Mathematics for Marine Engineering \u2013 II Detailed Syllabus for B.Tech second sem is covered here. This gives the details about credits, number of hours and other details along with reference books for the course.<\/p>\n
The detailed syllabus for Mathematics for Marine Engineering \u2013 II B.Tech 2016-2017 (R13) secondsem is as follows<\/p>\n
OBJECTIVES:<\/strong><\/p>\n To provide the required skill to apply the concepts of ordinary differential equations, vector calculus, complex variable and laplace transformation in marine engineering problems.<\/p>\n UNIT I : ORDINARY DIFFERENTIAL EQUATIONS \u2013 FIRST ORDER<\/strong> UNIT II : ORDINARY DIFFERENTIAL EQUATIONS \u2013 HIGHER ORDER AND APPLICATIONS \u00a0\u00a0<\/strong>\u00a0 \u00a0[12 hours] UNIT III : VECTOR CALCULUS<\/strong> \u00a0 \u00a0\u00a0\u00a0[12 hours]
\n AND APPLICATIONS \u00a0<\/strong> \u00a0 \u00a0 \u00a0[12 hours]
\nDefinition, order and degree, formation of differential equation. Solution of first order, first degree equations in variable separable form, homogeneous equations, other substitutions, Equations reducible to homogeneous and exact differential equations. Equations reducible to exact Integration Factor, Linear differential equation of first order first degree, reducible to linear, Applications to electrical circuits and orthogonal trajectories<\/p>\n
\nHigher (nth) order linear differential equations – definition and complementary solution, Methods of obtaining PI, Method of variation of parameters, Method of undetermined coefficients, Cauchy\u2019s Homogeneous LDE and Legendre\u2019s equations, System of Ordinary Differential Equations Simultaneous equations in symmetrical form , Applications to deflection of beams, struts and columns. Applications to electrical circuits and coupled circuits<\/p>\n
\nGradient Divergence and Curl \u2013 Directional derivative \u2013 Irrotational and solenoidal vector fields \u2013 Vector integration \u2013 Green\u2019s theorem in a plane, Gauss divergence theorem and stokes\u2019 theorem (excluding proofs) \u2013 Simple applications involving cubes and rectangular parallelopipeds.<\/p>\n