MATHEMATICS-I
By Department of Mathematics, IIT Roorkee (Autumn 2020)
By Department of Mathematics, IIT Roorkee (Autumn 2020)
Course Name: Mathematics-I Course Code: MAN-001 Credits: 4 Contact Hours per Week: 3 Lectures & 1 Tutorial
Welcome to webpage of MAN-001 (Mathematics-I) course.
This is a compulsory course for all first year undergraduate students. Here, you can find important notices, assignments and other stuff related to this course for the Autumn Semester 2020-21.
Objective: To provide essential knowledge of basic tools of Differential Calculus, Integral Calculus , Vector Calculus and Matrix Algebra for degree students.
Contents:
Matrix Algebra: Elementary operations and their use in getting the Rank, Inverse of a matrix and solution of linear simultaneous equations. Orthogonal, Symmetric, Skew-symmetric, Hermitian, Skew-Hermitian, Normal & Unitary matrices and their elementary properties. Eigen-values and Eigenvectors of a matrix, Cayley- Hamilton theorem, Diagonalization of a matrix.
Differential Calculus: Limit, Continuity and differentiability of functions of two variables, Euler’s theorem for homogeneous equations, Tangent plane and normal. Change of variables, chain rule, Jacobians, Taylor’s Theorem for two variables, Error approximations. Extrema of functions of two or more variables, Lagrange’s method of undetermined multipliers.
Integral Calculus: Review of curve tracing and quadric surfaces, Double and Triple integrals, Change of order of integration, Change of variables, Gamma and Beta functions, Dirichlet’s integral, Applications of Multiple integrals such as surface area, volumes, centre of gravity and moment of inertia.
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.
References:
E. Kreyszig, Advanced Engineering Mathematics, 10th edition, John Wiley and Sons, Inc., U.K, 2015
R.K. Jain and S.R.K. Iyenger, Advanced Engineering Mathematics,4th Edition, Narosa Publishing House, 2012
Jr. G. B. Thomas, M.D. Weir, J. R. Hass, Thomas’ Calculus, 12th Edition, Pearson Education, 2013
Tentative Evaluation Weightage: Total Marks 100: CWS 50 ETE 50
CWS 50 : TA 20 Quiz 20 Instructor 10
CWS: Class Work Sessional
TA 20: This part will be evaluated by the Tutorial Assistant (TA) on the basis of timely submission of assignments and performance in the tutorials.
Quiz 20: In this part, two quizzes will be conducted during the semester for 15-20 minutes each. Each of them will be of 10 marks.
Instructor 10: 10 marks will be given by instructor based on his interaction during the lectures.
ETE: End Term Examination
***** Please note that the above evaluation process is only tentative and can be changed as per the instructions given by the institute in future
Course Coordinators:
Co-odinator: Prof. Ankik Kumar Giri
Deputy Coordinator: Prof. Ram Krishna Pandey
Deputy Coordinator: Prof. Mahendra Kumar Verma