B.Tech. (EEE)Third Semester
EUREE 301 – Engineering Mathematics – IV
EUREE 301 – Engineering Mathematics – IV
UNIT-I:
Differentiation of Complex Functions:
Functions of a complex variable – analytical functions – Cauchy-Riemann equations – elementary functions of z – conformal mappings – bilinear transformation. Special conformal transformation (w = z2, w = z + 1/z, w = cosh z).
UNIT-II:
Integration of Complex Functions:
Integration in the complex plane, Cauchy’s theorem, Cauchy’s integral formula – series of complex functions – Taylor’s series – Laurent’s series – Residue theorem – evaluation of real definite integrals ( unit circle, semi circle)
UNIT-III:
Applications of partial differential equations:
Method of separation of variables – partial differential equations – wave equation – onedimensional heat flow – two-dimensional heat flow-solution of Laplace equation – Laplace equation in polar co-ordinates – transmission lines.
Probability Distribution:
Introduction to probability – Baye’s theorem – Random variables – Discrete Probability distribution – continuous probability distribution – expectations – moment generating function – Binomial distribution – Poisson distribution – Normal distribution – Uniform distribution.
UNIT-V:
Statistical Inference:
Sampling – Sampling distribution – standard error – testing of hypothesis – level of significance – confidence limits – simple sampling of attributes – large samples – Student’s distribution – Chi square distribution – test of goodness of fit – point estimation and interval of estimation.
Text Books:
1. Higher Engineering Mathematics by Dr.B.S.Grawel, Khanna publishers.
Reference books:
1. Kreyszig E., Advanced Engineering Mathematics, Wiley Eastern.
2. Probability and Statistics, 2/e, Spiegel, TMH.
3. Text Book of Engineering Mathematics by N.P. Bali et. al, Laxmi Publications (P) Ltd., New Delhi-110 002.
4. Higher Engineering Mathematics by Dr.M.K.Venkata Raman, National Pub.Co., Madras-1.
EUREE 302 – EMF Theory
UNIT-I:
Electrostatic Fields:
Electrostatic Fields:
Cartesian - Cylindrical and Spherical coordinate systems – review of vector calculus –\ Coulomb’s law – Electric field Intensity - EFI due to different charge Distributions - Concept of Electric flux density - Gauss law in Integral and point form – Applications of gauss Law - Electric Potential - Potential Gradient - Poisson’s and Laplace Equations and their Applications - Solution of Laplace equation in one variable -
Uniqueness theorem. Electric Dipole – Dipole Moment – Potential & EFI due to Dipole – Torque on a Electric Dipole in an Electric field – Method of Images - capacitance – Capacitance of parallel plate and spherical capacitors.
UNIT-II:
Conductors & Dielectrics:
Behavior of Conductors in an Electric field – Conductors & Dielectrics – EFI inside a Dielectric material - Concept of Polarization - Boundary conditions - Energy stored & Energy Density In a static electrostatic field – Current Density – Conduction & Convection Current Densities - Ohm’s law in point form – Equation of Continuity
UNIT-III:
Magneto-static Fields:
Steady current - Current distributions - Biot – Savart’s law – Magnetic field Intensity – MFI due to straight current carrying filament – MFI due to various configurations - Concept of Magnetic Flux Density – Relation between Magnetic flux, magnetic flux density & MFI - Ampere’s Circuital law in Integral and Differential form – Magnetic force – Moving charges in a magnetic filed – Lorentz force equation - Force on a Current Element in magnetic field – Magnetic dipole & dipole moment – A differential current loop as a magnetic dipole – Torque on a current loop placed in a magnetic field.
UNIT-IV:
Fields in Magnetic Material:
Scalar magnetic potential and its limitations – Vector Magnetic potential and its properties – Vector magnetic potential due to simple configurations – self and mutual inductance – Neumann’s formula – Determination of self inductance of solenoids and toroid and mutual inductance - Energy stored & density in a magnetic Field - boundary conditions
UNIT-V:
Electromagnetic Fields:
Maxwell’s Equations in both Differential and Integral form - phasor representation of Time – varying fields. Displacement current density - poynting theorem and applications - Depth of Penetration - Polarization - Wave Equations - Uniform plane wave - Reflection and Refraction of Plane wave - Normal and oblique incidence
Text Books:
1. Engineering Electromagnetics, W.H. Hayt Jr. McGraw Hill – New York .
2. Elements of Electromagnetics, M.N.O. Sadiku, Oxford press, 2002.
3. Introduction to Electro-dynamics, David J.Griffiths, PHI.
Reference Books:
1. EM Waves and Radiating Systems, E.C. Jordan, PHI, 1997.
2. Electromagnetics with applications, Kraus and Fleisch, McGraw Hill, 1999.
