Note for Mathematics-3 - M-3 By vtu rangers

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ENGINEERING MATHEMATICS-III 15MAT31 SYLLABUS ENGINEERING MATHEMATICS-III SUB CODE: 15MAT31 Hrs/Week: 04 Total Hrs: 50 IA Marks:20 Exam Hrs: 03 Exam Marks: 80 MODULE-I Fourier Series: 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. MODULE-II: Fourier Transforms: Infinite Fourier transforms, Fourier Sine and Cosine transforms, Inverse transform. 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 difference equations. MODULE- III 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 form, y ax b y ax 2 bx c y aebx y axb Numerical Methods: Numerical solution of algebraic and transcendental equations by: Regular-falsi method, Secant method, Newton -Raphsonmethod and Graphical method. MODULE IV 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 ) – Problems MODULE-V Vector integration: 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 Page 1

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ENGINEERING MATHEMATICS-III 15MAT31 Course Outcomes: On completion of this course, students are able to know the use of periodic signals and Fourier series to analyze circuits explain the general linear system theory for continuous-time signals and systems using the Fourier Transform analyze discrete-time systems using convolution and the z-transform use appropriate numerical methods to solve algebraic and transcendental equations and also to calculate a definite integral Use curl and divergence of a vector function in three dimensions, as well as apply the Green's Theorem, Divergence Theorem and Stokes' theorem in various applications Solve the simple problem of the calculus of variations DEPT OF MATHEMATICS,SJBIT Page 2

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ENGINEERING MATHEMATICS-III 15MAT31 Engineering Mathematics – III  Module 1: Fourier Series  Module 2: Fourier Transforms & Z Transforms…………………………28-55  Module 3;  Module 4: Finite Difference, Numerical Integration ……………….78-99  Module 5: Vector Integration, Calculus of Variation ……………………100-108 ……………………………4-27 Statistical Methods, Curve Fitting, Numerical Method ….56-77 DEPT OF MATHEMATICS,SJBIT Page 3

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ENGINEERING MATHEMATICS-III 15MAT31 MODULE- I FOURIER SERIES CONTENTS: Introduction Periodic function Trigonometric series and Euler’s formulae Fourier series of period 2 Fourier series of even and odd functions Fourier series of arbitrary period Half range Fourier series Complex form of Fourier series Practical Harmonic Analysis DEPT OF MATHEMATICS,SJBIT Page 4