IIT Delhi MTL1002 Linear Algebra and Differential Equations Guide

MTL1002 Mathematics II Linear Algebra and Differential Equations is the second first year mathematics course at the Indian Institute of Technology Delhi (IIT Delhi) in the curriculum for 2025 onwards. It carries 4 credits, with 3 lectures and 1 tutorial a week, and pairs with MTL1001 Mathematics I Calculus. This guide follows the official course template on the IIT Delhi curriculum site and focuses on the calculus you need for the differential equations half.

What MTL1002 covers

Linear algebra. Systems of linear equations, matrices and Gauss elimination, elementary row operations, row reduced echelon form, row space, column space, null space and rank; vector spaces over \mathbb{Q}, \mathbb{R} and \mathbb{C}, subspaces, independence, span, basis, dimension, sums and direct sums; inner products and norms; linear transformations, the rank-nullity theorem, matrix representation, change of basis and similarity; eigenvalues, eigenvectors, the characteristic polynomial and the Cayley-Hamilton theorem (without proof).

Differential equations. A review of first order equations, existence and uniqueness for initial value problems and Picard's theorem; linear independence of solutions, the dimension of the solution space and the Wronskian; linear ODEs with constant coefficients of second and higher order, Cauchy-Euler equations, the method of undetermined coefficients and variation of parameters; systems of linear ODEs with constant coefficients, the fundamental matrix and matrix methods; the Taylor series method; and the Laplace transform and its use in solving ODEs.

The course outcomes include using row reduction to find inverses, ranks and solutions of linear systems, diagonalising linear transformations, and modelling physical phenomena with differential equations solved using linear algebra.

MTL1002 topic map (calculus side)

PracticeCalculus does not teach linear algebra, so the table covers the differential equations topics and the calculus they rely on.

Example problems at the MTL1002 level

These are original practice problems.

1. A constant coefficient ODE. For y'' - 3y' + 2y = 0, the characteristic equation r^2 - 3r + 2 = 0 has roots 1 and 2, so y = C_1 e^{x} + C_2 e^{2x}.

2. A Laplace transform. For s > a,

3. A Wronskian. For y_1 = \cos x and y_2 = \sin x, W = y_1 y_2' - y_1' y_2 = \cos^2 x + \sin^2 x = 1 \ne 0, so the solutions are independent.

How to do well in MTL1002

• Keep your integration fluent. Laplace transforms are improper integrals, and inverse transforms usually need partial fractions.
• Link the two halves. The solution space of a linear ODE is a vector space, and the Wronskian is a test for linear independence, so the linear algebra makes the ODE theory make sense.
• Use the weekly tutorial to practise full solutions, including checking initial conditions at the end.
• Practise in short daily sessions on practice and revise from the formula sheet.