MA6152 Mathematics – II
Semester : 02
Department : Civil
Year : 1st Year (I Year)
Regulation : 2013
Subject Code / Name : MA6152 Mathematics – II
Content : Question Banks, Books, Lecture Notes, Important Part A 2 Marks Questions and Important Part B 16 Mark Questions
MA6251 MATHEMATICS – II
UNIT I VECTOR CALCULUS
Gradient, divergence and curl – Directional derivative – Irrotational and solenoidal vector fields – Vector integration – Green‟s theorem in a plane, Gauss divergence theorem and Stokes‟ theorem (excluding proofs) – Simple applications involving cubes and rectangular parallelopipeds.
UNIT II ORDINARY DIFFERENTIAL EQUATIONS
Higher order linear differential equations with constant coefficients – Method of variation of parameters – Cauchy‟s and Legendre‟s linear equations – Simultaneous first order linear equations with constant coefficients.
UNIT III LAPLACE TRANSFORM
Laplace transform – Sufficient condition for existence – Transform of elementary functions – Basic properties – Transforms of derivatives and integrals of functions - Derivatives and integrals of transforms - Transforms of unit step function and impulse functions – Transform of periodic functions. Inverse Laplace transform -Statement of Convolution theorem – Initial and final value theorems – Solution of linear ODE of second order with constant coefficients using Laplace transformation techniques.
UNIT IV ANALYTIC FUNCTIONS
Functions of a complex variable – Analytic functions: Necessary conditions – Cauchy-Riemann equations and sufficient conditions (excluding proofs) – Harmonic and orthogonal properties of analytic function – Harmonic conjugate – Construction of analytic functions – Conformal mapping: w = z+k, kz, 1/z, z2, ez and bilinear transformation.
UNIT V COMPLEX INTEGRATION
Complex integration – Statement and applications of Cauchy‟s integral theorem and Cauchy‟s integral formula – Taylor‟s and Laurent‟s series expansions – Singular points – Residues – Cauchy‟s residue theorem – Evaluation of real definite integrals as contour integrals around unit circle and semi-circle (excluding poles on the real axis).
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Part A - 2 Marks |
MA6152 Mathematics – II unit wise 16 marks with answers
- UNIT 1 to UNIT 5 - 16ARKS – DOWNLOAD
Question Papers |
MA6152 Mathematics – II Question Papers
· DOWNLOAD - MA6251 Engineering Mathematics II - November/December 2015 Question Paper
Question Banks |
MA6152 Mathematics – II Question Bank
- Collection 1 – DOWNLOAD
- Collection 2 – DOWNLOAD