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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 functionsillustrative 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, Jacobiansdirect evaluation. Taylor’s expansion of a function of two variablesillustrative examples*. Maxima and Minima for function of two variables. Applications – Errors and approximations. UNIT – 4 Vector Calculus Scalar and vector point functions – Gradient, Divergence, Curl, Laplacian, Solenoidal and Irrotational vectors. Vector Identities: div (øA), Curl (øA) Curl (grad ø ) 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 PARTB UNIT – V Integral Calculus 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 Differential Equations 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  orthogonal trajectories. UNIT – VII Linear Algebra1 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 nontrivial solutions). Solution of a system of nonhomogeneous equations by Gauss elimination and Gauss – Jordan methods. 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. 7 Text Books: 1. B.S. Grewal, Higher Engineering Mathematics, Latest edition, Khanna Publishers 2. Erwin Kreyszig, Advanced Engineering Mathematics, Latest edition, Wiley Publications. Reference Books: 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 ENGINEERING PHYSICS Sub Code : 10PHY12/10PHY22 IA Marks : 25 Hrs/ Week : 04 Exam Hours : 03 Total Hrs. : 52 Exam Marks : 100 PART – A UNIT1 Modern Physics Introduction to Blackbody radiation spectrum, Photoelectric effect, Compton effect. Wave particle Dualism. de Broglie hypothesis – de Broglie wavelength, extension to electron particle. – Davisson and Germer Experiment. 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. UNIT2 Quantum Mechanics Heisenberg’s uncertainity principle and its physical significance. Application of uncertainity principle (Nonexistence of electron in the nucleus, Explanation for βdecay 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 Schrödinger wave equation. Eigen values and Eigen functions. Application of Schrödinger wave equation – Energy Eigen values for a free particle. Energy Eigen values of a particle in a potential well of infinite depth. UNIT3 Electrical Conductivity in Metals Freeelectron concept. Classical freeelectron 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 freeelectron theory. Quantum freeelectron 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. 9 UNIT4 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. 7 Hours PART – B UNIT  5 Lasers Principle and production. Einstein’s coefficients (expression for energy density). Requisites of a Laser system. Condition for Laser action. Principle, Construction and working of HeNe and semiconductor Laser. Applications of Laser – Laser welding, cutting and drilling. Measurement of atmospheric pollutants. Holography – Principle of Recording and reconstruction of 3D images. Selected applications of holography. . UNIT6 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 UNIT7 Crystal Structure Space lattice, Bravais lattice  unit cell, primitive cell. Lattice parameters. Crystal systems. Direction and planes in a crystal. Miller indices. Expression for interplanar spacing. Coordination number. Atomic packing factor. Bragg’s Law. Determination of crystal structure by Bragg’s xray spectrometer. Crystal structures of NaCl, and diamond. 10 UNIT8 Material Science 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 nondestructive testing of materials. Measurements of velocity in solids and liquids, Elastic constants. To get full syllabus, you have to download the file.
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