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Characteristic equation – Eigen values and Eigen vectors of a real matrix – Properties of Eigen values – Cayley – Hamilton theorem orthogonal reduction of a symmetric matrix to diagonal form – Orthogonal matrices – Reduction of quadratic form to canonical form by orthogonal transformations.  Function of two variables – Partial derivatives – Total differential – Taylor's expansion – Maxima and Minima – Constrained Maxima and Minima by Lagrangian Multiplier method – Jacobians – Euler's theorem for homogeneous function.

 

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Periodic functions: Properties, Even & Odd functions: Properties, Special wave forms: Square wave, Half wave Rectifier, 

Full wave Rectifier, Saw-toothed wave, Triangular wave.

Euler's Formulae for Fourier Series, Fourier Series for functions of period 2π, Fourier Series for functions of period 2l, Dirichlet's conditions, Sum of  Fourier series. 

Theorem for the convergence of Fourier Series (statement only). Fourier Series of a function with its periodic  extension. Half Range Fourier Series: Construction of Half range Sine Series, Construction of Half range Cosine Series. Parseval's identity (statement only). Complex functions, Concept of Limit, Continuity and Differentiability. Analytic functions, Cauchy-Riemann Equations (statement only). Sufficient condition for a function to be analytic. Harmonic function and Conjugate Harmonic function, related problems. 

Construction of Analytic functions: Milne Thomson method, related problems.

Do You Know the difference between Truss and Beam ???

About Truss and Beams

Truss is a structure of connected elements forming triangular units, and a bridge whose load-bearing superstructure is composed of a truss is a truss bridge. The truss members like chords, verticals, and diagonals act only in either tension or compression. Short-span truss bridges are built as simply supported, while the large span truss bridges are generally built as continuous supported.

Beam is a structural element that primarily resists loads applied laterally to the beam's axis. The loads applied to the beam result in reaction forces at the beam's support points. The total effect of all the forces acting on the beam is to produce shear forces and bending moment within the beam, that in turn induce internal stresses, strains and deflections of the beam.

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