Kavayitri Bahinabai Chaudhari North Maharashtra University, Maharashtra, Computer Engineering Semester 2, Mathematics –II Syllabus

MATHEMATICS-II

Unit–I:

First order ordinary differential equations:
Exact equations, Integrating Factor, Equations reducible to exact , linear and Bernoulli‟s equations, Equations not of first degree: equations solvable for p, equations solvable for y, equations solvable for x and Clairaut‟s type.

Unit–II:

Linear Differential Equations with constant coefficients: Linear differential equations with constant coefficients ,Method to find Perticular Integral by shortcut methos, method of variation of parameters, Cauchy-Euler equation. Legendres Equations.

Unit–III:

Function of Complex Variable :
Differentiation, Cauchy-Riemann equations, analytic functions, harmonic functions, finding harmonic conjugate; zeros of analytic functions, singularities, Cauchy Integral formula (without proof), Cauchy Residue theorem(without proof)

Unit–IV:

Numerical methods:-Solution of Ordinary differential equations: by Taylor‟s series and Picard‟s Method. Runge-Kutta method of fourth order for solving first order equations.
Numerical integration: Trapezoidal rule and Simpson‟s 1/3rd and 3/8 rules.

Unit–V:

Multivariable Calculus (Integration):
Double integrals (limits Given and limits not given) by Cartesian and Polar coordinates. Triple integration by spherical polar coordinates. Applications: areas and volumes.

Text Books :
1. N.P. Bali and Manish Goyal, A text book of Engineering Mathematics, Laxmi Publications, Reprint, 2008.
2. H.K.DASS “Advance Engineering Mathematics” S. Chand publications.
3. Ravish R. Singh, Mukul Bhatt “Engineering Mathematics A Tutorial Approach.Tata McGrawHill Education Private Limited. New Delhi
Reference Books:
1. G.B. Thomas and R.L. Finney, Calculus and Analytic geometry, 9th Edition, Pearson, Reprint, 2002.
2. Erwin kreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley & Sons, 2006.
3. W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 9th Edn., Wiley India, 2009.
4. S. L. Ross, Differential Equations, 3rd Ed., Wiley India, 1984.
5. E. A. Coddington, An Introduction to Ordinary Differential Equations, Prentice Hall India,1995.

6. J. W. Brown and R. V. Churchill, Complex Variables and Applications, 7th Ed., Mc-GrawHill, 2004.

7. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 36th Edition, 2010