 Applied Mathematics – II-Nagpur - Grad Plus

# Applied Mathematics – II-Nagpur

Teaching Scheme
Lectures: 4 Hours/ Week
Tutorial: 1 Hours / Week

Examination Scheme
Theory
T (U) : 80 Marks
T (I) : 20 Marks
Duration of University Exam. : 03 Hours

UNIT – I : (10 Hrs)

Integral Calculus-I
Beta and Gamma functions, Differentiation of definite integral, Mean Value and Root Mean Square Values.

UNIT – II: (10 Hrs)

Integral Calculus-II
Tracing of curves (Cartesian and polar curves), Rectification of simple curves, Quadrature, volume and surface of solids of revolution (Cartesian, polar and parametric forms).

UNIT- III: (12 Hrs)

Multiple Integrals and their Applications
Elementary double integrals, Change of variable (simple transformations), Change of order of integration, (Cartesian and polar), Applications to find Mass, Area, Volume and Centre of Gravity (Cartesian and polar forms), Elementary triple integrals.

UNIT – IV: (8 Hrs)

Vector Differential Calculus
Vector triple product, Product of four vectors, Scalar point function, Vector point Function, Vector differentiation, Gradient, Divergence and Curl, Directional derivatives with their physical interpretation, Solenoidal and irrotational motions.

UNIT- V : (10 Hrs)

Vector Integral Calculus
Vector integration, Line, Surface and Volume integrals, Statement (without proof) of Stoke’s
theorem, Gauss divergence theorem and Green’s theorem, Simple applications of these
theorems.

UNIT – VI: (10 Hrs)

(A) Statistics
Fitting of straight line y=a+bx, Parabola y=a+bx+cx2 and Exponential curves by method
of least squares, Lines of regression and Correlation, Rank correlation.

(B) Finite Differences:
Operator E and , Factorial notations, Lagrange’s interpolation formula for unequal intervals,
Difference equations with constant coefficients.

Books Recommended:

1. Higher Engineering Mathematics: B. S. Grewal
2. Applied Mathematics Volume I & II: J. N. Wartikar
3. Textbook of Engineering Mathematics: Bali, Iyenger ( Laxmi Prakashan)

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