Module 1
Complex Integration: Line Integral –Cauchy’s integral theorem- Cauchy’s integral formula-Taylor’s series-Laurent’s series- zeros and singularities- Residues- residue theorem-Evaluation of real integrals using contour integration involving unit circle and semicircle.
Complex Integration: Line Integral –Cauchy’s integral theorem- Cauchy’s integral formula-Taylor’s series-Laurent’s series- zeros and singularities- Residues- residue theorem-Evaluation of real integrals using contour integration involving unit circle and semicircle.
Module 2
Numerical solution of algebraic and transcendental equations: Successive bisection method-Regula falsi method – Newton –Raphson method – solution of system of linear equations by Jacobi’s iteration method and Gauss-Siedel method.
Numerical solution of algebraic and transcendental equations: Successive bisection method-Regula falsi method – Newton –Raphson method – solution of system of linear equations by Jacobi’s iteration method and Gauss-Siedel method.
Module 3
Numerical solution of ordinary differential equation: Taylor’s series method- Euler’s method –Modified Eulers method – Runge – Kutta method (IV order)-Milne’s predictor corrector method.
Numerical solution of ordinary differential equation: Taylor’s series method- Euler’s method –Modified Eulers method – Runge – Kutta method (IV order)-Milne’s predictor corrector method.
Module 4
Z – Transforms: Definition of Z transform- properties –Z transform of polynomial functions – trigonometric functions, shifting property, convolution property- inverse transform – solution of 1st & 2nd order difference equations with constant coefficients using Z transforms.
Z – Transforms: Definition of Z transform- properties –Z transform of polynomial functions – trigonometric functions, shifting property, convolution property- inverse transform – solution of 1st & 2nd order difference equations with constant coefficients using Z transforms.
Module 5
Linear programming: graphical solution – solution using simplex method (non – degenerate case only) – Big-M method,two phase method- Duality in L.P.P.- Balanced T.P. – Vogels approximation method – Modi method.
Linear programming: graphical solution – solution using simplex method (non – degenerate case only) – Big-M method,two phase method- Duality in L.P.P.- Balanced T.P. – Vogels approximation method – Modi method.
References
1. Ervin Kreyszig, Advanced Engineering Mathematics, Wiley Eastern limited.
2. Dr. B.S.Grewal, Numerical methods in Engineering & Science, Kanna Publishers.
3. Dr. B.S.Grewal, Higher Engineering Mathematics, Kanna Publishers.
4. Dr. M.K.Venkitaraman, Numerical methods in Science & Engineering, National Publishing Company.
5. P.C.Tulsian & Vishal Pandey, Quantitative techniques Theory & Problems, Pearson Education Asia.
6. Churchill and Brown, Complex variables and applications, McGraw-Hill.
7. Panneer Selvam, Operations research, PHI.
8. S Arumugam, A.T.Isaac & A Somasundaram, Engineering Mathematics Vol. III, Scitech publications
9. T.K.M.Pillai, G.Ramanaigh & S.Narayanan, Advanced Mathematics for Engg. Students Vol. III- S.Vishwananthan printers & publishers.
2. Dr. B.S.Grewal, Numerical methods in Engineering & Science, Kanna Publishers.
3. Dr. B.S.Grewal, Higher Engineering Mathematics, Kanna Publishers.
4. Dr. M.K.Venkitaraman, Numerical methods in Science & Engineering, National Publishing Company.
5. P.C.Tulsian & Vishal Pandey, Quantitative techniques Theory & Problems, Pearson Education Asia.
6. Churchill and Brown, Complex variables and applications, McGraw-Hill.
7. Panneer Selvam, Operations research, PHI.
8. S Arumugam, A.T.Isaac & A Somasundaram, Engineering Mathematics Vol. III, Scitech publications
9. T.K.M.Pillai, G.Ramanaigh & S.Narayanan, Advanced Mathematics for Engg. Students Vol. III- S.Vishwananthan printers & publishers.