B.E Civil Engineering (Part Time)Yeshwantrao Chavan College of Engineering
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Fourier Series: Periodic function and their Fourier expansion, even and odd functions,
change of interval, half range expansion.
Partial Differential Equation: Partial Differential Equation of first order degree i.e.
LaGrange’s form, Linear homogeneous p.d.e of nth order with constant coefficient
method of separation of variables. Applications to simple problems of vibration of strings
& beams, elementary concept of double Fourier series & their applications to simple
problem of vibration of rectangular membrane.
Calculus of Variations: Maxima & Minima of functions, variation & its properties, Euler’s
equation, functionals dependent on first and second order Derivatives. The Rayleigh –
Ritz method, simple applications.
Matrices: Inverse of matrix by adjoint method & its use in solving simultaneous equations,
rank of a matrix, consistency of system of equation, inverse of matrix by partitions
method. Linear dependence, Linear & orthogonal transformations. Characteristics
equations, Eigen values and Eigen vectors. Reduction to diagonal form, Cayley-Hamiltone
Theorem (without proof) statement & verification, Sylvestor’s theorem, Quadric form
transformation of co- ordinates, transformation of forces and couples association of
matrices with liner differential equation of second order with constant coefficient.
Numerical Methods: Errors in numerical calculation, Errors in series approximation.
Rounding of error solutions of algebraic and transcendental equations. Iteration method,
Bisection method, False position method, Newton Rapphson method and their
convergence, Solution of System of linear equation, Gauss elimination method, Gauss
Jordan method, Gauss Seidel method, Crouts method & relaxation method. Numerical
solution of ordinary differential equation by Taylor’s series method, Picard's method,
Runge Kutta method, Euler modified method, Milene’s Predictor method.