Mathematics - II

Classes will commence from 2nd February 2026

Pre-requisites: 

Single Variable Calculus, Matrix & Determinant, and Vector Algebra (Class 12 NCERT level)

Course Syllabus: 

[Unit 1] - Vector Calculus: Differentiation of vectors, gradient, divergence, curl and their physical meaning. Identities involving gradient, divergence and curl. Line and surface integrals. Green’s, Gauss and Stroke’s theorem and their applications.

[Unit 2] - Linear Algebra: Introduction to linear equations, matrices, Gaussian elimination, LU-Decomposition, inverses. Vector spaces (VS), subspaces, linear independence, span, column space, row space, null space, basis, dimension. Computation of null space, rank, rank-nullity theorem and its applications. Linear transformations, matrix of a linear transformation, change of basis, similarity, determinants. Eigenvalues, eigenvectors, characteristic polynomials, minimal polynomials, Cayley-Hamilton theorem. Algebraic multiplicity, Geometric multiplicity, diagonalization. Inner product VS, Gram-Schmidt process, eigenvalues for various types of matrices.

[Unit 3] - Ordinary Differential Equations: First-order linear equations, Bernoulli’s equations, Exact equations and integrating factor, Higher order linear, differential equations with constant coefficients. Partial Differential Equations: First-order linear PDE, quasi-linear PDE, method of characteristics, Cauchy problem, first-order nonlinear PDE of special type.

Course Outcomes: 

Students will be able to understand

1. Vector-valued functions and, the integration associated with vector-valued functions. 

2. Solution procedure and challenges related to a system of linear equations. 

3. Vector space, linear transformation and importance of eigenvalues & eigenvectors. 

4. Fundamentals of differential equations (ordinary and partial) 

Recommended Books: 

Text Books:

1. B S Grewal, Higher Engineering Mathematics, Khanna Publishers, 44th edition, (2017).

2. G.B. Thomas and R.L. Finney, Calculus and Analytic Geometry, Pearson Education, 9th edition, (2007).

3. R.K. Jain and S.R.K Iyenger, Advanced Engineering Mathematics, Narosa Publishing House, 11th edition, (2011).

4. Kreyszig Erwin, Advanced Engineering Mathematics, John Wiley, 8th edition, (2006).

Reference Books:

1. V.K. Krishnamurthy, V.P. Mainra and J.L. Arora, An Introduction to Linear Algebra, Affiliated East West Press, (1976).

2. Stewart James., Essential Calculus, Thomson Publishers, 6th edition, (2007).

3. G.F. Simmons, Differential Equations (With Applications and Historical Notes), Tata McGraw Hill, (2009).

4. Gilbert Strang, Linear Algebra and Its Applications, Cengage Learning, 4th edition, (2006).

Evaluation Scheme: 

Students will be evaluated on a scale of 150 = {MTE, ETE, Practical, Self-Learning} where

MTE - Open Book Mid Term Exam - 50 Marks for 2 Hr duration

ETE - Open Book End Term Exam - 50 Marks for 2 Hr duration

Practical - MATLAB Coding Exam of 20 Marks for 1 Hr duration

Quiz - quiz (based on pattern of GATE/UPSC/NET) of 30 Marks 

Note: A minimum of 35 out of 150 marks is required to pass the course. The grading will be relative-scaled.

Exam/Test Schedule: 

(It will be updated soon.)