# RTM Nagpur University 1st SEM BE Syllabus

# Applied Mathematics I

UNIT- I: Differential Calculus: (12 Hrs)

Successive Differentiation, Taylor‟s & Maclaurin‟s series for one variable, indeterminate forms, Curvature and Radius of curvature, Circle of Curvature.

UNIT- II: Partial Differentiation: (12 Hrs)

Functions of several variables, First and Higher order derivatives, Euler‟s theorem , Chain rule and total differential coefficient, Jaccobians, Taylor‟s & Maclaurin‟s series for two variables, Maxima & Minima of functions of two variables, Langrage‟s method of undetermined multipliers.

UNIT – III: Matrices (06 Hrs)

Matrix, Inverse of Matrix by adjoint method, Inverse by Partitioning method, Solution of system of linear equations, Rank of Matrix, Consistency of linear system of equations

UNIT – IV: First Order Differential Equations (10 Hrs)

First order& first degree differential equations: Linear, Reducible to linear & Exact differential equations (excluding the case of I. F.).First order& higher degree differential equations Application of First order& first degree differential equations to simple electrical circuits.

UNIT – V: Higher Order Differential Equations (14 Hrs)Higher order differential equations with constant coefficients, P. I. by method of Variation of parameters, Cauchy„s & Legendres‟s homogeneous differential equations, Simultaneous differential equations, Differential equations. Applications of differential equations to Oscillations of a Spring, Oscillatory Electrical Circuits, Deflection of Beams.

UNIT – VI: Complex Numbers (06 Hrs)

Cartesian & Polar forms of Complex Numbers, Geometrical representation of fundamental operations on complex numbers, De Moivre‟s theorem, Hyperbolic functions and their inverse, Logarithm of complex number, Separation of real and imaginary parts.

Books Recommended:

1. Higher Engineering Mathematics by B. S. Grewal

2. Applied Mathematics Volume I & II, by J. N. Wartikar

3. Textbook of Engineering Mathematics by Bali, Iyenger (Laxmi Prakashan)