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207006: Engineering Mathematics-III

Credits
Th: 03

Unit I: Linear Differential Equations (LDE) and Applications 
LDE of nth 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) 
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 
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 
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 
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 
Functions of a Complex variable, Analytic functions, Cauchy-Riemann equations, Conformal
mapping, Bilinear transformation, Cauchy’s integral theorem, Cauchy’s integral formula and
Residue theorem.

Text 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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