M T W T F S S

# Paper: Applied Mathematics – I                                                       3          1          4

INSTRUCTIONS TO PAPER SETTERS:                                                                               MAXIMUM MARKS: 75

1.             Question No. 1 should be compulsory and cover the entire syllabus. This question should have objective or short answer type questions. It should be of 25 marks.

2.             Apart from question no. 1, rest of the paper shall consist of four units as per the syllabus. Every unit should have two questions. However, student may be asked to attempt only 1 question from each unit. Each question should be of 12.5 marks.

# UNIT I

COMPLEX NUMBERS AND INFINITE SERIES: De Moivre’s theorem and roots of complex numbers. Euler’s theorem, Logarithmic Functions, Circular, Hyperbolic Functions and their Inverses. Convergence and Divergence of Infinite series, Comparison test d’Alembert’s ratio test. Higher ratio test, Cauchy’s root test. Alternating series, Lebnitz test, Absolute and conditioinal convergence.                                                                         [No. of Hrs. 10]

# UNIT II

CALCULUS OF ONE VARIABLE: Successive differentiation. Leibnitz  theorem (without proof) McLaurin’s and Taylor’s expansion of functions, errors and approximation.

Asymptotes of Cartesian curves. Curveture of curves in Cartesian, parametric and polar coordinates, Tracing of curves in Cartesian, parametric and polar coordinates (like conics, astroid, hypocycloid, Folium of Descartes, Cycloid, Circle, Cardiode, Lemniscate of Bernoulli, equiangular spiral). Reduction Formulae for evaluating

Finding area under the curves, Length of the curves, volume and surface of solids of revolution.                                                                                                                          [No. of Hrs. 15]

# UNIT III

LINEAR ALGEBRA – MATERICES: Rank of matrix, Linear transformations, Hermitian and skeew – Hermitian forms, Inverse of matrix by elementary operations. Consistency of linear simultaneous equations, Diagonalisation of a matrix, Eigen values and eigen vectors. Caley – Hamilton theorem (without proof).                                                                 [No. of Hrs. 09]

# UNIT IV

ORDINARY DIFFERENTIAL EQUATIONS: First order differential equations – exact and reducible to exact form. Linear differential equations of higher order with constant coefficients. Solution of simultaneous differential equations. Variation of parameters, Solution of homogeneous differential equations – Canchy and Legendre forms.

(No. of Hrs. 10]

TEXT BOOKS:

1.         Kresyzig, E., “Advanced Engineering Mathematics”, John Wiley and Sons. (Latest edition).

2.         Jain, R. K. and Iyengar, S. R. K., “Advanced Engineering Mathematics”, Narosa, 2003 (2nd Ed.).

# REFERENCE BOOKS:

1.         Mitin, V. V.; Polis, M. P. and Romanov, D. A., “Modern Advanced Mathematics for Engineers”, John Wiley and Sons, 2001.

2.         Wylie, R., “Advanced Engineering Mathematics”, McGraw-Hill, 1995.

3.         “Advanced Engineering Mathematics”, Dr. A. B. Mathur, V. P. Jaggi (Khanna publications)

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