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 Nonhomogeneous 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, e 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 theoremStoke’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 transformsApplication of Laplace transforms to ordinary differential equations Partial fractionsHeaviside’s Partial fraction expansion theorem.
Text Books: 1. A text Book of Engineering Mathematics, Vol1 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
Reference: Http://www.jntu.ac.in/
