#### 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).

### Course Curriculum

 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

## 5

5
2 ratings
• 5 stars2
• 4 stars0
• 3 stars0
• 2 stars0
• 1 stars0
1. ### gud

5

easy to learn

2. ### Very usefull

5

Thanks for creating this system.

3495 STUDENTS ENROLLED
• • • • • • • • • • 66662
© BANDHE LEARNENGG SOLUTIONS PRIVATE LIMITED