SUB CODE: 15MAT31
Total Hrs: 50
Exam Hrs: 03
Exam Marks: 80
Periodic functions, Dirichlet’s condition, Fourier Series of Periodic functions with period
2π and with arbitrary period 2c, Fourier series of even and odd functions, Half range
Fourier Series, practical Harmonic analysis. Complex Fourier series.
Fourier Transforms: Infinite Fourier transforms, Fourier Sine and Cosine transforms,
Z-transform: Difference equations, basic definition, z-transform-definition, Standard ztransforms, Damping rule, Shifting rule, Initial value and final value theorems (without
proof) and problems, Inverse z-transform. Applications of z-transforms to solve
Statistical Methods: Correlation and rank Correlation coefficients, Regression and
Regression coefficients, lines of regression -problems
Curve fitting: Curve fitting by the method of least squares, fitting of the curves of the
ax b y
bx c y
Numerical Methods: Numerical solution of algebraic and transcendental equations by:
Regular-falsi method, Secant method, Newton -Raphsonmethod and Graphical method.
Finite differences: Forward and backward differences,Newton’s forward and backward
interpolation formulae. Divided differences-Newton’s divided difference formula.
Lagrange’s interpolation formula and inverse interpolation formula. Central DifferenceStirling’sand Bessel’s formulae (all formulae without proof)-Problems.
Numerical integration: Simpson’s 1/3, 3/8 rule, Weddle’s rule (without proof ) –
Line integrals-definition and problems, surface and volume integrals-definition, Green’s
theorem in a plane, Stokes and Gauss divergence theorem (without proof) and problems.
Calculus of Variations: Variation of function and Functional, variation problems,
Euler’s equation, Geodesics, minimal surface of revolution, hanging chain, problems
DEPT OF MATHEMATICS,SJBIT