# NIT Calicut 1st Year Syllabus Part I

MA1001 – MATHEMATICS – I

Module I: Preliminary Calculus & Infinite Series (9L + 3T)

Preliminary Calculus : Partial differentiation, Total differential and total derivative,

Exact differentials, Chain rule, Change of variables, Minima and Maxima of functions of two or

more variables.

Infinite Series : Notion of convergence and divergence of infinite series, Ratio test, Comparison

test, Raabe’s test, Root test, Series of positive and negative terms, Idea of absolute convergence,

Taylor’s and Maclaurin’s series.

Module II: Differential Equations (13L + 4T)

First order ordinary differential equations: Methods of solution, Existence and uniqueness of

solution, Orthogonal Trajectories, Applications of first order differential equations.

Linear second order equations: Homogeneous linear equations with constant coefficients,

fundamental system of solutions, Existence and uniqueness conditions, Wronskian, Non

homogeneous equations, Methods of Solutions, Applications.

Module III: Fourier Analysis (10 L+ 3T)

Periodic functions : Fourier series, Functions of arbitrary period, Even and odd functions, Half

Range Expansions, Harmonic analysis, Complex Fourier Series, Fourier Integrals, Fourier

Cosine and Sine Transforms, Fourier Transforms.

Module IV: Laplace Transforms (11L + 3T)

Gamma functions and Beta functions, Definition and Properties. Laplace Transforms, Inverse

Laplace Transforms, shifting Theorem, Transforms of derivatives and integrals, Solution of

differential Equations, Differentiation and Integration of Transforms, Convolution, Unit step

function, Second shifting Theorem, Laplace Transform of Periodic functions.

Text Book:

Kreyszig E, ‘Advanced Engineering Mathematics’ 8th Edition, John Wiley & Sons New York,

(1999)

Reference Books:

1. Piskunov, ‘Differential and Integral Calculus, MIR Publishers, Moscow (1974).

2. Wylie C. R. & Barret L. C ‘Advanced Engineering Mathematics’ 6th Edition, Mc

Graw Hill, New York, (1995).

3. Thomas G. B. ‘Calculus and Analytic Geometry’ Addison Wesley, London (1998).

MA1002 – MATHEMATICS II

L T P C

3 1 0 3

Module I (11 L + 3T)

Linear Algebra I: Systems of Linear Equations, Gauss’ elimination, Rank of a matrix,

Linear independence, Solutions of linear systems: existence, uniqueness, general form.

Vector spaces, Subspaces, Basis and Dimension, Inner product spaces, Gram-Schmidt

orthogonalization, Linear Transformations.

Module II (11 L+ 3T)

Linear Algebra II: Eigen values and Eigen vectors of a matrix, Some applications of Eigen

value problems, Cayley-Hamilton Theorem, Quadratic forms, Complex matrices, Similarity of

matrices, Basis of Eigen vectors – Diagonalization.

Module III (10L+3T)

Vector Calculus I: Vector and Scalar functions and fields, Derivatives, Curves, Tangents,

Arc length, Curvature, Gradient of a Scalar Field, Directional derivative, Divergence of a vector

field, Curl of a Vector field.

Module IV (11 L+4T)

Vector Calculus II: Line Integrals, Line Integrals independent of path, Double integrals,

Surface integrals, Triple Integrals, Verification and simple applications of Green’s Theorem,

Gauss’ Divergence Theorem and Stoke’s Theorem.

Text Book:

Kreyzig E, Advanced Engineering Mathematics, 8th Edn, John Wiley & Sons, New York

(1999).

Reference Books:

1. Wylie C. R & Barrret L. C, Advanced Engineering Mathematics, 6th Edn, Mc Graw

Hill, New York (1995).

2. Hoffman K & Kunze R, Linear Algebra, Prentice Hall of India, New Delhi (1971).

PH1001 PHYSICS

Module 1 – Theory of Relativity (6 hours)

Frames of reference, Galilean Relativity, Michelson-Morley experiment, postulates of Special

Theory of Relativity, Lorentz transformations, simultaneity, length contraction, time dilation,

velocity addition, Doppler effect for light, relativistic mass and dynamics, mass energy relations,

massless particles, Description of General Theory of Relativity.

Module 2 – Quantum Mechanics (10 hours)

Dual nature of matter, properties of matter waves, wave packets, uncertainty principle,

formulation of Schrödinger equation, physical meaning of wave function, expectation values,

time-independent Schrödinger equation, quantization of energy – bound states, application of

time-independent Schrödinger equation to free particle, infinite well, finite well, barrier

potential, tunneling, Simple Harmonic Oscillator, two-dimensional square box, the scanning

tunneling microscope.

Module 3 – Statistical Physics (12 hours)

Temperature, microstates of a system, equal probability hypothesis, Boltzman factor and

distribution, ideal gas, equipartition of energy, Maxwell speed distribution, average speed, RMS

speed, applications – Lasers and Masers, Quantum distributions – many particle systems, wave

functions, indistinguishable particles, Bosons and Fermions, Bose-Einstein and Fermi-Dirac

distribution, Bose-Einstein condensation, Specific heat of a solid, free electron gas and other

applications.

Module 4 – Applications to Solids (14 hours)

Band theory of solids, conductors, semi-conductors and insulators, metals – Drude model and

conductivity, electron wave functions in crystal lattices, E-k diagrams, band gaps, effective

mass, semiconductors, Fermi energy, doping of semiconductor, conductivity and mobility of

electrons, Hall effect, Fundamentals of mesoscopic physics and nano technology: size effects,

interference effect, quantum confinement and Coulomb blockade. Quantum wells, wires, dots,

nanotubes, semiconductor nano materials, Magnetism: dipole moments, paramagnetism, Curie’s

law, magnetization and hysterisis, Ferromagnetism and Anti-Ferromagnetism.

Text Books

1. Modern Physics for Scientists and Engineers, J. R. Taylor, C.D. Zafiratos and M. A. Dubson,

2nd Ed., Pearson (2007)

2. Concepts of Modern Physics Arthur Beiser, 6th Ed., Tata Mc Graw –Hill Publication (2009)

References

1. Quantum Physics of atoms, Molecules, Solids, Nuclei and Particle, Robert Eisberg and

Robert Resnick, 2nd Ed., John Wiley(2006)

2. Solid state Devices, B. G. Streetman, 5th Ed., Pearson (2006)