Civil Engineering Syllabus Nagpur University

I am looking for Nagpur University Applied Mathematics- III (Civil Engineering) program syllabus so would you plz let me know from where I can collect it ??

[Arvind Kumar]

As you are looking for Nagpur University Applied Mathematics- III (Civil Engineering) program syllabus so on your demand I am providing same :


UNIT –I : FOURIER SERIES (06Hrs)
Periodic functions and their Fourier expansions, Even and Odd functions, Change
of 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, Numerical solution of
ordinary differential equation :Taylor's series method, Picard’s method, Runge-
Kutta 4th order method, Euler modified method. Milne , s Predictor- Corrector
method.

UNIT – VI: INTRODUCTION TO OPTIMIZATION TECHNIQUES (08Hrs)
Linear programming problem: Formulation, Graphical method, Simplex method

Nagpur University Applied Mathematics- III (Civil Engineering) program syllabus