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+cx

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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