**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*).

**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.

**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.

- Prof. Sara Billey has some
**really great advice**for students which I recommend you read before starting this course. - I believe in the
**axioms laid down by Prof. Federico Ardila**which I recommend you familirize yourself with. - Along with learning mathematics it is also important that you learn how to write mathematics. I recommend this
**great resource**to get started with writing mathematics clearly. In fact, there is also a**grammar for mathematics**. - Finally, here is a
**study guide for mathematics**.

**Class Notes**

*Multivariable Calculus*

Review

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

*ODEs*

Introductory Lecture

**Tutorials**

*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

*ODEs*

Surprise Test 1, Section A

Assessment I, Sections A & B

Assessment I, Sections C & D

Assessment II, Sections A & B and Hints and Solutions