Mathematics I - JNTU Anantapur First Year Syllabus 2009 |
UNIT-I |
Differential equations of first order and first degree Exact, linear and Bernoulli equations. Applications: to Newton 's law of cooling, law of natural growth and decay, orthogonal trajectories.
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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 (excluding proof). Simple examples of Taylor's and Maclaurin's Series - Functions of several variables Jacobian Maxima and Minima of functions of two variables, Lagrangian method of Multipliers with three variables only. |
UNIT IV |
Raidus of Curvature Curve tracing Cartesian, polar and parametric curves. Applications of integration to lengths, volume and surface area of solids of revolution in Cartesian and polar coordinates.
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UNIT V |
Multiple integral: Double and triple integrals Change of Variables Change of order of integration. |
UNIT VI |
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 Laplace transform of Periodic function.
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UNIT VII |
Differentiation and integration of Laplace transform Application of Laplace transforms to ordinary differential equations of first and second order. |
UNIT VIII |
Vector Calculus: Gradient Divergence Curl and Their properties; Vector integration Line integral - Potential function Area , Surface and volume integrals. Vector integral theorems: Green's theorem Stoke's and Gauss's Divergence Theorem (excluding their proof). Verification of Green'sStoke's and Gauss's Theorems.
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REFERENCE |
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-1,E. Rukmangadachari, E. Keshava Reddy, Pearson
Education.
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Reference Books |
1. A Text Book of Engineering Mathematics, B.V. Ramana, Tata Mc Graw Hill.
2. A Text Book of Engineering Mathematics, Thomson Book Collection.
3. A Text Book of Advanced Engineering Mathematics A Computer Approach,
N.Bail, M.Goyal & C. Watkins.
4. Engineering Mathematics, Sarveswara Rao Koneru, Universities Press.
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