Instructions 1. The question paper will consist of five sections A, B, C, D and E. Section E will be Compulsory, it will consist of a single question with 10-20 subparts of short answer type, which will cover the entire syllabus and will carry 20% of the total marks of the semester end examination for the course. Section A, B, C and D will have two questions from the respective sections of the syllabus and each question will carry 20% of the total marks of the semester end examination for the course.

2. Candidates are required to attempt five questions in all selecting one question from each of the section A, B, C and D of the question paper and all the subparts of the questions in section E. Use of non-programmable calculators are allowed.

Section-A MATRICES Matrices, Related matrices, Complex matrices (Hermitian and skew-Hermitian matrices, Unitary matrix), Consistency of linear system of equations, Rank of a matrix, Normal form of a matrix, Vectors, Linear dependence, Consistency of a linear system of equations, System of linear homogeneous equations, Linear and orthogonal transformations, Characteristic equation, Eigen values, Eigen vectors, Properties of Eigen values, Cayley-Hamilton theorem, Quadratic forms and its reduction to canonical form. Section-B DIFFERENTIAL CALCULUS Indeterminate forms, Taylor‟s and Maclaurin‟s series, Partial Differentiation and its geometrical interpretation, Homogeneous functions, Euler‟s theorem and its extension, Total differentials, Composite function, Jacobian, Maxima and minima of functions of two variables, Method of undetermined multipliers. Section-C INTEGRAL CALCULUS Reduction formulas, Quadrature, Rectification, Surface and Volume of revolution for simple curves, Double integrals and their applications, Change of order of integration, Change of variables, Triple integrals and their applications, Change of variable, Beta and Gamma functions and their relationship. Section-D COMPLEX NUMBERS Applications of De Moivre‟s theorem, Root of a complex number, Exponential, Circular, Hyperbolic and Logarithmic functions of a complex variable, Inverse Hyperbolic functions, Real and imaginary parts of Circular and Hyperbolic functions, Summation of the series-„C+iS‟ method. 13

Text BOOKS 1. Advanced Engineering Mathematics: by Erwin Kreyszig, John Wiley and Sons, NC, New York. 2. Advanced Engineering Mathematics: by R. K. Jain & S. R. K Iyengar, Narosa Pub. House. REFERENCE BOOKS 1. Advanced Engineering Mathematics: by C. R. Wylie & L. C. Barrett, McGraw Hill 2. Differential & Integral Calculus: by N. Piskunov, MIR Publications. 3. Calculus and Analytic Geometry, by Thomes, G.B, Finney, R.L. Ninth Edition, Peason Education. 4. Advanced Engineering Mathematics, by Peter. V. O‟ Nil, Wordsworth Publishing Company. 5. Advanced Engineering Mathematics, by Jain, R.K and Lyengar, S.R.K., Narosa Publishing Company. 6. Higher Engineering Mathematics, by Grewal, B.S., Khanna Publishers, New Delhi. 7. Engineering Mathematics, by Taneja, H.C., Volume-I & Volume-II, I.K. Publisher.