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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).

 

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Course Curriculum

QUESTION BANK MA6251 MATHEMATICS FREE 00:00:00
IMPORTANT QUESTIONS
MA6251 Mathematics-II important 2 mark questions FREE 00:00:00
MA6251 Mathematics-II important big questions FREE 00:00:00
Unit 1
U1 Introduction FREE 00:15:00
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
Laplace operator 00:00:00
Vector integration, line integration 00:00:00
surface integral 00:00:00
Volume integral 00:00:00
Gauss divergence 00:00:00
Stokes theorem 00:00:00
Green’s theorem 00:00:00
Unit 2
U2- Introduction 00:00:00
Higher order differential equation with constant co efficients 00:00:00
Type 1 00:00:00
Type 2 00:00:00
Type 3 00:00:00
Type 4 00:00:00
Type 5 00:00:00
Type 6 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
Unit 3
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
Convolution theorem 00:30:00
solution of linear ODE of second order with constant co-efficient 00:00:00
Initial value theorem, final value theorem 00:00:00
Unit 4
Analytic function introduction 00:30:00
Analytic function problems 00:30:00
Harmonic conjugate 00:00:00
Harmonic conjugate problems 00:00:00
Construction of analytic function 00:30:00
Conformal mapping 00:30:00
Bilinear transformation 00:30:00
Bilinear transformation problem 00:30:00
unit 5
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
Singularities 00:00:00
Residues 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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