Sep-Dec 2026
ECS 103: Engineering Mathematics-I
Learning Objectives :
The course focuses on computational and mathematical aspects of engineering sciences. It includes exposure to mathematical software tools such as Matlab/Mathematica and others to solve mathematical problems in engineering applications.
Tutors : unknown
Teaching Assistants : Harsh Gupta(2210703), Suprabhat Sinha(2510708), Sameeksha Malviya(2610707), Ishika Das(2610703)
Prerequisites :
Other Prerequisites :
Text Books :
G. Strang, Linear Algebra and its Applications (4th Edition), Thomson, 2006.
E. Kreyszig, Advanced Engineering Mathematics (10th Edition), John Wiley, 2011.
T. M. Apostol, Calculus, Volumes 1 & 2 (2nd Edition), Wiley Eastern, 1980.
Reference Books :
B. S. Grewal, Higher Engineering Mathematics, 44th edition
Content :
Module A: (Linear Algebra)
Vectors on Rn, linear independence and dependence, linear span of a set of vectors, vector subspaces of Rn, basis of a vector subspace.
Systems of linear equations, matrices and Gauss elimination, row space, null space, and column space, rank of a matrix.
Determinants and rank of a matrix in terms of determinants.
Abstract vector spaces, linear transformations, matrix of a linear transformation, change of basis and similarity, rank-nullity theorem.
Inner product spaces, Gram-Schmidt process, orthonormal bases, projections and least squares approximation.
Eigenvalues and eigenvectors, characteristic polynomials, eigenvalues of special matrices (Orthogonal, unitary, hermitian, symmetric, skew-symmetric, normal)
Rayleigh quotient and its optimization for an eigenvector
Module B: (Calculus I/ Calculus of One Variable)
Review of limits, continuity, differentiation.
Mean value theorem, Taylor’s theorem, maxima and minima.
Fundamental theorem of calculus.
Definite integral, applications to area and volume.
Convergence of sequences and series: power series.
Partial derivatives, gradient and directional derivatives, chain rule, maxima and minima
Introductory concepts of multivariate calculus
Module C: Applications
Principal component analysis, examples and applications
Techniques and realization of Module A and B contents in Matlab/Mathematica
Homeworks and Notes are posted on Google classroom