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# JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY

I Year B.Tech. ITT P C

3+1*06

# 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, Sin ax, cos ax, polynomials in x, eV(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.

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