# Applied Mathematics-I-Nagpur

Teaching Scheme
Lectures: 4 Hours/ Week
Tutorial: 1 Hours / Week

Examination Scheme
Theory
T (U) : 40 Marks
T (I) : 20 Marks
Duration of University Exam. : 03 Hours

UNIT- I: Differential Calculus: (12Hrs)

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 of the type $latex \frac{d^2y}{dx^2}=f\left(x\right)\;and\;\frac{d^2y}{dx^2}=f\left(y\right).$ 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)

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