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 theoremText Books:
1. Higher Engineering Mathematics by B.V. Ramana (Tata McGraw-Hill). 2. Higher Engineering Mathematics by B. S. Grewal (Khanna Publication, Delhi). Reference Books:
1. Advanced Engineering Mathematics, 10e, by Erwin Kreyszig (Wiley India). 2. Advanced Engineering Mathematics, 2e, by M. D. Greenberg (Pearson Education). 3. Advanced Engineering Mathematics, 7e, by Peter V. O'Neil (Cengage Learning). 4. Differential Equations, 3e by S. L. Ross (Wiley India). 5. Introduction to Probability and Statistics for Engineers and Scientists, 5e, by Sheldon M. Ross
(Elsevier Academic Press). 6. Complex Variables and Applications, 8e, by J. W. Brown and R. V. Churchill (McGraw-Hill
Inc.).
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