Civil Engineering Nagpur University

Hii sir, I Wants to get the Syllabus of the Applied Mathematics- III (Civil Engineering of Nagpur University ?

[Rajkumar Agarwal]

As you Asking for Syllabus of the Applied Mathematics- III (Civil Engineering of Nagpur University the Syllabus is given below



UNIT –I : FOURIER SERIES (06Hrs)
Periodic functions and their Fourier expansions, Even and Odd functions, Changeof interval, Half range expansion.


UNIT - II: PARTIAL DIFFERENTIAL EQUATIONS(12Hrs)
Partial Differential Equations of first order first degree i.e. Lagrange’s form, Linear
Homogeneous Equations of higher order with constant coefficients. Method of
separations of variables, Applications to simple problems of vibration of strings and beams, Elementary concept of double Fourier series and their application to simple problems of vibration of rectangular membrane.


UNIT – III: CALCULUS OF VARIATIONS (08Hrs)
Maxima and minima of functional, Euler’s equation, Functionals dependent on
First & Second orders derivatives. Rayleigh-Ritz method, Simple applications.

UNIT –IV: MATRICES(12Hrs)
Linear and Orthogonal transformations, Linear dependence of vectors,
Characteristics equations, Eigen values and Eigen vectors. Reduction to diagonal form, statement and verification of Cayley Hamilton Theorem [without proof.] Sylvester’s theorem, Quadratic form Transformation of co-ordinates,Transformation of forces and couples, Association of matrices with linear differential equation of second order with constant coefficients.


UNIT – V: NUMERICAL METHODS(14Hrs)
Error in numerical calculations, Errors in series approximation, Rounding of
errors, Solution of Algebraic and Transcendental Equation: Bisection method, False position method, Newton –Raphson method and their convergence , Solution of system of simultaneous linear equations: Gauss elimination method, Gauss Jordon method. Gauss Seidel method, Crouts method, Numer ical solution ofordinary differential equation :Taylor's series method, Picard’s method, RungeKutta 4th order method, Euler modified method. Milne, s Predictor- Corrector method.

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Contact details :
Nagpur University
Address: Chhatrapati Shivaji Maharaj Administrative Premises, Ravindranath Tagore Marg, Nagpur, Maharashtra 440001
Phone: 0712 253 3452