207006: Engineering Mathematics-III book pdf free download

207006: Engineering Mathematics-III book pdf free download 

Prerequisites: - Differential & Integral calculus, Taylor series, Differential equations of first

order and first degree, Fourier series, Collection, classification & representation of data, Vector

algebra and Algebra of complex numbers. Course Objectives:

To make the students familiarize with concepts and techniques in Ordinary differential equations, Laplace transform, Fourier transform & Z-transform, Statistics & Probability, Vector Calculus

and functions of a Complex Variable. The aim is to equip them with the techniques to understand

advanced level mathematics and its applications that would enhance analytical thinking power, useful in their disciplines. Course Outcomes:At the end of this course, students will be able to:

CO1:Solve higher order linear differential equation using appropriate techniques to model and

analyze electrical circuits. CO2: Apply Integral transforms such as Laplace transform, Fourier transform and Z-Transform

to solve problems related to signal processing and control systems. CO3: Apply Statistical methods like correlation, regression and Probability theory as applicable

to analyze and interpret experimental data related to energy management, power systems, testing

and quality control. CO4: Perform Vector differentiation and integration, analyze the vector fields and apply to wave

theory and electro-magnetic fields. CO5: Analyze Complex functions, conformal mappings, and perform contour integration in the

study of electrostatics, signal and image processing. Unit I: Linear Differential Equations (LDE) and Applications (08 Hours)

LDE of n

th order with constant coefficients, Complementary Function, Particular Integral, General method, Short methods, Method of variation of parameters, Cauchy’s and Legendre’s

DE, Simultaneous and Symmetric simultaneous DE. Modeling of Electrical circuits. Unit II: Laplace Transform (LT) (07Hours)

Definition of LT, Inverse LT, Properties & theorems, LT of standard functions, LT of some

special functions viz. Periodic, Unit Step, Unit Impulse. Applications of LT for solving Linear

differential equations. Unit III: Fourier and Z - transforms (08 Hours)

Fourier Transform (FT): Complex exponential form of Fourier series, Fourier integral theorem, Fourier Sine & Cosine integrals, Fourier transform, Fourier Sine & Cosine transforms and their

inverses. Z - Transform (ZT): Introduction, Definition, Standard properties, ZT of standard sequences and

their inverses. Solution of difference equations. Unit IV: Statistics and Probability (07 Hours)

Measures of central tendency, Measures of dispersion, Coefficient of variation, Moments, Skewness and Kurtosis, Correlation and Regression, Reliability of Regression estimates. Probability, Probability density function, Probability distributions: Binomial, Poisson, Normal, Test of hypothesis: Chi-square test. Unit V: Vector Calculus (08 Hours)

Vector differentiation, Gradient, Divergence and Curl, Directional derivative, Solenoidal and

Irrotational fields, Vector identities. Line, Surface and Volume integrals, Green’s Lemma, Gauss’s Divergence theorem and Stoke’s theorem. Unit VI: Complex Variables (08 Hours)

Functions of a Complex variable, Analytic functions, Cauchy-Riemann equations, Conformal

mapping, Bilinear transformation, Cauchy’s integral theorem, Cauchy’s integral formula and

Residue theore

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