# JNTU Kakinada EEE Mathematics I Syllabus

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY

KAKINADA

I Year B.Tech EEE T P C

3+1* 0 6

MATHEMATICS – I

UNIT – I

Differential equations of first order and first degree – exact, linear and Bernoulli. Applications to Newton’s

Law of cooling, Law of natural growth and decay, orthogonal trajectories.

UNIT – II

Non-homogeneous linear differential equations of second and higher order with constant coefficients with

RHS term of the type e ax , Sin ax, cos ax, polynomials in x, e ax V(x), xV(x), method of variation of

parameters.

UNIT – III

Rolle’s Theorem – Lagrange’s Mean Value Theorem – Cauchy’s mean value Theorem – Generalized

Mean Value theorem (all theorems without proof) Functions of several variables – Functional dependence-

Jacobian- Maxima and Minima of functions of two variables with constraints and without constraints

UNIT – IV

Radius, Centre and Circle of Curvature – Evolutes and Envelopes Curve tracing – Cartesian , polar and

Parametric curves.

UNIT – V

Applications of integration to lengths, volumes and surface areas in Cartesian and polar coordinates

multiple integrals – double and triple integrals – change of variables – change of order of integration.

UNIT – VI

Sequences – series – Convergences and divergence – Ratio test – Comparison test – Integral test –

Cauchy’s root test – Raabe’s test – Absolute and conditional convergence

UNIT – VII

Vector Calculus: Gradient- Divergence- Curl and their related properties of sums- products- Laplacian and

second order operators. Vector Integration – Line integral – work done – Potential function – area- surface

and volume integrals Vector integral theorems: Green’s theorem-Stoke’s and Gauss’s Divergence

Theorem (With out proof). Verification of Green’s – Stoke’s and Gauss’s Theorems.

UNIT – VIII

Laplace transform of standard functions – Inverse transform – first shifting Theorem, Transforms of

derivatives and integrals – Unit step function – second shifting theorem – Dirac’s delta function –

Convolution theorem – Periodic function – Differentiation and integration of transforms-Application of

Laplace transforms to ordinary differential equations Partial fractions-Heaviside’s Partial fraction

expansion theorem.

Text Books:

1. A text Book of Engineering Mathematics, Vol-1 T. K. V. Iyengar, B. Krishna Gandhi and Others,

S. Chand & Company.

2. A text Book of Engineering Mathematics, C. Sankaraiah, V. G. S. Book Links.

3. A text Book of Engineering Mathematics, Shahnaz Bathul, Right Publishers.

4. A text Book of Engineering Mathematics, P. Nageshwara Rao, Y. Narasimhulu & N. Prabhakar

Rao, Deepthi Publications.

References:

1. A text Book of Engineering Mathematics, B. V. Raman, Tata Mc Graw Hill.

2. Advanced Engineering Mathematics, Irvin Kreyszig, Wiley India Pvt. Ltd.

3. A text Book of Engineering Mathematics, Thamson Book Collection.