Re: VTU Syllabus 1st Sem BE
You want to get the syllabus of the BE 1st year program. So I am providing the syllabus.
UNIT – 1
Differential Calculus - 1
Determination of nth derivative of standard functions-illustrative examples .
Leibnitz’s theorem (without proof) and problems.
Rolle’s Theorem – Geometrical interpretation. Lagrange’s and Cauchy’s
mean value theorems. Taylor’s and Maclaurin’s series expansions of function
of one variable (without proof).
UNIT – 2
Differential Calculus - 2
Indeterminate forms – L’Hospital’s rule (without proof), Polar curves: Angle
between polar curves, Pedal equation for polar curves. Derivative of arc
length – concept and formulae without proof. Radius of curvature - Cartesian,
parametric, polar and pedal forms.
UNIT – 3
Differential Calculus - 3
Partial differentiation: Partial derivatives, total derivative and chain rule,
Taylor’s expansion of a function of two variables-illustrative examples*.
Maxima and Minima for function of two variables. Applications – Errors and
UNIT – 4
Scalar and vector point functions – Gradient, Divergence, Curl, Laplacian,
Solenoidal and Irrotational vectors.
Vector Identities: div (°A), Curl (°A) Curl (grad ° ) div (CurlA) div (A x B )
& Curl (Curl A) .
Orthogonal Curvilinear Coordinates – Definition, unit vectors, scale factors,
orthogonality of Cylindrical and Spherical Systems. Expression for Gradient,
Divergence, Curl, Laplacian in an orthogonal system and also in Cartesian,
Cylindrical and Spherical System as particular cases – No problems
UNIT – V
Differentiation under the integral sign – simple problems with constant
limits. Reduction formulae for the integrals of
sin , cos , n n x x s i n c o s m n x x and evaluation of these integrals with
standard limits - Problems.
Tracing of curves in Cartesian, Parametric and polar forms – illustrative
examples*. Applications – Area, Perimeter, surface area and volume.
Computation of these in respect of the curves – (i) Astroid:
2 2 2
3 3 3 x y a
(ii) Cycloid: sin , 1 cos x a y a and (iii) Cardioid:
1 cos r a
UNIT – VI
Solution of first order and first degree equations: Recapitulation of the
method of separation of variables with illustrative examples*. Homogeneous,
Exact, Linear equations and reducible to these forms. Applications -
UNIT – VII
Recapitulation of Matrix theory. Elementary transformations, Reduction of
the given matrix to echelon and normal forms, Rank of a matrix, consistency
of a system of linear equations and solution. Solution of a system of linear
homogeneous equations (trivial and non-trivial solutions). Solution of a
system of non-homogeneous equations by Gauss elimination and Gauss –
UNIT – VIII:
Linear Algebra -2
Linear transformations, Eigen values and eigen vectors of a square matrix,
Similarity of matrices, Reduction to diagonal form, Quadratic forms,
Reduction of quadratic form into canonical form, Nature of quadratic forms
Note: * In the case of illustrative examples, questions are not to be set.
1. B.S. Grewal, Higher Engineering Mathematics, Latest edition,
2. Erwin Kreyszig, Advanced Engineering Mathematics, Latest
edition, Wiley Publications.
1. B.V. Ramana, Higher Engineering Mathematics, Latest edition, Tata
Mc. Graw Hill Publications.
2. Peter V. O’Neil, Engineering Mathematics, CENGAGE Learning
India Pvt Ltd.Publishers
Sub Code : 10PHY12/10PHY22 IA Marks : 25
Hrs/ Week : 04 Exam Hours : 03
Total Hrs. : 52 Exam Marks : 100
PART – A
Introduction to Blackbody radiation spectrum, Photo-electric effect, Compton
effect. Wave particle Dualism. de Broglie hypothesis – de Broglie
wavelength, extension to electron particle. – Davisson and Germer
Matter waves and their Characteristic properties. Phase velocity, group
velocity and Particle velocity. Relation between phase velocity and group
velocity. Relation between group velocity and particle velocity. Expression
for deBroglie wavelength using group velocity.
Heisenberg’s uncertainity principle and its physical significance. Application
of uncertainity principle (Non-existence of electron in the nucleus,
Explanation for β-decay and kinetic energy of electron in an atom). Wave
function. Properties and Physical significance of a wave function. Probability
density and Normalisation of wave function. Setting up of a one dimensional,
time independent Schr÷dinger wave equation. Eigen values and Eigen
functions. Application of Schr÷dinger wave equation – Energy Eigen values
for a free particle. Energy Eigen values of a particle in a potential well of
Electrical Conductivity in Metals
Free-electron concept. Classical free-electron theory - Assumptions. Drift
velocity. Mean collision time and mean free path. Relaxation time.
Expression for drift velocity. Expression for electrical conductivity in metals.
Effect of impurity and temperature on electrical resistivity of metals. Failures
of classical free-electron theory.
Quantum free-electron theory - Assumptions. Fermi - Dirac Statistics.Fermienergy
– Fermi factor. Density of states (No derivation). Expression for
electrical resistivity / conductivity. Temperature dependence of resistivity of
metals. Merits of Quantum free – electron theory.
Dielectric & Magnetic Properties of Materials
Dielectric constant and polarisation of dielectric materials. Types of
polarisation. Equation for internal field in liquids and solids (one
dimensional). Classius – Mussoti equation. Ferro and Piezo – electricity
(qualitative). Frequency dependence of dielectric constant. Important
applications of dielectric materials. Classification of dia, para and ferromagnetic
materials. Hysterisis in ferromagnetic materials. Soft and Hard
magnetic materials. Applications.
PART – B
UNIT - 5
Principle and production. Einstein’s coefficients (expression for energy
density). Requisites of a Laser system. Condition for Laser action.
Principle, Construction and working of He-Ne and semiconductor Laser.
Applications of Laser – Laser welding, cutting and drilling. Measurement of
atmospheric pollutants. Holography – Principle of Recording and
reconstruction of 3-D images. Selected applications of holography.
Optical Fibers & Superconductivity
Propagation mechanism in optical fibers. Angle of acceptance. Numerical
aperture. Types of optical fibers and modes of propagation. Attenuation.
Applications – block diagram discussion of point to point communication.
Temperature dependence of resistivity in superconducting materials. Effect
of magnetic field (Meissner effect). Type I and Type II superconductors -
Temperature dependence of critical field. BCS theory (qualitative). High
temperature superconductors. Applications of superconductors–
Superconducting magnets, Maglev vehicles and squids
Space lattice, Bravais lattice - unit cell, primitive cell. Lattice parameters.
Crystal systems. Direction and planes in a crystal. Miller indices. Expression
for inter-planar spacing. Co-ordination number. Atomic packing factor.
Bragg’s Law. Determination of crystal structure by Bragg’s x-ray
spectrometer. Crystal structures of NaCl, and diamond.
Introduction to Nanoscience and Nanotechnology. Nanomaterials: Shapes of
nanomaterials, Methods of preparation of nanomaterials, Wonders of
nanotechnology: Discovery of Fullerene and carbon nanotubes, Applications.
Ultrasonic non-destructive testing of materials. Measurements of velocity in
solids and liquids, Elastic constants.
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Last edited by Sashwat; February 8th, 2014 at 11:30 AM.