • Start series early. It comes first and feels different from Class 12 calculus. The series practice lesson builds the habit of picking a test fast.
  • Visualise in 3D. Sketch surfaces and regions before you set up multiple integrals.
  • Connect the big theorems. Green, Gauss and Stokes all trade a boundary integral for an integral over the inside.
  • Practise in short daily sessions on practice and keep the formula sheet close before quizzes and the comprehensive exam.

Practice it now

Series and partial sums

Solve real problems on this topic with instant feedback, hints and a step-by-step walkthrough for every answer. Free, no sign-up needed to start.

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Frequently asked questions

What is MATH F101 at BITS Pilani?
MATH F101 Multivariable Calculus is a 3 unit first year course listed in the BITS Pilani Bulletin 2025-2026. Its description covers convergence of sequences and series of real numbers, Taylor series, polar coordinates and integrals, functions of several variables, partial derivatives, multiple integrals and vector calculus including the theorems of Green, Gauss and Stokes.

Is MATH F101 the same as MATH F111?
They cover similar ground, but they are separate courses. The bulletin's note for the BITS-Iowa State 2+2 programme says MATH F111 Mathematics I is replaced by MATH F101 Multivariable Calculus. Most B.E. semester-wise patterns in the 2025-26 bulletin list MATH F101, while the B.E. Robotics and Industrial Automation pattern still lists MATH F111.

When do BITS students take MATH F101?
In the 2025-26 semester-wise patterns for B.E. programmes such as Computer Science, Mechanical, Electrical and Electronics, Chemical and Civil, MATH F101 is in the first semester of the first year, alongside courses such as PHY F101 and CHEM F101.

How should I prepare for MATH F101?
Make sure Class 12 differentiation and integration are fluent, because the course starts with series and moves quickly to several variables. Practise convergence tests and partial derivatives a little every day.

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