15MAT31 Engineering Mathematics –III syllabus for IS

Fourier Series:
Periodic functions, Dirichlet’s condition, Fourier Series ofperiodic functions with period 2π and with arbitrary period 2c. Fourier series ofeven and odd functions. Half range Fourier Series, practical harmonicanalysis-Illustrative examples from engineering field.

Fourier Series:
Periodic functions, Dirichlet’s condition, Fourier Series ofperiodic functions with period 2π and with arbitrary period 2c. Fourier series ofeven and odd functions. Half range Fourier Series, practical harmonicanalysis-Illustrative examples from engineering field.

Fourier Transforms:
Infinite Fourier transforms, Fourier sine and cosinetransforms. Inverse Fourier transform.
Z-transform:
Difference equations, basic definition, z-transform-definition,Standard z-transforms, Damping rule, Shifting rule, Initial value and final valuetheorems (without proof) and problems, Inverse z-transform. Applications of ztransformsto solve difference equations.

Fourier Transforms:
Infinite Fourier transforms, Fourier sine and cosinetransforms. Inverse Fourier transform.
Z-transform:
Difference equations, basic definition, z-transform-definition,Standard z-transforms, Damping rule, Shifting rule, Initial value and final valuetheorems (without proof) and problems, Inverse z-transform. Applications of ztransformsto solve difference equations.

Statistical Methods:
Review of measures of central tendency and dispersion.Correlation-Karl Pearson’s coefficient of correlation-problems. Regressionanalysis- lines of regression (without proof) –problems
Curve Fitting:
Curve fitting by the method of least squares- fitting of the curvesof the form, y = ax + b, y = ax2 + bx + c and y = aebx.
Numerical Methods:
Numerical solution of algebraic and transcendentalequations by Regula- Falsi Method and Newton-Raphson method.

Statistical Methods:
Review of measures of central tendency and dispersion.Correlation-Karl Pearson’s coefficient of correlation-problems. Regressionanalysis- lines of regression (without proof) –problems
Curve Fitting:
Curve fitting by the method of least squares- fitting of the curvesof the form, y = ax + b, y = ax2 + bx + c and y = aebx.
Numerical Methods:
Numerical solution of algebraic and transcendentalequations by Regula- Falsi Method and Newton-Raphson method.

Finite differences:
Forward and backward differences, Newton’s forwardand backward interpolation formulae. Divided differences- Newton’sdivided difference formula. Lagrange’s interpolation formula and inverseinterpolation formula (all formulae without proof)-Problems.
Numerical integration:
Simpson’s (1/3)th and (3/8)th rules, Weddle’s rule(without proof ) –Problems.

Finite differences:
Forward and backward differences, Newton’s forwardand backward interpolation formulae. Divided differences- Newton’sdivided difference formula. Lagrange’s interpolation formula and inverseinterpolation formula (all formulae without proof)-Problems.
Numerical integration:
Simpson’s (1/3)th and (3/8)th rules, Weddle’s rule(without proof ) –Problems.

Vector integration:
Line integrals-definition and problems, surface and volume integralsdefinition,Green’s theorem in a plane, Stokes and Gauss-divergencetheorem(without proof) and problems.
Calculus of Variations:
Variation of function and Functional, variationalproblems. Euler’s equation, Geodesics, hanging chain, problems.

Vector integration:
Line integrals-definition and problems, surface and volume integralsdefinition,Green’s theorem in a plane, Stokes and Gauss-divergencetheorem(without proof) and problems.
Calculus of Variations:
Variation of function and Functional, variationalproblems. Euler’s equation, Geodesics, hanging chain, problems.