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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