C122 ENGINEERING MATHEMATICS -II

Unit No 01: ODE of First order and Degree and Application

1.1 Order, degree and general solution of differential equations, non homogeneous differential equations.

1.2 Exact differential equations, non- exact reducible to exact, linear differential equations, non linear reducible to linear.

1.3 Applications to orthogonal trajectories, electrical and mechanical engineering (projectile motion and Newton’s law of cooling)

Unit No 02: Infinite Series

2.1 Infinite sequences , infinite series, types of series

2.2 Test of convergence, absolute and conditional convergence,

2.3 Cauchy test, comparison test and De Alembert’s test

Unit No 03:Complex Variable (Differentiation)

3.1 Statement of De-Moivre’s Theorem (without proof), application of De-Moivre’s theorem –roots of algebraic equations,

3.2 Circular and Hyperbolic functions

3.3 Differentiation, Cauchy Riemann Equations(Without Proof), Analytic Functions, Elementary Analytic Functions(Exponential, Trigonometric and Logarithmic function)

3.4 Harmonic Functions and Conjugates, Construction of Analytic Function

Section II

Unit No 04: Integral Calculus

4.1 Gamma function and properties,

4.2 Beta function and properties, duplication formula with proof.

4.3 Differentiation under integral sign with constant limit

Unit No 05: Curve Tracing

5.1 Tracing of Cartesian curves-

5.2 Tracing of polar curves

5.3 Tracing of parametric curves

Unit No 06: Multivariable Integral Calculus

6.1 Direct evaluation of Double integral, Evaluation over the given region,

6.2 Change of order of integration, change to polar, triple integration

6.3 Application of double integral to find area and mass of lamina.

Text Books:
1. A Text Book of Applied Mathematics, P.N. and J.N. Wartikar, Vol.1, Pune Vidyarthi Griha
Prakashan.
2. Advanced Engineering Mathematics, H. K. Dass, S. Chand Publications, Delhi.
3. Engineering Mathematics (Volume I), ITL Education, Cengage Learning.
4. Engineering Mathematics, Ravish R Sing and Mukul Bhatt, McGraw Hill.
5. Applied Mathematics-I,II, Kreyzig’s, Wiley.
6. A text book of Engineering Mathematics, N.P. Bali and Manish Goyal, Laxmi
Publications, 2008.

 Reference Books:
1. Higher Engineering Mathematics (42nd Edition), B.S. Grewal Khanna Publications, Delhi.
2. Engineering Mathematics, Srimanta Pal and Subodh C. Bhunia, Oxford Higher Education.
3. Mathematics for Engineering Applications, Kuldip S. Rattan and Naathan W. Klingbeil Wiley.
(Modeling and Core Engineering Application)
4. Higher Engineering Mathematics, Ramana B.V., Tata McGraw Hill New Delhi, 2010.

C011 ENGINERING PHYSICS

Unit No 01: Semiconductor Physics

1.1 Classification of solids, Fermi level (definition), Fermi-Dirac probability distribution function (introduction only)

1.2 Fermi level in intrinsic and extrinsic semiconductors, effect of impurity concentration on Fermi level, derivation for EFin

1.3 Hall effect and its applications, numericals on this chapter

Unit No 02: Crystallography

2.1 Introduction to crystal systems, characteristics of cubic unit cell: number of atoms per unit cell, atomic radius, co-ordination number

2.2 Atomic packing factor, void space, density of crystal, symmetry elements (axis, center and plane),Bragg’s Law

2.3 Miller indices, inter planner distance (by using Miller indices), numericals on this chapter

Unit No 03: Sound Engineering

3.1 Acoustics: Introduction, reverberation, reverberation time, absorption coefficient (definition only), Sabine’s formula, basic requirements for acoustically good hall

3.2 Factors affecting acoustics of auditorium and their remedies, numericals on this chapter

3.3 Ultrasonic :Introduction, piezoelectric effect and magnetostriction effect (introduction), properties of ultrasonic waves, detection methods of ultrasonic waves and applications.

Unit No 04: Relativistic Mechanics

4.1 Introduction, postulates of special theory of relativity, Lorentz transformation of space and time,numericals on this chapter

4.2 Length contraction, time dilation,

4.3 Equivalence of mass and energy

Unit No 05: Wave Optics

5.1 Diffraction:Introduction, resolving power, Rayleigh criterion, theory of diffraction grating and its resolving power.

5.2 Polarization: concept, optic axis, Malus law, positive and negative crystals

5.3 Optical activity, specific rotation, Laurent’s half shade polarimeter, Numericals on this chapter

Unit No 06: LASER

6.1 Interaction of radiation with matter- Stimulated absorption, spontaneous and stimulated emission, population inversion, pumping,

6.2 He-Ne gas laser

6.3 Holography (construction and reconstruction), applications of laser (science, engineering and medical),

Unit No 07: Optical Fibers

7.1 Introduction, structure of optical fiber, basic principle of optical fiber (total internal reflection)

7.2 Derivation for acceptance angle, acceptance cone and numerical aperture, fractional refractive index change, numericals on this chapter

7.3 Classification of optical fibers- single mode and multi-mode fiber,step index and graded index fibers,advatntages of optical fibers over conducting wires

Unit No 08: Introduction to Quantum Mechanics and Nanotechnology

8.1 De Broglie hypothesis, De Broglie wavelength of matter waves: in terms of kinetic energy and associated with particle in thermal equilibrium, properties of matter waves

8.2 Davisson-Germer experiment (apparatus, investigations and analysis), numericals on this chapter

8.3 Nanotechnology: introduction,carbon nano tubes and its classification, applications of nanotechnology- electronics, energy, automobiles, space and defense, medical, environmental, textile, cosmetics