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VTU B.E Engineering Mathematics III Scheme - 2015
 No Units Titles Sub Titles Chapters 1 UNIT/BLOCK TITLE SUB HEADING VIEW CHAPTERS 2 UNIT 1 FOURIER SERIES Periodic functions, Dirichlet s condition, Fourier Series of periodic functions with period 2À and with arbitrary period 2c, Fourier series of even and odd functions, Half range Fourier Series, practical harmonic analysis-Illustrative examples from engineering field, VIEW CHAPTERS 3 UNIT 2 FOURIER TRANSFORMS Infinite Fourier transforms, Fourier sine and cosine transforms, Inverse Fourier transform VIEW CHAPTERS Z-TRANSFORMS Difference equations, basic definition, z-transform-definition, Standard z-transforms, Damping rule, Shifting rule, Initial value and final value theorems (without proof) and problems, Inverse z-transform, Applications of ztransforms to solve difference equations VIEW CHAPTERS 4 UNIT 3 Statistical Methods Review of measures of central tendency and dispersion, Correlation-Karl Pearson s coefficient of correlation-problems, Regression analysis- lines of regression (without proof)  problems VIEW CHAPTERS Curve Fitting Curve fitting by the method of least squares- fitting of the curves of the form, y = ax + b, y = ax2 + bx + c and y = aebx VIEW CHAPTERS Numerical Methods Numerical solution of algebraic and transcendental equations by Regula- Falsi Method and Newton-Raphson method VIEW CHAPTERS 5 UNIT 4 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 (all formulae without proof)-Problems, VIEW CHAPTERS Numerical integration Simpson s (1/3)th and (3/8)th rules, Weddle s rule (without proof )  Problems, VIEW CHAPTERS 6 UNIT 5 Vector integration Line integrals-definition and problems, surface and volume integralsdefinition, Green s theorem in a plane, Stokes and Gauss-divergence theorem(without proof) and problems, VIEW CHAPTERS 7 UNIT 6 Calculus of Variations Variation of function and Functional, variational problems, Euler s equation, Geodesics, hanging chain, problems, VIEW CHAPTERS

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