MODULE-1(18 HOURS) – MATRIX
Elementary transformation-echelon form-rank using elementary transformation by reducing in to echelon form- solution of linear homogeneous and non- homogeneous equations using elementary transformation. Linear dependence and independence of vectors- eigen vectors – properties of eigen values and eigen vectors – linear transformation – orthogonal transformation-digitalization- reduction of quadratic form into sum of squares using orthogonal transformation – rank, index , signature of quadratic form
MODULE 2 (18 HOURS) – PARTIAL DIFFERENTIATION
Partial differential : chain rules – statement of eulers theorem for homogeneous functions – jacobian – application of taylers series for function of variables- maxima and of function of two variable.
MODULE 3 (18 HOURS) – MULTIPLE INTEGRALS
Double integrals in Cartesian and polar co-ordinates – change of order of integration – area using double integrals- change of variables using jacobian – triple integrals in Cartesian, cylindrical and spherical co-ordinates – volume using triple integrals – change of variables using jacobian – simple problems.
MODULE 4 (18 HOURS) – ORDINARY DIFFERENTIAL EQUATIONS
Linear differential equation with constant coeffients – complimentary function and particular integral – finding particular integral using method of variation of parameters – eulers Cauchy equations – ledgers equations.
MODULE 5 (18 HOURS) – LAPLACE TRANSFORMS
Laplace transforms – shifting theorem – differentiation and integration of transforms – laplace transforms of derivatives and integrals – inverse transforms – application of convolution property – laplace transformation of unit step function – second shifting theorem – laplace transform of unit impulse function and periodic function – solution of linear differential equation with constant coefficients using laplace transforms.
For engineering physics syllabus visit http://knol.google.com/k/jean-joy/syllabus-of-m-g-university-2010/3ibgwunvqi9mp/16
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