Multivariable Calculus & Ordinary Differential Equations


Instructor: Dr Manjil Pratim Saikia

Contact: [email protected] (please only use this email address to send me emails related to this course)

Lecture Time & Place:

Section A: M 1000, T 1000, W 1000 and Th 1000 in Room 5

Section B: M 1200, T 1200, W 1200 and F 1000 in Room 6

Office Hours: T 1700-1800 and Th 1700-1800 in Faculty Block - II, Office F-7 (also by appointment)

My schedule is available here (please login via your IIIT email account to view the calendar).

Course Prerequisites: It will be assumed that students are familiar with the course MA1011.

Attendance Policy: Attendance is mandatory, institute policy is minimum 75% continous attendance failing which the student is not allowed to sit in exams. If you have a genuine reason for missing the lectures please talk to me or the HoD as soon as possible (talking just a few weeks before the exam will not be sufficient).

Course Details

Multivariable Calculus: Vector functions of one variable – continuity, differentiation and integration; functions of several variables - continuity, partial derivatives, directional derivatives, gradient, differentiability, chain rule; tangent planes and normals, maxima and minima, Lagrange multiplier method; repeated and multiple integrals with applications to volume, surface area, moments of inertia, change of variables; vector fields, line and surface integrals; Green’s, Gauss’s and Stokes’ theorems and their applications.

Ordinary Differential Equations: First order differential equations - exact differential equations, integrating factors, Bernoulli equations, existence and uniqueness theorem, applications; higher-order linear differential equations - solutions of homogeneous and non-homogeneous equations, method of variation of parameters, series solutions of linear differential equations, Legendre equation and Legendre polynomials, Bessel equation and Bessel functions of first and second kinds. Laplace and inverse Laplace transforms; properties, convolutions; solution of ODE by Laplace transform. Systems of first-order equations, two-dimensional linear autonomous system, phase plane, critical points, stability.


  • We will follow relative grading.
  • 50% of the total marks will come from the end semester exam (of 100 marks).
  • 16.67% of the total will come from Assessment I (of 25 marks), another 16.67% of the total will come from Assessment II (of 25 marks).
  • All these three exams will be closed book and annonced before hand.
  • The rest of the 16.66% will come from two suprise tests (of 12.5 marks each) which will not be announced beforehand.

Reading Materials

Textbook: I will use my own notes.

I still recommend that you follow a book of your own. I recommended the following textbook for the first part of the course: A Course in Multivariable Calculus and Analysis by Sudhir R. Ghorpade and Balmohan V. Limaye (Springer, 2019 printing) and the following textbook for the second part of the course: Differential Equations with Applications and Historical Notes (third edition) by George F. Simmons (CRC Press, 2017).

Two other books which are good resources are Calculus and Analytic Geometry (9th ed.) by Goerge B. Thomas, Jr. and Ross L. Finney (Pearson India, 2010) and Differential Equations (3rd ed.) by Shepley L. Ross (Wiley, 2007).

You can choose any book of your choice. Make sure to solve all the practice problems that are assigned or discussed in the tutorials for a full understanding of the course.

Advice for Students

Notes and Tutorials

Class Notes

Multivariable Calculus

Vector Valued Functions
Functions of Several Variable: Limits, Continuity and Differentiability
Directional Derivatives, Gradient and Tangent Plane
Theorems on Differentiable Functions; Maxima and Minima
Langrange Multiplier Method
Double Integrals & Change of Variables
Triple Integrals
Parametric Surfaces & Surface Integrals
Line Integrals & Green’s Theorem
Curl, Divergence & Stoke’s Theorem


Introductory Lecture


Multivariable Calculus

Problem Sheet 1
Problem Sheet 2
Problem Sheet 3
Problem Sheet 4
Problem Sheet 5
Problem Sheet 6
Problem Sheet 7
Problem Sheet 8



Surprise Test 1, Section A
Assessment I, Sections A & B
Assessment I, Sections C & D
Assessment II, Sections A & B and Hints and Solutions