# Applied Mathematics-II

Section A

1-2

# Unit I:

Scalar triple product, vector triple product, quadruple product of vectors. First order first degree differential equation, variable separable, homogeneous reducible to homogeneous, linear, reducible to linear and exact differential equations (excluding the cases of integrating factor).

Unit II:

Linear differential equation with constant coefficients, the operator l/f(D), method of variation of parameters, simple simultaneous diff. equation, homogeneous differential equations, differential equations of the type d2y/dx2 = f(Y), Application of differential equations to simple Electrical circuits and Mechanics. (only up to second order)

Unit III:

Differentiation of vectors, Gradient of Scalar point function, directional derivatives, divergence and curl of vector point function, solenoidal motion and irrotational motion.

Vector integration, line, surface and volume integrals, stoke's theorem, Gauss divergence theorem, Green's theorem in plane (statement only),Greens identities and their simple applications.

Section B

Unit IV: Finite Differences:

Difference table, operator E and factorials, functions Newton's forward and backwardinter-polation formula, central differences, stirling's formula (without proof), Lagrange's interpolation formula, Numerical differentiation and integration, difference equations with constant coefficients.

Unit V: Statistics and Probability:

Fitting of a straight line Y = a + bx , parabola y = a + bx+cx2, and the curves Y = abx And Y = axb by method of Least square, Linear regression and correlation, rank correlation, Binomial, Poisson and Normal distribution, fitting of these curves.

Unit-VI: Multiple Integrals and Their Applications:

Elementary double integrals, change of variable a (simple transformation), change of order of integration (Cartesian and polar), applications to mass, area, volume and center of gravity (Cartesian & polar form), elementary triple integrals.

Text Books:

1. Engg. Mathematics:H.K.Das(S.Chand & Co)

2. Vector analysis: M. R. Spiegel. (McGraw Hill)

3. Finite Differences: H. C. Saxena(S.Chand & Co).

3. Applied mathematics: Ramana murthy

Reference Books:

1. Text book of

**Engineering**Mathematics: Deshpande & Ghangrekar (Asmita Publishers,**Nagpur**)2. Finite Differences: H. C. Saxena (McGraw Hill)

3. Mathematics for engineers: Chandrika prasad, (Prasad Mudranalaya, Allahabad)

4. Higher

**Engineering**Mathematics: B. S. Grewal(Khanna Publishers, N Delhi)
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