Polar Form of Complex Numbers, Triangle Inequality. Curves and Regions in complex Plane.

Roots. Euler Formulae, Demoivre’s Theorem. Limits. Derivatives. Analytic Functions. Cauchy-

Riemann Equations. Laplace’s Equation. Rational Functions. Exponential Functions.

Trigonometric and Hyperbolic Functions. Logarithmic Function and General Power Line

Integral in the Complex Plane. Basic Properties of the Complex Line Integral. Cauchy’s Integral

Theorem. Evaluation of Line Integrals by Indefinite Integration. Cauchy’s Integral Formula.

Study of the mechanical behavior of solid bodies (Rods, shafts, beams, etc.) under various types of loading. Mechanical and thermal stresses and strains; Stress-strain relations; Axial deformation; Statically indeterminate bars and rods; Shear and bending moments in beams; Stresses in beams; Torsion of shafts and thin walled tubes; Combined loadings; Analysis of plane stress and plane strain; Thin walled vessels.

Introduction to materials engineering; Structure and characteristics of metals; polymers and ceramics; Equilibrium-phase diagrams; Microstructures of alloys; Imperfections; Diffusion; Mechanical properties of metals, polymers, ceramics; Heat treatment of plain-carbon steels, cast irons and precipitation hardening.Ceramics and polmers.

Fuel, Hydrogen, Energy Balance ( 4 weeks)
Motors, converter and connection , wind farm ( 2 weeks)
Wind ,Hydro, tide,wave, Geothermal ( 5 weeks) 
Biomass ( 2 weeks)