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MA05363 / MA05363 / MA07363 Mathematics I Syllabus
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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, 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 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.
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.
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.