Mathematics-I Syllabus

A Hunt for Reaching Horizon of Science

Syllabus

UNIT — I

Linear Algebra: Introduction to Matrices, Elementary row and column operations, Rank of a Matrix, Echelon form, System of linear equations, Eigenvalues, Eigenvectors, Cayley-Hamilton theorem, Diagonalization, Quadratic forms, signature and Index.

UNIT — II

Infinite Series: Sequences, Infinite series, Convergence and Divergence , P-Series test, Geometric Series test, Comparison tests, D’Alembert’s Ratio test, Raabe’s test, Cauchy’s nth root test, Alternating series, Leibnitz’s test, Absolute Convergence, Conditional Convergence.

UNIT — III

Differential Calculus: Rolle’s theorem, Lagrange’s and Cauchy’s mean value theorems, Taylor’s series, Curvature, Radius of curvature , Envelopes, Evolutes and Involutes, Asymptotes of a curve, Curve sketching (cartesian).

UNIT — IV

Functions of Several Variables: Limits and Continuity of Functions of two variables, Partial derivatives, Total differentials and derivatives, Derivatives ofcomposite and implicit functions, Higher order partial deriyatives, Taylor’s theorem for functions of two variables, Maxima and minima of functions of two variables, Jacobian, Change of variables. 

UNIT — V 

Vector Calculus: Scalar and vector fields, Vector differentiation, Gradient of a scalar field, Directional derivative, Divergence and Curl of a vector field, Line, Surface and Volume integrals , Green’s theorem in a plane, Gauss’s divergence theorem, Stoke’s theorem(without proof) and their applications.

 Suggested Reading : 

1) Larry Turyn, “Advanced Engineering Mathematics” , CRC Publications, 2014. • 
2) R.K.Jain and S.R.K.Iyengar, “Advanced Engineering Mathematics”, Narosa Publications, Fourth Edition, 2014.
 3) Srimanta Pal and Subodh C. Bhunia, ” Engineering Mathematics”, Oxford University Press,2015. 
4) Peter V.O’Neil ” Advanced Engineering Mathematics”, CENGAGE Learnig, 7th Edition,2013. 
5) Eerwin Kreyszig, “Advanced Engineering Mathematics”, Wiley- India, 9thEdition, 2012. 6) Manice D. Weir, Joel Hass, Frank R. Giordano, “Thomas’ Calculus”, Pearson Publications, 11thEdition.