# MA1012

Multivariable Calculus & Ordinary Differential Equations

# Information

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

Section C

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

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.

Textbook: The recommended textbook for the first part of the course is A Course in Multivariable Calculus and Analysis by Sudhir R. Ghorpade and Balmohan V. Limaye (Springer, 2019 printing). The recommended textbook for the second part of the course is Differential Equations with Applications and Historical Notes (third edition) by George F. Simmons (CRC Press, 2017). I will supplement some of the topics with my own notes.

Class Notes

Multivariable Calculus

ODEs

Problem Sheets

Multivariable Calculus

ODEs

Exams