MA6251 – ENGINEERING MATHEMATICS – II SYLLABUS (REGULATION 2013) ANNA UNIVERSITY
UNIT I: VECTOR CALCULUS
(MA6251) 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).
|Gradient, Directional derivative, normal derivative,unit normal vector||FREE||00:00:00|
|Angle b/w the surface , scalar potential||FREE||00:30:00|
|Divergence, solenoidal, curl & irrotational vector||FREE||00:30:00|
|Vector integration, line integration||00:00:00|
|Higher order differential equation with constant co efficients||00:00:00|
|Method of variation of parameter||00:00:00|
|Homogeneous equation of Euler type Cauchy’s type||00:00:00|
|Homogeneous equation of legendre’s type||00:00:00|
|Simultaneous first order linear differential equation with constant co efficient||00:00:00|
|Unit 2 Conclusion||00:00:00|
|Laplace transforms introduction||00:30:00|
|Laplace transformation basic problems||00:00:00|
|First shifting theorem||00:30:00|
|Transforms of derivatives & integrals of functions||00:00:00|
|Integrals of transform||00:00:00|
|Laplace transform of integrals||00:00:00|
|Transform of periodic function||00:00:00|
|Inverse laplace transform||00:00:00|
|Inverse laplace transform of derivatives of F(s)||00:00:00|
|Partial fraction method||00:00:00|
|solution of linear ODE of second order with constant co-efficient||00:00:00|
|Initial value theorem, final value theorem||00:00:00|
|Analytic function introduction||00:30:00|
|Analytic function problems||00:30:00|
|Harmonic conjugate problems||00:00:00|
|Construction of analytic function||00:30:00|
|Bilinear transformation problem||00:30:00|
|Complex integration introduction||00:30:00|
|Complex integration theorem||00:30:00|
|Cauchy’s integral formula||00:30:00|
|Cauchys integral formula for derivatives||00:30:00|
|Taylor and laurents series||00:00:00|
|Cauchys residues theorem||00:30:00|
|Contour integration Type 1||00:30:00|
|Contour integration type 2||00:30:00|
|Contour integration type 3||00:30:00|
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