 # JNTU B Tech 1st Sem Syllabus for Mathematics I

## JNTU B Tech 1st Sem Syllabus for Mathematics I

University: Jawaharlal Nehru Technological University Hyderabad

MATHEMATICS- I
B.Tech. I Year I Sem. L T/P/D C
Course Code: MA101BS 3 1/0/0 3

UNIT – I Sequences – Series

Basic definitions of Sequences and series – Convergences and divergence – Ratio test – Comparison test– Integral test – Cauchy’s root test – Raabe’s test – Absolute and conditional convergence

UNIT – II Functions of Single Variable

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 – III Application of Single variables

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

UNIT – IV Integration & its applications

Riemann Sums , Integral Representation for lengths, Areas, Volumes and Surface areas in Cartesian and polar coordinates multiple integrals – double and triple integrals – change of order of integration- change
of variable

UNIT – V Differential equations of first order and their applications

Overview of differential equations- exact, linear and Bernoulli. Applications to Newton’s Law of cooling, Law of natural growth and decay, orthogonal trajectories and geometrical applications.

UNIT – VI Higher Order Linear differential equations and their applications

Linear differential equations of second and higher order with constant coefficients, RHS term of the type f(X)= e ax , Sin ax, Cos ax, and xn, e ax V(x), x n V(x), method of variation of parameters. Applications bending of beams, Electrical circuits, simple harmonic motion.

UNIT – VII Laplace transform and its applications to Ordinary differential equations

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.

UNIT – VIII Vector Calculus

Vector Calculus: Gradient- Divergence- Curl and their related properties Potential function – Laplacian and second-order operators. Line integral – work is done ––- Surface integrals – Flux of a vector-valued function.
Vector integrals theorems: Green’s -Stoke’s and Gauss’s Divergence Theorems (Statement & their Verification).

### TEXTBOOKS:

1. Engineering Mathematics – I by P.B. Bhaskara Rao, S.K.V.S. Rama Chary, M. Bhujanga Rao.
2. Engineering Mathematics – I by C. Shankaraiah, VGS Booklinks.